#line 1 "verify/aizu-online-judge/itp1_1_a/0001.test.cpp"
/*
* @uni_kakurenbo
* https://github.com/uni-kakurenbo/competitive-programming-workspace
*
* CC0 1.0 http://creativecommons.org/publicdomain/zero/1.0/deed.ja
*/
/* #language C++ GCC */
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A"
#line 2 "include/all.hpp"
#line 2 "include/actions.hpp"
#line 2 "action/base.hpp"
#include <cstddef>
#include <concepts>
#line 2 "internal/dev_env.hpp"
#ifdef LOCAL_JUDGE
inline constexpr bool DEV_ENV = true;
inline constexpr bool NO_EXCEPT = false;
#else
inline constexpr bool DEV_ENV = false;
inline constexpr bool NO_EXCEPT = true;
#endif // LOCAL_JUDGE
#if __cplusplus >= 202100L
#define CPP20 true
#define CPP23 true
#elif __cplusplus >= 202002L
#define CPP20 true
#define CPP23 false
#else
#define CPP20 false
#define CPP23 false
#endif
#line 2 "internal/types.hpp"
#include <cstdint>
namespace uni {
namespace internal {
using size_t = std::int64_t;
using int128_t = __int128_t;
using uint128_t = __uint128_t;
} // namesapce internal
} // namespace uni
#line 2 "internal/dummy.hpp"
namespace uni {
namespace internal {
struct dummy {};
} // namespace internal
} // namespace uni
#line 11 "action/base.hpp"
#line 2 "algebraic/internal/concepts.hpp"
#include <type_traits>
#line 6 "algebraic/internal/concepts.hpp"
#line 2 "internal/concepts.hpp"
#line 6 "internal/concepts.hpp"
#include <ranges>
#include <limits>
#include <functional>
namespace uni {
namespace internal {
template<class R, class T>
concept convertibel_range = std::convertible_to<std::ranges::range_value_t<R>, T>;
template<class T, class V>
concept item_or_convertible_range = std::convertible_to<T, V> || convertibel_range<T, V>;
template<class Structure>
concept available =
requires () {
typename Structure;
};
template<
template<class...> class Structure,
class... TemplateParameters
>
concept available_with = available<Structure<TemplateParameters...>>;
template<class T> concept arithmetic = std::is_arithmetic_v<T>;
template<class T> concept pointer = std::is_pointer_v<T>;
template<class T> concept structural = std::is_class_v<T>;
template<class Large, class Small>
concept has_double_digits_of = (std::numeric_limits<Large>::digits == 2 * std::numeric_limits<Small>::digits);
template<class Large, class Small>
concept has_more_digits_than = (std::numeric_limits<Large>::digits > std::numeric_limits<Small>::digits);
template<class Large, class Small>
concept has_or_more_digits_than = (std::numeric_limits<Large>::digits >= std::numeric_limits<Small>::digits);
template<class T>
concept has_static_zero = requires { T::zero; };
template<class T>
concept has_static_one = requires { T::one; };
template<class L, class R = L>
concept weakly_bitand_calcurable = requires (L lhs, R rhs) { lhs & rhs; };
template<class L, class R = L>
concept weakly_bitor_calcurable = requires (L lhs, R rhs) { lhs | rhs; };
template<class L, class R = L>
concept weakly_bitxor_calcurable = requires (L lhs, R rhs) { lhs ^ rhs; };
template<class L, class R = L>
concept weakly_addable = requires (L lhs, R rhs) { lhs + rhs; };
template<class L, class R = L>
concept weakly_subtractable = requires (L lhs, R rhs) { lhs - rhs; };
template<class L, class R = L>
concept weakly_multipliable = requires (L lhs, R rhs) { lhs * rhs; };
template<class L, class R = L>
concept weakly_divisable = requires (L lhs, R rhs) { lhs / rhs; };
template<class L, class R = L>
concept weakly_remainder_calculable = requires (L lhs, R rhs) { lhs % rhs; };
template<class L, class R = L>
concept weakly_bitand_assignable = requires (L lhs, R rhs) { lhs += rhs; };
template<class L, class R = L>
concept weakly_bitor_assignable = requires (L lhs, R rhs) { lhs |= rhs; };
template<class L, class R = L>
concept weakly_bitxor_assignable = requires (L lhs, R rhs) { lhs ^= rhs; };
template<class L, class R = L>
concept weakly_addition_assignable = requires (L lhs, R rhs) { lhs += rhs; };
template<class L, class R = L>
concept weakly_subtraction_assignable = requires (L lhs, R rhs) { lhs -= rhs; };
template<class L, class R = L>
concept weakly_multipliation_assignalbe = requires (L lhs, R rhs) { lhs *= rhs; };
template<class L, class R = L>
concept weakly_division_assignable = requires (L lhs, R rhs) { lhs /= rhs; };
template<class L, class R = L>
concept weakly_remainder_assignable = requires (L lhs, R rhs) { lhs /= rhs; };
template<class L, class R = L>
concept bitand_calculable =
weakly_bitand_calcurable<L, R> &&
weakly_bitand_calcurable<std::invoke_result_t<std::bit_and<>&, L, R>, R> &&
weakly_bitand_calcurable<L, std::invoke_result_t<std::bit_and<>&, L, R>> &&
weakly_bitand_calcurable<std::invoke_result_t<std::bit_and<>&, L, R>, std::invoke_result_t<std::bit_and<>&, L, R>>;
template<class L, class R = L>
concept bitor_calculable =
weakly_bitor_calcurable<L, R> &&
weakly_bitor_calcurable<std::invoke_result_t<std::bit_or<>&, L, R>, R> &&
weakly_bitor_calcurable<L, std::invoke_result_t<std::bit_or<>&, L, R>> &&
weakly_bitor_calcurable<std::invoke_result_t<std::bit_or<>&, L, R>, std::invoke_result_t<std::bit_or<>&, L, R>>;
template<class L, class R = L>
concept bitxor_calculable =
weakly_bitxor_calcurable<L, R> &&
weakly_bitxor_calcurable<std::invoke_result_t<std::bit_xor<>&, L, R>, R> &&
weakly_bitxor_calcurable<L, std::invoke_result_t<std::bit_xor<>&, L, R>> &&
weakly_bitxor_calcurable<std::invoke_result_t<std::bit_xor<>&, L, R>, std::invoke_result_t<std::bit_xor<>&, L, R>>;
template<class L, class R = L>
concept addable =
weakly_addable<L, R> &&
weakly_addable<std::invoke_result_t<std::plus<>&, L, R>, R> &&
weakly_addable<L, std::invoke_result_t<std::plus<>&, L, R>> &&
weakly_addable<std::invoke_result_t<std::plus<>&, L, R>, std::invoke_result_t<std::plus<>&, L, R>>;
template<class L, class R = L>
concept subtractable =
weakly_subtractable<L, R> &&
weakly_subtractable<std::invoke_result_t<std::minus<>&, L, R>, R> &&
weakly_subtractable<L, std::invoke_result_t<std::minus<>&, L, R>> &&
weakly_subtractable<std::invoke_result_t<std::minus<>&, L, R>, std::invoke_result_t<std::minus<>&, L, R>>;
template<class L, class R = L>
concept multipliable =
weakly_multipliable<L, R> &&
weakly_multipliable<std::invoke_result_t<std::multiplies<>&, L, R>, R> &&
weakly_multipliable<L, std::invoke_result_t<std::multiplies<>&, L, R>> &&
weakly_multipliable<std::invoke_result_t<std::multiplies<>&, L, R>, std::invoke_result_t<std::multiplies<>&, L, R>>;
template<class L, class R = L>
concept divisable =
weakly_divisable<L, R> &&
weakly_divisable<std::invoke_result_t<std::divides<>&, L, R>, R> &&
weakly_divisable<L, std::invoke_result_t<std::divides<>&, L, R>> &&
weakly_divisable<std::invoke_result_t<std::divides<>&, L, R>, std::invoke_result_t<std::divides<>&, L, R>>;
template<class L, class R = L>
concept remainder_calculable =
weakly_remainder_calculable<L, R> &&
weakly_remainder_calculable<std::invoke_result_t<std::modulus<>&, L, R>, R> &&
weakly_remainder_calculable<L, std::invoke_result_t<std::modulus<>&, L, R>> &&
weakly_remainder_calculable<std::invoke_result_t<std::modulus<>&, L, R>, std::invoke_result_t<std::modulus<>&, L, R>>;
template<class L, class R = L>
concept bitand_assignable =
weakly_bitand_assignable<L, R> &&
weakly_bitand_assignable<std::invoke_result_t<std::bit_and<>&, L, R>, R> &&
weakly_bitand_assignable<L, std::invoke_result_t<std::bit_and<>&, L, R>> &&
weakly_bitand_assignable<std::invoke_result_t<std::bit_and<>&, L, R>, std::invoke_result_t<std::bit_and<>&, L, R>>;
template<class L, class R = L>
concept bitor_assignable =
weakly_bitor_calcurable<L, R> &&
weakly_bitor_calcurable<std::invoke_result_t<std::bit_or<>&, L, R>, R> &&
weakly_bitor_calcurable<L, std::invoke_result_t<std::bit_or<>&, L, R>> &&
weakly_bitor_calcurable<std::invoke_result_t<std::bit_or<>&, L, R>, std::invoke_result_t<std::bit_or<>&, L, R>>;
template<class L, class R = L>
concept bitxor_assignable =
weakly_bitxor_calcurable<L, R> &&
weakly_bitxor_calcurable<std::invoke_result_t<std::bit_xor<>&, L, R>, R> &&
weakly_bitxor_calcurable<L, std::invoke_result_t<std::bit_xor<>&, L, R>> &&
weakly_bitxor_calcurable<std::invoke_result_t<std::bit_xor<>&, L, R>, std::invoke_result_t<std::bit_xor<>&, L, R>>;
template<class L, class R = L>
concept addition_assignable =
weakly_addition_assignable<L, R> &&
weakly_addition_assignable<std::remove_cvref_t<std::invoke_result_t<std::plus<>&, L, R>>, R> &&
weakly_addition_assignable<L, std::invoke_result_t<std::plus<>&, L, R>> &&
weakly_addition_assignable<std::remove_cvref_t<std::invoke_result_t<std::plus<>&, L, R>>, std::invoke_result_t<std::plus<>&, L, R>>;
template<class L, class R = L>
concept subtraction_assignable =
weakly_subtraction_assignable<L, R> &&
weakly_subtraction_assignable<std::remove_cvref_t<std::invoke_result_t<std::minus<>&, L, R>>, R> &&
weakly_subtraction_assignable<L, std::invoke_result_t<std::minus<>&, L, R>> &&
weakly_subtraction_assignable<std::remove_cvref_t<std::invoke_result_t<std::minus<>&, L, R>>, std::invoke_result_t<std::minus<>&, L, R>>;
template<class L, class R = L>
concept multipliation_assignalbe =
weakly_multipliation_assignalbe<L, R> &&
weakly_multipliation_assignalbe<std::remove_cvref_t<std::invoke_result_t<std::multiplies<>&, L, R>>, R> &&
weakly_multipliation_assignalbe<L, std::invoke_result_t<std::multiplies<>&, L, R>> &&
weakly_multipliation_assignalbe<std::remove_cvref_t<std::invoke_result_t<std::multiplies<>&, L, R>>, std::invoke_result_t<std::multiplies<>&, L, R>>;
template<class L, class R = L>
concept division_assignable =
weakly_division_assignable<L, R> &&
weakly_division_assignable<std::remove_cvref_t<std::invoke_result_t<std::divides<>&, L, R>>, R> &&
weakly_division_assignable<L, std::invoke_result_t<std::divides<>&, L, R>> &&
weakly_division_assignable<std::remove_cvref_t<std::invoke_result_t<std::divides<>&, L, R>>, std::invoke_result_t<std::divides<>&, L, R>>;
template<class L, class R = L>
concept remainder_assignable =
weakly_remainder_assignable<L, R> &&
weakly_remainder_assignable<std::remove_cvref_t<std::invoke_result_t<std::modulus<>&, L, R>>, R> &&
weakly_remainder_assignable<L, std::invoke_result_t<std::modulus<>&, L, R>> &&
weakly_remainder_assignable<std::remove_cvref_t<std::invoke_result_t<std::modulus<>&, L, R>>, std::invoke_result_t<std::modulus<>&, L, R>>;
template<class T>
concept weakly_incrementable =
std::movable<T> &&
requires (T v) {
{ ++v } -> std::same_as<T&>;
v++;
};
template<class T>
concept weakly_decrementable =
std::movable<T> &&
requires (T v) {
{ --v } -> std::same_as<T&>;
v--;
};
template<class T>
concept incrementable =
std::regular<T> &&
weakly_incrementable<T> &&
requires (T v) {
{ v++ } -> std::same_as<T>;
};
template<class T>
concept decrementable =
std::regular<T> &&
weakly_decrementable<T> &&
requires (T v) {
{ v-- } -> std::same_as<T>;
};
template<class L, class R = L>
concept weakly_arithmetic_operable =
weakly_addable<L, R> &&
weakly_subtractable<L, R> &&
weakly_multipliable<L, R> &&
weakly_divisable<L, R>;
template<class L, class R = L>
concept weakly_arithmetic_operation_assignable =
weakly_addition_assignable<L, R> &&
weakly_subtraction_assignable<L, R> &&
weakly_multipliation_assignalbe<L, R> &&
weakly_division_assignable<L, R>;
template<class L, class R = L>
concept arithmetic_operable =
weakly_arithmetic_operable<L, R> &&
addable<L, R> &&
subtractable<L, R> &&
multipliable<L, R> &&
divisable<L, R>;
template<class L, class R = L>
concept arithmetic_operation_assignable =
weakly_arithmetic_operation_assignable<L, R> &&
addition_assignable<L, R> &&
subtraction_assignable<L, R> &&
multipliation_assignalbe<L, R> &&
division_assignable<L, R>;
template<class T>
concept unary_addable =
requires (T v) {
{ +v } -> std::same_as<T>;
};
template<class T>
concept unary_subtractable =
requires (T v) {
{ -v } -> std::same_as<T>;
};
template<class T>
concept numeric =
std::regular<T> &&
arithmetic_operable<T> &&
arithmetic_operation_assignable<T> &&
weakly_incrementable<T> &&
unary_addable<T> &&
unary_subtractable<T>;
} // namespace internal
} // namespace uni
#line 9 "algebraic/internal/concepts.hpp"
#line 2 "algebraic/base.hpp"
#include <utility>
#line 6 "algebraic/base.hpp"
#line 2 "numeric/arithmetic.hpp"
#include <cassert>
#include <cstring>
#line 7 "numeric/arithmetic.hpp"
#include <string>
#line 10 "numeric/arithmetic.hpp"
#include <optional>
#include <algorithm>
#line 13 "numeric/arithmetic.hpp"
#include <bit>
#include <atcoder/math>
#line 2 "snippet/aliases.hpp"
#line 6 "snippet/aliases.hpp"
#include <vector>
#line 8 "snippet/aliases.hpp"
#line 2 "snippet/internal/types.hpp"
#line 4 "snippet/internal/types.hpp"
namespace uni {
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
#ifdef __GNUC__
using i128 = __int128_t;
using u128 = __uint128_t;
using f128 = __float128;
#endif
using uint = unsigned;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
} // namespace uni
#line 12 "snippet/aliases.hpp"
#define until(...) while(!(__VA_ARGS__))
#define CONTINUE(...) { __VA_ARGS__; continue; }
#define BREAK(...) { __VA_ARGS__; break; }
#define ALL(x) std::ranges::begin((x)),std::ranges::end((x))
#define RALL(x) std::ranges::rbegin((x)),std::ranges::rend((x))
#define $F first
#define $S second
namespace uni {
constexpr char LN = '\n';
constexpr char SPC = ' ';
constexpr std::pair<int,int> DIRS4[] = { { -1, 0 }, { 0, 1 }, { 1, 0 }, { 0, -1 } };
constexpr std::pair<int,int> DIRS4P[] = { { -1, 0 }, { 0, 1 }, { 1, 0 }, { 0, -1 }, { 0, 0 } };
constexpr std::pair<int,int> DIRS8[] = { { -1, 0 }, { -1, 1 }, { 0, 1 }, { 1, 1 }, { 1, 0 }, { 1, -1 }, { 0, -1 }, { -1, -1 } };
constexpr std::pair<int,int> DIRS8P[] = { { -1, 0 }, { -1, 1 }, { 0, 1 }, { 1, 1 }, { 1, 0 }, { 1, -1 }, { 0, -1 }, { -1, -1 }, { 0, 0 } };
template<class T> using spair = std::pair<T,T>;
} // namespace uni
namespace std {
using bit_reference = std::vector<bool>::reference;
bit_reference operator |= (bit_reference a, const bool b) noexcept(NO_EXCEPT) { return a = a | b; }
bit_reference operator &= (bit_reference a, const bool b) noexcept(NO_EXCEPT) { return a = a & b; }
}
#line 2 "snippet/iterations.hpp"
#line 2 "macro/overload.hpp"
#define $OVERLOAD2(arg0, arg1, cmd, ...) cmd
#define $OVERLOAD3(arg0, arg1, arg2, cmd, ...) cmd
#define $OVERLOAD4(arg0, arg1, arg2, arg3, cmd, ...) cmd
#define $OVERLOAD5(arg0, arg1, arg2, arg3, arg4, cmd, ...) cmd
#define $OVERLOAD6(arg0, arg1, arg2, arg3, arg4, arg5, cmd, ...) cmd
#line 2 "macro/basic.hpp"
#define TO_STRING_AUX(x) #x
#define TO_STRING(x) TO_STRING_AUX(x)
#define CONCAT_AUX(x, y) x##y
#define CONCAT(x, y) CONCAT_AUX(x, y)
#define UNPAREN_AUX(...) __VA_ARGS__
#define UNPAREN(...) __VA_ARGS__
#line 6 "snippet/iterations.hpp"
#define LOOP(n) REPI(CONCAT(_$, __COUNTER__), n)
#define REPI(i,n) for(std::remove_cvref_t<decltype(n)> i=0, CONCAT(i, $)=(n); i<CONCAT(i, $); ++i)
#define REPF(i,l,r) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>> i=(l), CONCAT(i, $)=(r); i<CONCAT(i, $); ++i)
#define REPIS(i,l,r,s) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>,std::remove_cvref_t<decltype(s)>> i=(l), CONCAT(i, $)=(r); i<CONCAT(i, $); i+=(s))
#define REPR(i,n) for(auto i=(n); --i>=0;)
#define REPB(i,l,r) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>> i=(r), CONCAT(i, $)=(l); --i>=CONCAT(i, $);)
#define REPRS(i,l,r,s) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>,std::remove_cvref_t<decltype(s)>> i=(l)+((r)-(l)-1)/(s)*(s), CONCAT(i, $)=(l); i>=CONCAT(i, $); (i-=(s)))
#define REP(...) $OVERLOAD4(__VA_ARGS__, REPIS, REPF, REPI, LOOP)(__VA_ARGS__)
#define REPD(...) $OVERLOAD4(__VA_ARGS__, REPRS, REPB, REPR)(__VA_ARGS__)
#define FORO(i,n) for(int i=0, CONCAT(i, $)=static_cast<int>(n); i<=CONCAT(i, $); ++i)
#define FORI(i,l,r) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>> i=(l), CONCAT(i, $)=(r); i<=CONCAT(i, $); ++i)
#define FORIS(i,l,r,s) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>,std::remove_cvref_t<decltype(s)>> i=(l), CONCAT(i, $)=(r); i<=CONCAT(i, $); i+=(s))
#define FORRO(i,n) for(auto i=(n); i>=0; --i)
#define FORR(i,l,r) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>> i=(r), CONCAT(i, $)=(l); i>=CONCAT(i, $); --i)
#define FORRS(i,l,r,s) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>,std::remove_cvref_t<decltype(s)>> i=(l)+((r)-(l))/(s)*(s), CONCAT(i, $)=(l); i>=CONCAT(i, $); i-=(s))
#define FOR(...) $OVERLOAD4(__VA_ARGS__, FORIS, FORI, FORO)(__VA_ARGS__)
#define FORD(...) $OVERLOAD4(__VA_ARGS__, FORRS, FORR, FORRO)(__VA_ARGS__)
#define ITR1(e0,v) for(const auto &e0 : (v))
#define ITRP1(e0,v) for(auto e0 : (v))
#define ITRR1(e0,v) for(auto &e0 : (v))
#define ITR2(e0,e1,v) for(const auto [e0, e1] : (v))
#define ITRP2(e0,e1,v) for(auto [e0, e1] : (v))
#define ITRR2(e0,e1,v) for(auto &[e0, e1] : (v))
#define ITR3(e0,e1,e2,v) for(const auto [e0, e1, e2] : (v))
#define ITRP3(e0,e1,e2,v) for(auto [e0, e1, e2] : (v))
#define ITRR3(e0,e1,e2,v) for(auto &[e0, e1, e2] : (v))
#define ITR4(e0,e1,e2,e3,v) for(const auto [e0, e1, e2, e3] : (v))
#define ITRP4(e0,e1,e2,e3,v) for(auto [e0, e1, e2, e3] : (v))
#define ITRR4(e0,e1,e2,e3,v) for(auto &[e0, e1, e2, e3] : (v))
#define ITR5(e0,e1,e2,e3,e4,v) for(const auto [e0, e1, e2, e3, e4] : (v))
#define ITRP5(e0,e1,e2,e3,e4,v) for(auto [e0, e1, e2, e3, e4] : (v))
#define ITRR5(e0,e1,e2,e3,e4,v) for(auto &[e0, e1, e2, e3, e4] : (v))
#define ITR(...) $OVERLOAD6(__VA_ARGS__, ITR5, ITR4, ITR3, ITR2, ITR1)(__VA_ARGS__)
#define ITRP(...) $OVERLOAD6(__VA_ARGS__, ITRP5, ITRP4, ITRP3, ITRP2, ITRP1)(__VA_ARGS__)
#define ITRR(...) $OVERLOAD6(__VA_ARGS__, ITRR5, ITRR4, ITRR3, ITRR2, ITRR1)(__VA_ARGS__)
#line 21 "numeric/arithmetic.hpp"
#line 25 "numeric/arithmetic.hpp"
#line 2 "utility/internal/functional_base.hpp"
namespace uni {
template<class P>
requires
requires(P p) {
p.first;
p.second;
}
inline P swapped(P& pair) {
return P{ pair.second, pair.first };
}
} // namespace uni
#line 27 "numeric/arithmetic.hpp"
#line 2 "numeric/internal/number_base.hpp"
#line 6 "numeric/internal/number_base.hpp"
#include <string_view>
#line 14 "numeric/internal/number_base.hpp"
#line 18 "numeric/internal/number_base.hpp"
#line 2 "adaptor/string.hpp"
#line 6 "adaptor/string.hpp"
#line 2 "adaptor/internal/advanced_container.hpp"
#line 8 "adaptor/internal/advanced_container.hpp"
#line 11 "adaptor/internal/advanced_container.hpp"
#line 15 "adaptor/internal/advanced_container.hpp"
#line 2 "numeric/internal/mod.hpp"
#line 6 "numeric/internal/mod.hpp"
namespace uni {
template<class T, class R>
requires
internal::remainder_calculable<T, R> &&
internal::subtractable<T, R> &&
internal::unary_subtractable<T>
inline T mod(T x, const R& r) noexcept(NO_EXCEPT) {
if(x >= 0) return x % r;
x = -x % r;
if(x != 0) x = r - x;
return x;
}
} // namespace uni
#line 2 "iterable/internal/operation_base.hpp"
#line 5 "iterable/internal/operation_base.hpp"
#include <iterator>
#include <sstream>
#include <numeric>
#line 11 "iterable/internal/operation_base.hpp"
namespace uni {
template<std::input_iterator I, std::sentinel_for<I> S>
std::string join(I first, S last, const char* sep = "") noexcept(NO_EXCEPT) {
if(first == last) return "";
std::ostringstream res;
while(true) {
res << *first;
std::ranges::advance(first, 1);
if(first == last) break;
res << sep;
}
return res.str();
}
template<std::ranges::input_range R>
std::string join(R&& range, const char* sep = "") noexcept(NO_EXCEPT) {
return join(ALL(range), sep);
}
template<class I, class T = std::iter_value_t<I>>
requires std::sentinel_for<I, I>
T sum(I first, I last, const T& base = T()) noexcept(NO_EXCEPT) {
return std::accumulate(first, last, base);
}
template<std::ranges::input_range R, class T = std::ranges::range_value_t<R>>
auto sum(R&& range, T base = T()) noexcept(NO_EXCEPT) {
auto&& r = range | std::views::common;
return sum(ALL(r), base);
}
} // namesapce uni
#line 18 "adaptor/internal/advanced_container.hpp"
#define UNI_ADVANCED_CONTAINER_OPERATOR(op_assign, op, concepts) \
auto& operator op_assign(const value_type& v) noexcept(NO_EXCEPT) \
requires concepts<value_type> \
{ \
if constexpr(concepts<Base, value_type>) { \
this->Base::operator op_assign(v); \
} \
else { \
REP(itr, ALL(*this)) *itr op_assign v; \
} \
return *this; \
} \
\
auto& operator op_assign(const advanced_container& rhs) noexcept(NO_EXCEPT) \
requires concepts<value_type> \
{ \
if constexpr(concepts<Base>) { \
this->Base::operator op_assign(*rhs._base()); \
} \
else { \
auto itr = std::ranges::begin(*this), rhs_itr = std::ranges::begin(rhs); \
auto end = std::ranges::end(*this); \
for(; itr != end; ++itr, ++rhs_itr) { \
*itr op_assign *rhs_itr; \
} \
} \
return *this; \
} \
\
template<class T = value_type> \
requires \
concepts<value_type> && \
(std::convertible_to<T, value_type> || std::same_as<T, advanced_container>) \
friend auto operator op(advanced_container lhs, const T& rhs) noexcept(NO_EXCEPT) { \
return lhs op_assign rhs; \
} \
\
template<class T = value_type> \
requires \
concepts<value_type> && std::convertible_to<T, value_type> \
friend auto operator op(const T& lhs, advanced_container rhs) noexcept(NO_EXCEPT) { \
return advanced_container(rhs.size(), lhs) op_assign rhs; \
}
namespace uni {
namespace internal {
template<class Base>
struct advanced_container : Base {
private:
inline Base* _base() noexcept(NO_EXCEPT) {
return static_cast<Base*>(this);
}
inline const Base* _base() const noexcept(NO_EXCEPT) {
return static_cast<const Base*>(this);
}
public:
using Base::Base;
advanced_container(const Base& base) : Base(base) {}
using size_type = decltype(std::ranges::size(std::declval<Base>()));
using value_type = Base::value_type;
inline auto ssize() const noexcept(NO_EXCEPT) { return std::ranges::ssize(*this->_base()); }
inline const auto& operator[](internal::size_t p) const noexcept(NO_EXCEPT) {
p = p < 0 ? p + this->size() : p;
assert(0 <= p && p < this->ssize());
return this->Base::operator[](p);
}
inline auto& operator[](internal::size_t p) noexcept(NO_EXCEPT) {
p = p < 0 ? p + this->size() : p;
assert(0 <= p && p < this->ssize());
return this->Base::operator[](p);
}
inline auto& fill(const value_type& v) noexcept(NO_EXCEPT) {
std::ranges::fill(*this, v);
return *this;
}
inline auto& swap(const size_type i, const size_type j) noexcept(NO_EXCEPT) {
std::swap(this->operator[](i), this->operator[](j));
return *this;
}
inline auto& sort() noexcept(NO_EXCEPT) {
std::ranges::sort(*this);
return *this;
}
template<class F>
inline auto& sort(F&& f) noexcept(NO_EXCEPT) {
std::ranges::sort(*this, std::forward<F>(f));
return *this;
}
inline auto& stable_sort() noexcept(NO_EXCEPT) {
std::ranges::stable_sort(*this);
return *this;
}
template<class F>
inline auto& stable_sort(F&& f) noexcept(NO_EXCEPT) {
std::ranges::stable_sort(*this, std::forward<F>(f));
return *this;
}
inline auto& reverse() noexcept(NO_EXCEPT) {
std::ranges::reverse(*this);
return *this;
}
inline auto count(const value_type& v) const noexcept(NO_EXCEPT) {
return std::ranges::count(*this, v);
}
template<class F>
inline auto count_if(F&& f) const noexcept(NO_EXCEPT) {
return std::ranges::count_if(*this, std::forward<F>(f));
}
inline auto& resize(const size_type k) noexcept(NO_EXCEPT) {
this->Base::resize(k);
return *this;
}
inline auto& resize(const size_type k, const value_type v) noexcept(NO_EXCEPT) {
this->Base::resize(k, v);
return *this;
}
template<class F>
inline auto& shuffle(F&& f) noexcept(NO_EXCEPT) {
std::ranges::shuffle(*this, std::forward<F>(f));
return *this;
}
inline auto& unique() noexcept(NO_EXCEPT) {
const auto rest = std::ranges::unique(*this);
this->erase(ALL(rest));
return *this;
}
template<class T>
inline auto binary_search(const T& v) noexcept(NO_EXCEPT) {
return std::ranges::binary_search(*this, v);
}
template<class T>
inline auto lower_bound(const T& v) noexcept(NO_EXCEPT) {
return std::ranges::lower_bound(*this, v);
}
template<class T>
inline auto upper_bound(const T& v) noexcept(NO_EXCEPT) {
return std::ranges::upper_bound(*this, v);
}
inline auto join(const char* sep = "") noexcept(NO_EXCEPT) {
return uni::join(*this, sep);
}
inline auto sum() const noexcept(NO_EXCEPT) { return uni::sum(*this); }
inline auto max() const noexcept(NO_EXCEPT) { return std::ranges::max(*this->_base()); }
inline auto min() const noexcept(NO_EXCEPT) { return std::ranges::min(*this); }
inline auto begin() noexcept(NO_EXCEPT) { return std::ranges::begin(*this->_base()); }
inline auto begin() const noexcept(NO_EXCEPT) { return std::ranges::begin(*this->_base()); }
inline auto end() noexcept(NO_EXCEPT) { return std::ranges::end(*this->_base()); }
inline auto end() const noexcept(NO_EXCEPT) { return std::ranges::end(*this->_base()); }
UNI_ADVANCED_CONTAINER_OPERATOR(+=, +, internal::weakly_addition_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(-=, -, internal::weakly_subtraction_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(*=, *, internal::weakly_multipliation_assignalbe)
UNI_ADVANCED_CONTAINER_OPERATOR(/=, /, internal::weakly_division_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(%=, %, internal::weakly_remainder_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(&=, &, internal::weakly_bitand_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(|=, |, internal::weakly_bitor_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(^=, ^, internal::weakly_bitxor_assignable)
};
} // namespace internal
} // namespace uni
#undef UNI_ADVANCED_CONTAINER_OPERATOR
#line 8 "adaptor/string.hpp"
namespace uni {
using string = internal::advanced_container<std::string>;
} // namespace uni
namespace std {
template<>
struct hash<uni::string> {
inline auto operator()(const uni::string& key) const noexcept(NO_EXCEPT) {
return std::hash<std::string>{}(static_cast<std::string>(key));
}
};
}
#line 2 "adaptor/vector.hpp"
#line 6 "adaptor/vector.hpp"
#line 9 "adaptor/vector.hpp"
namespace uni {
template<class... Args>
using vector = internal::advanced_container<std::vector<Args...>>;
} // namespace uni
#line 21 "numeric/internal/number_base.hpp"
namespace uni {
template<std::size_t B, class T>
uni::string to_base_n_string(T v) noexcept(NO_EXCEPT) {
constexpr std::string_view CHARS = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
static_assert(0 < B and B <= std::ranges::size(CHARS));
assert(0 <= v);
uni::string res;
while(v > 0) {
res += CHARS[v%B];
v /= B;
}
std::reverse(ALL(res));
return res;
}
template<class T>
uni::string to_base_n_string(T v, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
constexpr std::string_view CHARS = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
assert(1 < b && b <= std::ranges::ssize(CHARS));
assert(0 <= v);
if(v == 0) return "0";
uni::string res;
while(v > 0) {
res += CHARS[v % b];
v /= b;
}
std::reverse(ALL(res));
return res;
}
template<class T>
uni::vector<T> to_base_n_vector(T v, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
assert(1 < b);
assert(0 <= v);
uni::vector<T> res;
while(v > 0) {
res.push_back(v%b);
v /= b;
}
return res;
}
template<std::bidirectional_iterator I, class T = typename std::iterator_traits<I>::value_type>
T from_base_n_sequence(I begin, I end, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
assert(1 < b);
if(begin == end) return 0;
T res = 0;
for(auto itr=end; itr-- != begin; ) {
res *= b;
res += *itr;
}
return res;
}
template<class T, std::forward_iterator I>
T from_base_n_string(I begin, I end, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
assert(1 < b);
if(begin == end) return 0;
T sgn = 1;
if(*begin == '-') {
sgn = -1;
++begin;
}
T res = 0;
for(auto itr=begin; itr != end; ++itr) {
res *= b;
if('0' <= *itr && *itr <= '9') {
res += *itr - '0';
}
else if('a' <= *itr && *itr <= 'z') {
res += *itr - 'a' + 10;
}
else if('A' <= *itr && *itr <= 'Z'){
res += *itr - 'A' + 10;
}
else {
assert(false);
}
}
return res * sgn;
}
template<std::ranges::bidirectional_range R, class T = std::ranges::range_value_t<R>>
requires std::ranges::common_range<R>
T from_base_n_sequence(R range, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
return from_base_n_sequence(std::ranges::begin(range), std::ranges::end(range), b);
}
template<class T, std::ranges::bidirectional_range R>
requires std::ranges::common_range<R>
T from_base_n_string(R range, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
return from_base_n_string<T>(std::ranges::begin(range), std::ranges::end(range), b);
}
} // namespace uni
#line 29 "numeric/arithmetic.hpp"
#line 2 "iterable/operation.hpp"
#line 6 "iterable/operation.hpp"
#include <initializer_list>
#line 9 "iterable/operation.hpp"
#include <valarray>
#line 17 "iterable/operation.hpp"
#line 21 "iterable/operation.hpp"
#line 2 "internal/type_traits.hpp"
#include <iostream>
#line 9 "internal/type_traits.hpp"
#line 12 "internal/type_traits.hpp"
namespace uni {
namespace internal {
template<class... Ts> struct tuple_or_pair { using type = std::tuple<Ts...>; };
template<class T, class U> struct tuple_or_pair<T,U> { using type = std::pair<T, U>; };
template <class... Ts> using tuple_or_pair_t = typename tuple_or_pair<Ts...>::type;
template<class T>
constexpr std::underlying_type_t<T> to_underlying(const T& v) noexcept(NO_EXCEPT) {
return static_cast<std::underlying_type_t<T>>(v);
}
template<class T, class... Ts>
using are_same = std::conjunction<std::is_same<T, Ts>...>;
template<class T, class... Ts>
inline constexpr bool are_same_v = are_same<T, Ts...>::value;
template<class T, class... Ts>
using is_same_as_any_of = std::disjunction<std::is_same<T, Ts>...>;
template<class T, class... Ts>
inline constexpr bool is_same_as_any_of_v = is_same_as_any_of<T, Ts...>::value;
template<class T, class... Ts>
concept same_as_any_of = is_same_as_any_of_v<T, Ts...>;
template<class Base, class... Derived>
using is_base_of_all = std::conjunction<std::is_base_of<Base, Derived>...>;
template<class Base, class... Derived>
inline constexpr bool is_base_of_all_v = is_base_of_all<Base, Derived...>::value;
template<class Base, class... Derived>
using is_base_of_any = std::disjunction<std::is_base_of<Base, Derived>...>;
template<class Base, class... Derived>
inline constexpr bool is_base_of_any_v = is_base_of_any<Base, Derived...>::value;
template<class T> struct remove_cvref {
using type = typename std::remove_cv_t<std::remove_reference_t<T>>;
};
template<class T> using remove_cvref_t = typename remove_cvref<T>::type;
template<class T> struct literal_operator { static constexpr const char* value = ""; };
template<> struct literal_operator<unsigned> { static constexpr const char* value = "U"; };
template<> struct literal_operator<long> { static constexpr const char* value = "L"; };
template<> struct literal_operator<unsigned long> { static constexpr const char* value = "UL"; };
template<> struct literal_operator<long long> { static constexpr const char* value = "LL"; };
template<> struct literal_operator<unsigned long long> { static constexpr const char* value = "ULL"; };
template<> struct literal_operator<float> { static constexpr const char* value = "F"; };
template<> struct literal_operator<double> { static constexpr const char* value = "D"; };
template<> struct literal_operator<long double> { static constexpr const char* value = "LD"; };
#ifdef __SIZEOF_INT128__
template<> struct literal_operator<__int128_t> { static constexpr const char* value = "LLL"; };
template<> struct literal_operator<__uint128_t> { static constexpr const char* value = "ULLL"; };
#endif
template<class T> inline constexpr auto literal_operator_v = literal_operator<T>::value;
template <std::size_t N, typename... Types>
struct nth_type {};
template <class Head, class... Tail>
struct nth_type<0, Head, Tail...> {
using type = Head;
};
template <std::size_t N, class Head, class... Tail>
struct nth_type<N, Head, Tail...> : public nth_type<N - 1, Tail...> {};
template <std::size_t N, typename... Types>
using nth_type_t = typename nth_type<N, Types...>::type;
template<template <class...> class, class> struct is_template_of : std::false_type {};
template<template <class...> class Template, class... Args> struct is_template_of<Template, Template<Args...>> : std::true_type {};
template<template <class...> class Template, class Type>
inline constexpr bool is_template_of_v = is_template_of<Template, Type>::value;
template<class Type, template <class...> class Template>
concept substituted_from = is_template_of_v<Template, Type>;
template<template <class...> class Base, class Derived>
struct _is_basic_tempalte_of
{
template<class... Ts>
static constexpr std::true_type test(const Base<Ts...> *);
static constexpr std::false_type test(...);
using type = decltype(test(std::declval<Derived*>()));
};
template<template <class...> class Base, class Derived>
using is_basic_tempalte_of = _is_basic_tempalte_of<Base, Derived>::type;
template<template <class...> class Base, class Derived>
inline constexpr bool is_basic_tempalte_of_v = is_basic_tempalte_of<Base, Derived>::value;
template<class Derived, template <class...> class Base>
concept derived_from_template = is_basic_tempalte_of_v<Base, Derived>;
template<class T> struct is_loggable {
template<class U>
static constexpr auto External(U &&v) -> decltype(_debug(v), std::true_type());
static constexpr std::false_type External(...);
template<class U>
static constexpr auto Member(U &&v) -> decltype(v._debug(), std::true_type());
static constexpr std::false_type Member(...);
static constexpr bool value = (
decltype(External(std::declval<T>()))::value ||
decltype(Member(std::declval<T>()))::value
);
};
template<class T>
inline constexpr auto is_loggable_v = is_loggable<T>::value;
template<class T>
concept loggable = is_loggable_v<T>;
template<class T> struct _has_iterator {
template<class U>
static constexpr auto ADL(U &&v) -> decltype(begin(v), end(v), std::true_type());
static constexpr std::false_type ADL(...);
template<class U>
static constexpr auto STL(U &&v) -> decltype(std::begin(v), std::end(v), std::true_type());
static constexpr std::false_type STL(...);
template<class U>
static constexpr auto Member(U &&v) -> decltype(v.begin(), v.end(), std::true_type());
static constexpr std::false_type Member(...);
};
template<class T> struct has_iterator {
struct ADL : decltype(_has_iterator<T>::ADL(std::declval<T>())) {};
struct STL : decltype(_has_iterator<T>::STL(std::declval<T>())) {};
struct Member : decltype(_has_iterator<T>::Member(std::declval<T>())) {};
static constexpr auto adl_v = ADL::value;
static constexpr auto stl_v = STL::value;
static constexpr auto member_v = Member::value;
};
template<class T>
struct is_iterable {
static constexpr bool value = has_iterator<T>::adl_v || has_iterator<T>::stl_v || has_iterator<T>::member_v;
};
template<class T>
inline constexpr auto is_iterable_v = is_iterable<T>::value;
template<class T>
concept iterable = is_iterable_v<T>;
namespace iterator_resolver {
template<class T>
inline constexpr auto begin(T&& v) noexcept(NO_EXCEPT) {
static_assert(is_iterable_v<T>);
if constexpr(has_iterator<T>::member_v) {
return v.begin();
}
else { // ADL
using std::begin;
return begin(std::forward<T>(v));
}
}
template<class T>
inline constexpr auto end(T&& v) noexcept(NO_EXCEPT) {
static_assert(is_iterable_v<T>);
if constexpr(has_iterator<T>::member_v) {
return v.end();
}
else { // ADL
using std::end;
return end(std::forward<T>(v));
}
}
};
template<class C> using iterator_t = decltype(iterator_resolver::begin(std::declval<C&>()));
template<class C> using container_size_t = decltype(std::size(std::declval<C&>()));
template<bool Const, class T>
using maybe_const_t = std::conditional_t<Const, const T, T>;
template<class T> using with_ref = T&;
template<class T> concept can_reference = requires { typename with_ref<T>; };
} // namespace internal
} // namespace uni
#line 2 "internal/exception.hpp"
namespace uni {
namespace internal {
template<class... T> inline constexpr bool EXCEPTION_ON_TYPE = false;
template<auto T> inline constexpr bool EXCEPTION_ON_VALUE = false;
} // namespace internal
} // namespace uni
#line 2 "internal/iterator.hpp"
#line 7 "internal/iterator.hpp"
#include <variant>
#include <compare>
#line 10 "internal/iterator.hpp"
#line 13 "internal/iterator.hpp"
#line 16 "internal/iterator.hpp"
namespace uni {
namespace internal {
template<class T>
struct iterator_interface {
using iterator_category = std::output_iterator_tag;
using difference_type = size_t;
using value_type = T;
using pointer = T*;
using reference = T&;
// virtual T operator*() const noexcept(NO_EXCEPT) { return 0; };
};
template<class T>
struct forward_iterator : iterator_interface<T> {
using iterator_category = std::forward_iterator_tag;
// virtual bidirectional_iterator_interface& operator++() = 0;
};
template<class T>
struct bidirectional_iterator_interface : forward_iterator<T> {
using iterator_category = std::bidirectional_iterator_tag;
// virtual bidirectional_iterator_interface& operator--() = 0;
};
template<class T>
struct random_access_iterator_base : bidirectional_iterator_interface<T> {
using iterator_category = std::random_access_iterator_tag;
using difference_type = typename bidirectional_iterator_interface<T>::difference_type;
public:
// virtual random_access_iterator_base& operator+=(const difference_type count) = 0;
// virtual random_access_iterator_base& operator-=(const difference_type count) = 0;
friend inline random_access_iterator_base operator+(random_access_iterator_base itr, const difference_type count) noexcept(NO_EXCEPT) { return itr += count, itr; }
friend inline random_access_iterator_base operator-(random_access_iterator_base itr, const difference_type count) noexcept(NO_EXCEPT) { return itr -= count, itr; }
};
template<class T, class Container, class Derived>
struct container_iterator_interface : random_access_iterator_base<T> {
using difference_type = std::make_signed_t<typename Container::size_type>;
private:
using derived = std::remove_cvref_t<Derived>;
Container* _ref;
difference_type _pos;
static_assert(std::three_way_comparable<difference_type>);
inline auto* _derived() noexcept(NO_EXCEPT) {
return static_cast<derived*>(this);
}
inline const auto* _derived() const noexcept(NO_EXCEPT) {
return static_cast<const derived*>(this);
}
public:
container_iterator_interface() noexcept = default;
container_iterator_interface(Container *const ref, const difference_type pos) noexcept(NO_EXCEPT) : _ref(ref), _pos(pos) {}
inline auto ref() const noexcept(NO_EXCEPT) { return this->_ref; }
inline auto pos() const noexcept(NO_EXCEPT) { return this->_pos; }
inline auto& pos() { return this->_pos; }
inline auto& operator++() noexcept(NO_EXCEPT) { return ++this->_pos, *this->_derived(); }
inline auto& operator--() noexcept(NO_EXCEPT) { return --this->_pos, *this->_derived(); }
inline auto operator++(int) noexcept(NO_EXCEPT) { auto res = *this->_derived(); return ++this->_pos, res; }
inline auto operator--(int) noexcept(NO_EXCEPT) { auto res = *this->_derived(); return --this->_pos, res; }
inline auto& operator+=(const difference_type count) noexcept(NO_EXCEPT) { return this->_pos += count, *this->_derived(); }
inline auto& operator-=(const difference_type count) noexcept(NO_EXCEPT) { return this->_pos -= count, *this->_derived(); }
inline auto operator*() const noexcept(NO_EXCEPT) { return this->ref()->get(this->_pos); }
inline auto operator[](const difference_type count) const noexcept(NO_EXCEPT) { return *(*this->_derived() + count); }
inline auto operator-(const derived& other) const noexcept(NO_EXCEPT) { return this->_pos - other._pos; }
friend inline bool operator==(const derived& lhs, const derived& rhs) noexcept(NO_EXCEPT) {
if(lhs.ref() == rhs.ref()) return lhs._pos == rhs._pos;
return false;
}
friend inline std::partial_ordering operator<=>(const derived& lhs, const derived& rhs) noexcept(NO_EXCEPT) {
if(lhs.ref() != rhs.ref()) return std::partial_ordering::unordered;
return lhs._pos <=> rhs._pos;
}
};
namespace iterator_impl {
template<class... Tags>
using is_all_random_access_iterator = is_base_of_all<std::random_access_iterator_tag,Tags...>;
template<class... Tags>
using is_all_bidirectional_iterator = is_base_of_all<std::bidirectional_iterator_tag,Tags...>;
template<class... Tags>
using is_all_forward_iterator = is_base_of_all<std::forward_iterator_tag,Tags...>;
template<class... Tags>
using is_all_input_iterator = is_base_of_all<std::input_iterator_tag,Tags...>;
template<class... Tags>
constexpr auto _most_primitive_iterator_tag() {
if constexpr(is_all_random_access_iterator<Tags...>::value) {
return std::random_access_iterator_tag{};
}
else if constexpr(is_all_bidirectional_iterator<Tags...>::value) {
return std::bidirectional_iterator_tag{};
}
else if constexpr(is_all_forward_iterator<Tags...>::value) {
return std::forward_iterator_tag{};
}
else {
return std::input_iterator_tag{};
}
}
} // namespace iterator_impl
template<class... Tags>
using most_primitive_iterator_tag = decltype(iterator_impl::_most_primitive_iterator_tag<Tags...>());
template<class T, class = void>
struct is_iterator {
static constexpr bool value = false;
};
template<class T>
struct is_iterator<T, typename std::enable_if<!std::is_same<typename std::iterator_traits<T>::value_type, void>::value>::type> {
static constexpr bool value = true;
};
template<class T>
inline constexpr bool is_iterator_v = is_iterator<T>::value;
template<class T>
using is_iterator_t = std::enable_if_t<is_iterator_v<T>>;
template<class T>
using iota_diff_t = std::make_signed_t<T>;
} // namespace internal
} // namespace uni
#line 2 "internal/ranges.hpp"
#line 6 "internal/ranges.hpp"
#include <tuple>
#line 11 "internal/ranges.hpp"
namespace uni {
namespace internal {
template<class Range>
concept resizable_range
= std::ranges::range<Range> &&
requires (Range& r) { r.resize(0); };
template<class range>
concept simple_view
= std::ranges::view<range> && std::ranges::range<const range> &&
std::same_as<std::ranges::iterator_t<range>, std::ranges::iterator_t<const range>> &&
std::same_as<std::ranges::sentinel_t<range>, std::ranges::sentinel_t<const range>>;
template<class... Ranges>
concept zip_is_common = (sizeof...(Ranges) == 1 && (std::ranges::common_range<Ranges> && ...))
|| (!(std::ranges::bidirectional_range<Ranges> && ...) && (std::ranges::common_range<Ranges> && ...))
|| ((std::ranges::random_access_range<Ranges> && ...) && (std::ranges::sized_range<Ranges> && ...));
template<bool Const, class... Views>
concept all_contiguous = (std::ranges::contiguous_range<maybe_const_t<Const, Views>> && ...);
template<bool Const, class... Views>
concept all_random_access = (std::ranges::random_access_range<maybe_const_t<Const, Views>> && ...);
template<bool Const, class... Views>
concept all_bidirectional = (std::ranges::bidirectional_range<maybe_const_t<Const, Views>> && ...);
template<bool Const, class... Views>
concept all_forward = (std::ranges::forward_range<maybe_const_t<Const, Views>> && ...);
template<bool Const, class... Views> struct zip_view_iterator_category {};
template<bool Const, class... Views>
requires all_forward<Const, Views...>
struct zip_view_iterator_category<Const, Views...> {
using iterator_category = std::input_iterator_tag;
};
template<bool Const, class... Views>
static auto _most_primitive_iterator_concept() noexcept(NO_EXCEPT) {
if constexpr(all_random_access<Const, Views...>)
return std::random_access_iterator_tag{};
else if constexpr(all_bidirectional<Const, Views...>)
return std::bidirectional_iterator_tag{};
else if constexpr(all_forward<Const, Views...>)
return std::forward_iterator_tag{};
else
return std::input_iterator_tag{};
}
template<bool Const, class... Views>
using most_primitive_iterator_concept = decltype(_most_primitive_iterator_concept<Const, Views...>());
template<class Range, bool Const>
using range_iterator_category = typename std::iterator_traits<
std::ranges::iterator_t<maybe_const_t<Const, Range>>
>::iterator_category;
template<class Range>
static constexpr auto _iterator_concept() noexcept(NO_EXCEPT) {
if constexpr(std::ranges::random_access_range<Range>)
return std::random_access_iterator_tag{};
else if constexpr(std::ranges::bidirectional_range<Range>)
return std::bidirectional_iterator_tag{};
else if constexpr(std::ranges::forward_range<Range>)
return std::forward_iterator_tag{};
else
return std::input_iterator_tag{};
}
template<class Range>
using iterator_concept = decltype(_iterator_concept<Range>());
template<std::ranges::range Range> struct cached_position {
constexpr bool has_value() const { return false; }
constexpr std::ranges::iterator_t<Range> get(const Range&) const {
__builtin_unreachable();
}
constexpr void set(const Range &, const std::ranges::iterator_t<Range> &) const {}
};
template<std::ranges::forward_range Range>
struct cached_position<Range> : protected std::optional<std::ranges::iterator_t<Range>> {
using std::optional<std::ranges::iterator_t<Range>>::optioanl;
using std::optional<std::ranges::iterator_t<Range>>::has_value;
constexpr std::ranges::iterator_t<Range> get(const Range&) const {
assert(this->has_value());
return **this;
}
constexpr void set(const Range&, const std::ranges::iterator_t<Range>& itr) {
assert(!this->has_value());
this->emplace(*itr);
}
};
template<std::ranges::random_access_range Range>
requires(sizeof(std::ranges::range_difference_t<Range>) <= sizeof(std::ranges::iterator_t<Range>))
struct cached_position<Range> {
private:
std::ranges::range_difference_t<Range> _offset = -1;
public:
cached_position() = default;
constexpr cached_position(const cached_position &) = default;
constexpr cached_position(cached_position &&other) noexcept {
*this = std::move(other);
}
constexpr cached_position &operator=(const cached_position &) = default;
constexpr cached_position &operator=(cached_position &&other) noexcept {
// Propagate the cached offset, but invalidate the source.
this->_offset = other._offset;
other._offset = -1;
return *this;
}
constexpr bool has_value() const { return this->_offset >= 0; }
constexpr std::ranges::iterator_t<Range> get(Range& range) const {
assert(this->has_value());
return std::ranges::begin(range) + this->_offset;
}
constexpr void set(Range &range, const std::ranges::iterator_t<Range> &itr) {
assert(!this->has_value());
this->_offset = itr - std::ranges::begin(range);
}
};
template<typename T, int Disc>
struct absent { };
template<bool PRESENT, class T, int Disc = 0>
using maybe_present_t = std::conditional_t<PRESENT, T, absent<T, Disc>>;
} // namespace internal
namespace views::adaptor {
template<class Adaptor, class... Args>
concept adaptor_invocable = requires { std::declval<Adaptor>()(std::declval<Args>()...); };
template<class Adaptor, class... Args>
concept adaptor_partial_app_viable =
(Adaptor::arity > 1) && (sizeof...(Args) == Adaptor::arity - 1) &&
(std::constructible_from<std::remove_cvref_t<Args>, Args> && ...);
template<class Adaptor, class... Args> struct partial;
template<class, class> struct pipe;
template<class Derived> struct range_adaptor_closure {};
template<class T, class U>
requires(!std::same_as<T, range_adaptor_closure<U>>)
void is_range_adaptor_closure_fn(const T &, const range_adaptor_closure<U> &);
template<class T>
concept is_range_adaptor_closure = requires(T t) { adaptor::is_range_adaptor_closure_fn(t, t); };
template<class Self, class Range>
requires is_range_adaptor_closure<Self> && adaptor_invocable<Self, Range>
constexpr auto operator|(Range&& range, Self&& self) {
return std::forward<Self>(self)(std::forward<Range>(range));
}
template<class Lhs, class Rhs>
requires is_range_adaptor_closure<Lhs> && is_range_adaptor_closure<Rhs>
constexpr auto operator|(Lhs&& lhs, Rhs&& rhs) {
return pipe<std::remove_cvref_t<Lhs>, std::remove_cvref_t<Rhs>>{ std::forward<Lhs>(lhs), std::forward<Rhs>(rhs)};
}
template<class Derived> struct range_adaptor {
template<class... Args>
requires adaptor_partial_app_viable<Derived, Args...>
inline constexpr auto operator()(Args&& ..._args) const noexcept(NO_EXCEPT) {
return partial<Derived, std::remove_cvref_t<Args>...>{
std::forward<Args>(_args)...
};
}
};
template<class Adaptor>
concept closure_has_simple_call_op = Adaptor::has_simple_call_op;
template<class Adaptor, class... Args>
concept adaptor_has_simple_extra_args =
Adaptor::has_simple_extra_args ||
Adaptor::template has_simple_extra_args<Args...>;
template<class Adaptor, class... Args>
struct partial : range_adaptor_closure<partial<Adaptor, Args...>> {
std::tuple<Args...> args;
constexpr partial(Args... _args) noexcept(NO_EXCEPT) : args(std::move(_args)...) {}
template<class Range>
requires adaptor_invocable<Adaptor, Range, const Args &...>
inline constexpr auto operator()(Range&& range) const & noexcept(NO_EXCEPT) {
const auto forwarder = [&range](const auto &..._args) constexpr noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), _args...);
};
return std::apply(forwarder, this->args);
}
template<class Range>
requires adaptor_invocable<Adaptor, Range, Args...>
inline constexpr auto operator()(Range&& range) && noexcept(NO_EXCEPT) {
const auto forwarder = [&range](auto &..._args) constexpr noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), std::move(_args)...);
};
return std::apply(forwarder, this->args);
}
template<class Range>
inline constexpr auto operator()(Range&& range) const && = delete;
};
template<class Adaptor, class Arg>
struct partial<Adaptor, Arg> : range_adaptor_closure<partial<Adaptor, Arg>> {
Arg arg;
constexpr partial(Arg _arg) noexcept(NO_EXCEPT) : arg(std::move(_arg)) {}
template<class Range>
requires adaptor_invocable<Adaptor, Range, const Arg &>
inline constexpr auto operator()(Range&& range) const & noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), this->arg);
}
template<class Range>
requires adaptor_invocable<Adaptor, Range, Arg>
inline constexpr auto operator()(Range&& range) && noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), std::move(this->arg));
}
template<class Range>
inline constexpr auto operator()(Range&& range) const && = delete;
};
template<class Adaptor, class... Args>
requires adaptor_has_simple_extra_args<Adaptor, Args...> && (std::is_trivially_copyable_v<Args> && ...)
struct partial<Adaptor, Args...> : range_adaptor_closure<partial<Adaptor, Args...>> {
std::tuple<Args...> args;
constexpr partial(Args... _args) noexcept(NO_EXCEPT) : args(std::move(_args)...) {}
template<class Range>
requires adaptor_invocable<Adaptor, Range, const Args &...>
inline constexpr auto operator()(Range&& range) const noexcept(NO_EXCEPT) {
const auto forwarder = [&range](const auto &..._args) constexpr noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), _args...);
};
return std::apply(forwarder, this->args);
}
static constexpr bool has_simple_call_op = true;
};
template<class Adaptor, class Arg>
requires adaptor_has_simple_extra_args<Adaptor, Arg> &&
std::is_trivially_copyable_v<Arg>
struct partial<Adaptor, Arg> : range_adaptor_closure<partial<Adaptor, Arg>> {
Arg arg;
constexpr partial(Arg _arg) noexcept(NO_EXCEPT) : arg(std::move(_arg)) {}
template<class Range>
requires adaptor_invocable<Adaptor, Range, const Arg &>
inline constexpr auto operator()(Range&& range) const noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), this->arg);
}
static constexpr bool has_simple_call_op = true;
};
template<class Lhs, class Rhs, class Range>
concept pipe_invocable = requires {
std::declval<Rhs>()(std::declval<Lhs>()(std::declval<Range>()));
};
template<class Lhs, class Rhs> struct pipe : range_adaptor_closure<pipe<Lhs, Rhs>> {
[[no_unique_address]] Lhs lhs;
[[no_unique_address]] Rhs rhs;
constexpr pipe(Lhs _lhs, Rhs _rhs) noexcept(NO_EXCEPT) : lhs(std::move(_lhs)), rhs(std::move(_rhs)) {}
template<class Range>
requires pipe_invocable<const Lhs &, const Rhs &, Range>
inline constexpr auto operator()(Range&& range) const & noexcept(NO_EXCEPT) {
return rhs(lhs(std::forward<Range>(range)));
}
template<class Range>
requires pipe_invocable<Lhs, Rhs, Range>
inline constexpr auto operator()(Range&& range) && noexcept(NO_EXCEPT) {
return std::move(rhs)(std::move(lhs)(std::forward<Range>(range)));
}
template<class Range>
inline constexpr auto operator()(Range&& range) const && = delete;
};
template<class Lhs, class Rhs>
requires closure_has_simple_call_op<Lhs> && closure_has_simple_call_op<Rhs>
struct pipe<Lhs, Rhs> : range_adaptor_closure<pipe<Lhs, Rhs>> {
[[no_unique_address]] Lhs lhs;
[[no_unique_address]] Rhs rhs;
constexpr pipe(Lhs _lhs, Rhs _rhs) noexcept(NO_EXCEPT) : lhs(std::move(_lhs)), rhs(std::move(_rhs)) {}
template<class Range>
requires pipe_invocable<const Lhs &, const Rhs &, Range>
inline constexpr auto operator()(Range&& range) const noexcept(NO_EXCEPT) {
return rhs(lhs(std::forward<Range>(range)));
}
static constexpr bool has_simple_call_op = true;
};
} // namespace views::adaptor
} // namespace uni
#line 28 "iterable/operation.hpp"
#line 2 "iterable/z_array.hpp"
#line 6 "iterable/z_array.hpp"
#line 9 "iterable/z_array.hpp"
#line 2 "adaptor/valarray.hpp"
#line 11 "adaptor/valarray.hpp"
#line 14 "adaptor/valarray.hpp"
#line 16 "adaptor/valarray.hpp"
namespace uni {
template<class T> struct valarray : internal::advanced_container<std::valarray<T>> {
private:
using base = internal::advanced_container<std::valarray<T>>;
public:
using size_type = internal::size_t;
using iterator = T*;
using const_iterator = const T*;
protected:
inline bool _validate_index_in_right_open([[maybe_unused]] const size_type p) const noexcept(NO_EXCEPT) {
return 0 <= p and p < this->size();
}
inline bool _validate_index_in_closed([[maybe_unused]] const size_type p) const noexcept(NO_EXCEPT) {
return 0 <= p and p <= this->size();
}
inline bool _validate_rigth_open_interval([[maybe_unused]] const size_type l, [[maybe_unused]] const size_type r) const noexcept(NO_EXCEPT) {
return 0 <= l and l <= r and r <= this->size();
}
inline size_type _positivize_index(const size_type p) const noexcept(NO_EXCEPT) {
return p < 0 ? this->size() + p : p;
}
public:
valarray() noexcept(NO_EXCEPT) {}
explicit valarray(const std::size_t length, const T& val = T{}) noexcept(NO_EXCEPT) : base(val, length) {}
template<std::input_iterator I, std::sentinel_for<I> S>
valarray(I first, S last) noexcept(NO_EXCEPT) : base(std::ranges::distance(first, last)) { std::ranges::copy(first, last, std::ranges::begin(*this)); }
template<class U> valarray(const U* pointer, const size_t n) noexcept(NO_EXCEPT) : base(pointer, n) {};
valarray(const std::slice_array<T>& arr) noexcept(NO_EXCEPT) : base(arr) {};
valarray(const std::gslice_array<T>& arr) noexcept(NO_EXCEPT) : base(arr) {};
valarray(const std::mask_array<T>& arr) noexcept(NO_EXCEPT) : base(arr) {};
valarray(const std::indirect_array<T>& arr) noexcept(NO_EXCEPT) : base(arr) {};
valarray(const std::initializer_list<T>& init) noexcept(NO_EXCEPT) : base(init) {}
valarray(const internal::advanced_container<std::valarray<T>>& arr) noexcept(NO_EXCEPT) : base(arr) {}
#ifdef __GNUC__
template<class Dom> valarray(const std::_Expr<Dom,T>& expr) noexcept(NO_EXCEPT) : base(expr) {}
#endif
inline auto size() const noexcept(NO_EXCEPT) { return static_cast<size_type>(this->base::size()); }
inline void reserve(const size_type) noexcept(NO_EXCEPT) { /* do nothing */ }
template<std::input_iterator I, std::sentinel_for<I> S>
inline void assign(I first, S last) noexcept(NO_EXCEPT) {
this->resize(std::ranges::distance(first, last));
std::ranges::copy(first, last, std::ranges::begin(*this));
}
inline void assign(const std::size_t length, const T& val = T{}) noexcept(NO_EXCEPT) {
this->base::resize(length, val);
}
inline void resize(const std::size_t length, const T& val = T{}) noexcept(NO_EXCEPT) {
base temp = *this;
this->assign(length, val);
std::move(std::begin(temp), std::min(std::end(temp), std::next(std::begin(temp), length)), std::begin(*this));
}
inline const T& operator[](size_type pos) const noexcept(NO_EXCEPT) {
pos = this->_positivize_index(pos), assert(this->_validate_index_in_right_open(pos));
return this->base::operator[](pos);
}
inline T& operator[](size_type pos) noexcept(NO_EXCEPT) {
pos = this->_positivize_index(pos), assert(this->_validate_index_in_right_open(pos));
return this->base::operator[](pos);
}
inline const T& back() const noexcept(NO_EXCEPT) { return *std::prev(this->end()); }
inline T& back() noexcept(NO_EXCEPT) { return *std::prev(this->end()); }
inline const T& front() const noexcept(NO_EXCEPT) { return *this->begin(); }
inline T& front() noexcept(NO_EXCEPT) { return *this->begin(); }
inline auto rbegin() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(std::ranges::end(*this)); }
inline auto rend() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(std::ranges::begin(*this)); }
inline auto rbegin() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(std::ranges::end(*this)); }
inline auto rend() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(std::ranges::begin(*this)); }
};
} // namespace uni
#line 11 "iterable/z_array.hpp"
namespace uni {
// Thanks to: atcoder::z_algorithm
template<class SizeType = internal::size_t, class Container = valarray<SizeType>>
struct z_array : Container {
using size_type = SizeType;
template<std::input_iterator I, std::sentinel_for<I> S>
z_array(I first, S last) : Container(std::ranges::distance(first, last), {}) {
const size_type n = static_cast<size_type>(std::ranges::distance(first, last));
if(n == 0) return;
for(size_type i = 1, j = 0; i < n; ++i) {
size_type& k = this->operator[](i);
k = (j + this->operator[](j) <= i) ? 0 : std::ranges::min(j + this->operator[](j) - i, this->operator[](i - j));
while(i + k < n and first[k] == first[i + k]) ++k;
if(j + this->operator[](j) < i + this->operator[](i)) j = i;
}
*this->begin() = n;
}
template<std::ranges::input_range R>
explicit z_array(R&& range) : z_array(ALL(range)) {}
};
} // namespace uni
#line 31 "iterable/operation.hpp"
#line 2 "view/concat.hpp"
#line 11 "view/concat.hpp"
#line 18 "view/concat.hpp"
namespace uni {
namespace internal {
namespace view_impl {
template<std::ranges::input_range V0, std::ranges::input_range V1>
requires std::ranges::view<V0> && std::ranges::view<V1>
struct concat_view : std::ranges::view_interface<concat_view<V0, V1>> {
private:
V0 _b0;
V1 _b1;
template<bool Const> using B0 = internal::maybe_const_t<Const, V0>;
template<bool Const> using B1 = internal::maybe_const_t<Const, V1>;
template<bool Const> struct iterator_tag {};
template<bool Const>
requires std::ranges::forward_range<B0<Const>> && std::ranges::forward_range<B1<Const>>
struct iterator_tag<Const> {
public:
using iterator_category = uni::internal::most_primitive_iterator_tag<
typename std::iterator_traits<std::ranges::iterator_t<B0<Const>>>::iterator_category,
typename std::iterator_traits<std::ranges::iterator_t<B1<Const>>>::iterator_category
>;
};
public:
template<bool> class iterator;
constexpr explicit concat_view(V0 v0, V1 v1) noexcept(NO_EXCEPT)
: _b0(std::move(v0)), _b1(std::move(v1))
{}
inline constexpr std::pair<V0, V1> base() const & noexcept(NO_EXCEPT)
requires std::copy_constructible<V0> && std::copy_constructible<V0>
{
return { this->_b0, this->_b1 };
}
inline constexpr std::pair<V0,V1> base() && noexcept(NO_EXCEPT) {
return { std::move(this->_b0), std::move(this->_b1) };
}
inline constexpr auto begin() noexcept(NO_EXCEPT)
requires (!internal::simple_view<V0> && !internal::simple_view<V1>)
{
return iterator<false>(this, std::ranges::begin(this->_b0), std::ranges::begin(this->_b1), 0);
}
inline constexpr auto begin() const noexcept(NO_EXCEPT)
requires std::ranges::range<const V0> && std::ranges::range<const V1>
{
return iterator<true>(this, std::ranges::begin(this->_b0), std::ranges::begin(this->_b1), 0);
}
inline constexpr auto end() noexcept(NO_EXCEPT)
requires (!internal::simple_view<V0> && !internal::simple_view<V1>)
{
if constexpr(std::ranges::common_range<V0> && std::ranges::common_range<V1>) {
return iterator<false>(this, std::ranges::end(this->_b0), std::ranges::end(this->_b1), 1);
}
else {
return std::default_sentinel;
}
}
inline constexpr auto end() const noexcept(NO_EXCEPT)
requires std::ranges::range<const V0> && std::ranges::range<const V1>
{
if constexpr(std::ranges::common_range<const V0> && std::ranges::common_range<const V1>) {
return iterator<true>(this, std::ranges::end(this->_b0), std::ranges::end(this->_b1), 1);
}
else {
return std::default_sentinel;
}
}
inline constexpr auto size() noexcept(NO_EXCEPT)
requires std::ranges::sized_range<V0> && std::ranges::sized_range<V1>
{
return static_cast<std::size_t>(std::ranges::distance(this->_b0) + std::ranges::distance(this->_b1));
}
inline constexpr auto size() const noexcept(NO_EXCEPT)
requires std::ranges::sized_range<const V0> && std::ranges::sized_range<const V1>
{
return static_cast<std::size_t>(std::ranges::distance(this->_b0) + std::ranges::distance(this->_b1));
}
};
template<std::ranges::input_range V0, std::ranges::input_range V1>
requires std::ranges::view<V0> && std::ranges::view<V1>
template<bool Const>
struct concat_view<V0, V1>::iterator : iterator_tag<Const> {
private:
using Parent = internal::maybe_const_t<Const, concat_view>;
using B0 = concat_view::B0<Const>;
using B1 = concat_view::B1<Const>;
std::ranges::iterator_t<B0> _c0 = std::ranges::iterator_t<B0>();
std::ranges::iterator_t<B0> _b0 = std::ranges::iterator_t<B0>();
std::ranges::sentinel_t<B0> _e0 = std::ranges::sentinel_t<B0>();
std::ranges::iterator_t<B1> _c1 = std::ranges::iterator_t<B1>();
std::ranges::iterator_t<B1> _b1 = std::ranges::iterator_t<B1>();
std::ranges::sentinel_t<B1> _e1 = std::ranges::sentinel_t<B1>();
int _block = 0;
constexpr iterator(Parent *const parent, const std::ranges::iterator_t<B0> c0, const std::ranges::iterator_t<B1> c1, const int block) noexcept(NO_EXCEPT)
: _c0(std::move(c0)), _b0(std::ranges::begin(parent->_b0)), _e0(std::ranges::end(parent->_b0)),
_c1(std::move(c1)), _b1(std::ranges::begin(parent->_b1)), _e1(std::ranges::end(parent->_b1)),
_block(block || std::ranges::empty(parent->_b0))
{}
friend concat_view;
public:
using difference_type = std::common_type_t<std::ranges::range_difference_t<B0>, std::ranges::range_difference_t<B1>>;
using value_type = std::common_type_t<std::ranges::range_value_t<B0>, std::ranges::range_value_t<B1>>;
using reference_type = std::common_reference_t<std::ranges::range_reference_t<B0>, std::ranges::range_reference_t<B1>>;
using iterator_concept = most_primitive_iterator_concept<Const, V0, V1>;
iterator() noexcept(NO_EXCEPT)
requires std::default_initializable<std::ranges::iterator_t<B0>> &&
std::default_initializable<std::ranges::iterator_t<B0>>
= default;
constexpr iterator(iterator<!Const> itr) noexcept(NO_EXCEPT)
requires
Const &&
std::convertible_to<std::ranges::iterator_t<V0>, std::ranges::iterator_t<B0>> &&
std::convertible_to<std::ranges::sentinel_t<V0>, std::ranges::sentinel_t<B0>> &&
std::convertible_to<std::ranges::iterator_t<V1>, std::ranges::iterator_t<B1>> &&
std::convertible_to<std::ranges::sentinel_t<V1>, std::ranges::sentinel_t<B1>>
: _c0(std::move(itr._c0)), _b0(std::move(itr._b0)), _e0(std::move(itr._e0)),
_c1(std::move(itr._c0)), _b1(std::move(itr._b0)), _e1(std::move(itr._e1)),
_block(itr._block)
{}
inline constexpr std::variant<std::ranges::iterator_t<B0>, std::ranges::iterator_t<B1>>
base() && noexcept(NO_EXCEPT) {
if(this->_block == 0) return std::move(this->_c0);
else return std::move(this->_C1);
}
inline constexpr
std::variant<
std::reference_wrapper<const std::ranges::iterator_t<B0>>,
std::reference_wrapper<const std::ranges::iterator_t<B1>>
>
base() const & noexcept {
if(this->_block == 0) return std::move(this->_c0);
else return std::move(this->_c1);
}
inline constexpr reference_type operator*() const noexcept(NO_EXCEPT)
{
if(this->_block == 0) return *this->_c0;
else return *this->_c1;
}
inline constexpr iterator& operator++() noexcept(NO_EXCEPT)
{
assert(this->_c0 != this->_e0 or this->_c1 != this->_e1);
if(this->_block == 0) {
if(++this->_c0 == this->_e0) {
this->_block = 1;
assert(this->_c1 == this->_b1);
}
}
else {
++this->_c1;
}
return *this;
}
inline constexpr void operator++(int) noexcept(NO_EXCEPT) { ++*this; }
inline constexpr iterator operator++(int) noexcept(NO_EXCEPT)
requires std::ranges::forward_range<B0> && std::ranges::forward_range<B1>
{
const auto res = *this; ++*this; return res;
}
inline constexpr iterator& operator--() noexcept(NO_EXCEPT)
requires
std::ranges::bidirectional_range<B0> && std::ranges::bidirectional_range<B1> &&
std::bidirectional_iterator<std::ranges::sentinel_t<B0>>
{
if(this->_block == 1) {
if(this->_c1 == this->_b1) {
this->_block = 0;
this->_c0 = std::ranges::prev(this->_e0);
}
else {
--this->_c1;
}
}
else {
--this->_c0;
}
return *this;
}
inline constexpr iterator operator--(int) noexcept(NO_EXCEPT)
requires std::ranges::bidirectional_range<B0> && std::ranges::bidirectional_range<B1>
{
const auto res = *this; --*this; return res;
}
inline constexpr iterator& operator+=(const difference_type diff) noexcept(NO_EXCEPT)
requires
std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
if(diff > 0) {
if(this->_block == 0) {
const auto missing = std::ranges::advance(this->_c0, diff, this->_e0);
if(this->_c0 == this->_e0) {
this->_block = 1;
assert(this->_c1 == this->_b1);
std::ranges::advance(this->_c1, missing, this->_e1);
}
}
else {
std::ranges::advance(this->_c1, diff, this->_e1);
}
}
if(diff < 0) {
if(this->_block == 1) {
const auto missing = std::ranges::advance(this->_c1, diff, this->_b1);
if(missing < 0) {
this->_block = 0;
assert(this->_c0 == this->_e0);
std::ranges::advance(this->_c0, missing, this->_b0);
}
}
else {
std::ranges::advance(this->_c0, diff, this->_b0);
}
}
return *this;
}
inline constexpr iterator& operator-=(const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
return *this += -diff;
}
inline constexpr decltype(auto) operator[](const difference_type diff) const noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
return *(*this + diff);
}
friend inline constexpr bool operator==(const iterator& lhs, std::default_sentinel_t) noexcept(NO_EXCEPT)
{
if(lhs._block == 0) return false;
if(lhs._block == 1) return lhs._c1 == lhs._e1;
assert(false);
}
friend inline constexpr bool operator==(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires
std::equality_comparable<std::ranges::iterator_t<B0>> &&
std::equality_comparable<std::ranges::iterator_t<B1>>
{
if(lhs._block != rhs._block) return false;
return lhs._block == 0 ? lhs._c0 == rhs._c0 : lhs._c1 == rhs._c1;
}
friend inline constexpr auto operator<=>(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
if(lhs._block != rhs._block) return lhs._block <=> rhs._block;
return lhs._block == 0 ? lhs._c0 <=> rhs._c0 : lhs._c1 <=> rhs._c1;
}
friend inline constexpr iterator operator+(const iterator& itr, const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
auto res = itr; res += diff; return res;
}
friend inline constexpr iterator operator+(const difference_type diff, const iterator& itr) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
return itr + diff;
}
friend inline constexpr iterator operator-(const iterator& itr, const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
auto res = itr; res -= diff; return res;
}
friend inline constexpr const difference_type operator-(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires
std::sized_sentinel_for<std::ranges::iterator_t<B0>, std::ranges::iterator_t<B0>> &&
std::sized_sentinel_for<std::ranges::iterator_t<B1>, std::ranges::iterator_t<B1>>
{
if(lhs._block == rhs._block) {
return lhs._block == 0 ? std::ranges::distance(rhs._c0, lhs._c0) : std::ranges::distance(rhs._c1, lhs._c1);
}
if(lhs._block > rhs._block) return std::ranges::distance(rhs._c0, rhs._e0) + std::ranges::distance(lhs._b1, lhs._c1);
if(lhs._block < rhs._block) return -(rhs - lhs);
assert(false);
}
friend inline constexpr const difference_type operator-(std::default_sentinel_t, const iterator& rhs) noexcept(NO_EXCEPT)
requires
std::sized_sentinel_for<std::ranges::sentinel_t<B0>, std::ranges::iterator_t<B0>> &&
std::sized_sentinel_for<std::ranges::sentinel_t<B1>, std::ranges::iterator_t<B1>>
{
if(rhs._block == 0) return std::ranges::distance(rhs._c0, rhs._e0) + std::ranges::distance(rhs._b1, rhs._e1);
if(rhs._block == 1) return std::ranges::distance(rhs._c1, rhs._e1);
assert(false);
}
friend inline constexpr const difference_type operator-(const iterator& lhs, std::default_sentinel_t rhs) noexcept(NO_EXCEPT)
requires
std::sized_sentinel_for<std::ranges::sentinel_t<B0>, std::ranges::iterator_t<B0>> &&
std::sized_sentinel_for<std::ranges::sentinel_t<B1>, std::ranges::iterator_t<B1>>
{
return -(rhs - lhs);
}
friend inline constexpr
std::common_reference_t<
std::ranges::range_rvalue_reference_t<B0>,
std::ranges::range_rvalue_reference_t<B1>
>
iter_move(const iterator& itr) noexcept(NO_EXCEPT)
{
if(itr._block == 0) return std::ranges::iter_move(itr._c0);
if(itr._block == 1) return std::ranges::iter_move(itr._c1);
assert(false);
}
friend inline constexpr void iter_swap(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires
std::indirectly_swappable<std::ranges::iterator_t<B0>> &&
std::indirectly_swappable<std::ranges::iterator_t<B1>> &&
std::indirectly_swappable<std::ranges::iterator_t<B0>, std::ranges::iterator_t<B1>>
{
if(lhs._block == 0 && rhs._block == 0) std::ranges::iter_swap(lhs._c0, rhs._c0);
if(lhs._block == 0 && rhs._block == 1) std::ranges::iter_swap(lhs._c0, rhs._c1);
if(lhs._block == 1 && rhs._block == 0) std::ranges::iter_swap(lhs._c1, rhs._c0);
if(lhs._block == 1 && rhs._block == 1) std::ranges::iter_swap(lhs._c1, rhs._c1);
assert(false);
}
};
} // namespace view_impl
} // namespace internal
template<class...> struct concat_view;
template<class T>
struct concat_view<T> : std::views::all_t<T> {
using std::views::all_t<T>::all_t;
};
template<class T0, class T1>
struct concat_view<T0, T1> : internal::view_impl::concat_view<std::views::all_t<T0>, std::views::all_t<T1>> {
explicit concat_view(T0&& v0, T1&& v1) noexcept(NO_EXCEPT)
: internal::view_impl::concat_view<std::views::all_t<T0>, std::views::all_t<T1>>(std::forward<T0>(v0), std::forward<T1>(v1))
{}
};
template<class T0, class T1, class... Ts>
struct concat_view<T0, T1, Ts...> : concat_view<concat_view<T0, T1>, Ts...> {
explicit concat_view(T0&& v0, T1&& v1, Ts&&... vs) noexcept(NO_EXCEPT)
: concat_view<concat_view<T0, T1>, Ts...>(
concat_view<T0, T1>(std::forward<T0>(v0), std::forward<T1>(v1)), std::forward<Ts>(vs)...
)
{}
};
namespace views {
namespace internal {
template<class... Ts>
concept can_concat_view = requires { concat_view<Ts...>(std::declval<Ts>()...); };
} // namespace internal
struct Concat {
template<class... Ts>
requires (sizeof...(Ts) == 0 || internal::can_concat_view<Ts...>)
inline constexpr auto operator() [[nodiscard]] (Ts&&... vs) const {
if constexpr(sizeof...(Ts) == 0) return std::views::empty<std::nullptr_t>;
else return concat_view<std::views::all_t<Ts>...>(std::forward<Ts>(vs)...);
}
};
inline constexpr Concat concat;
} // namespace views
} // namespace uni.
namespace std::ranges {
template<class... Views>
inline constexpr bool enable_borrowed_range<uni::concat_view<Views...>> = (enable_borrowed_range<Views> && ...);
}
#line 2 "global/constants.hpp"
#line 7 "global/constants.hpp"
#include <cmath>
#line 11 "global/constants.hpp"
#line 14 "global/constants.hpp"
#line 2 "numeric/limits.hpp"
#line 6 "numeric/limits.hpp"
#line 9 "numeric/limits.hpp"
#line 11 "numeric/limits.hpp"
namespace uni {
template<class T>
struct numeric_limits : std::numeric_limits<T> {
static constexpr long double FLOAT_EPSILON = 1E-14;
static constexpr T arithmetic_infinity() noexcept(NO_EXCEPT) {
return std::numeric_limits<T>::max() / 2 - 1;
}
static constexpr T arithmetic_negative_infinity() noexcept(NO_EXCEPT) {
return std::numeric_limits<T>::lowest() / 2 + 1;
}
static constexpr T arithmetic_epsilon() noexcept(NO_EXCEPT) {
if constexpr(std::is_floating_point_v<T>) {
return numeric_limits::FLOAT_EPSILON;
}
else {
return 0;
}
}
};
constexpr i32 INF32 = numeric_limits<i32>::arithmetic_infinity();
constexpr i64 INF64 = numeric_limits<i64>::arithmetic_infinity();
template<class T>
constexpr T INF = numeric_limits<T>::arithmetic_infinity();
template<class T>
constexpr T EPSILON = numeric_limits<T>::arithmetic_epsilon();
} // namespace uni
#line 16 "global/constants.hpp"
namespace uni {
namespace internal {
template<class T>
consteval auto get_pi() {
if constexpr(std::integral<T>) {
return static_cast<T>(3);
}
else if constexpr(std::same_as<T, float>) {
return M_PIf;
}
else if constexpr(std::same_as<T, double>) {
return M_PI;
}
else if constexpr(std::same_as<T, ld>) {
return M_PIl;
}
else {
static_assert(EXCEPTION_ON_TYPE<T>);
}
}
} // namespace internal
template<class T = ld>
constexpr auto PI = internal::get_pi<T>();
enum class comparison : std::uint8_t {
equal_to,
not_equal_to,
equals = equal_to,
eq = equal_to,
under,
over,
or_under,
or_over,
less = under,
more = over,
less_than = under,
more_than = over,
not_less_than = or_over,
not_more_than = or_under,
leq = or_under,
geq = or_over
};
enum class interval_notation : std::uint8_t {
right_open,
left_open,
open,
closed,
};
enum class replacement_policy : std::uint8_t {
insert_sync,
overwrite_sync,
overwrite_async
};
enum class rotation : std::int8_t {
clockwise,
counter_clockwise,
anti_clockwise = counter_clockwise,
};
enum class positional_relation : std::int8_t {
clockwise,
counter_clockwise,
anti_clockwise = counter_clockwise,
backward,
forward,
in,
on,
out,
included = in,
inscribed,
intersecting,
circumscribed,
distant,
};
enum class alignment : std::int8_t {
left,
center,
right
};
} // namespace uni
#line 35 "iterable/operation.hpp"
namespace uni {
template<std::ranges::input_range R0, std::ranges::input_range R1>
requires std::constructible_from<
R0, std::common_type_t<std::ranges::range_size_t<R0>,std::ranges::range_size_t<R1>>
>
R0 concat(R0&& r0, R1&& r1) noexcept(NO_EXCEPT) {
R0 res(std::ranges::size(r0) + std::ranges::size(r1));
std::ranges::copy(r0, std::ranges::begin(res));
std::ranges::copy(r1, std::ranges::next(std::ranges::begin(res), std::ranges::size(r0)));
return res;
}
template<std::ranges::input_range R, std::ranges::input_range... Rs>
R concat(R&& range, Rs&&... tails) noexcept(NO_EXCEPT) {
return uni::concat(range, uni::concat(tails...));
}
template<std::ranges::input_range R>
requires
requires(R r) {
r.erase(std::ranges::unique(ALL(r)), std::ranges::end(r));
}
inline auto unique(R range) noexcept(NO_EXCEPT) {
std::ranges::sort(range);
range.erase(std::ranges::unique(ALL(range)), std::ranges::end(range));
return range;
}
template<
std::input_iterator I,
std::sentinel_for<I> S,
class T = std::iter_value_t<I>
>
T mex(I first, S last, const T& base = T()) noexcept(NO_EXCEPT) {
std::vector<T> val(first, last);
std::ranges::sort(val);
{
auto range = std::ranges::unique(val);
val.erase(ALL(range));
}
val.erase(val.begin(), std::ranges::lower_bound(val, base));
T i = 0;
while(i < std::ranges::ssize(val) && val[i] == i + base) ++i;
return T{i} + base;
}
template<std::ranges::input_range R>
auto mex(R&& range, const std::ranges::range_value_t<R>& base = std::ranges::range_value_t<R>()) noexcept(NO_EXCEPT) {
return mex(ALL(range), base);
}
template<class T>
auto mex(const std::initializer_list<T> v, const T& base = T()) noexcept(NO_EXCEPT) {
return mex(ALL(v), base);
}
template<std::input_iterator I, std::sentinel_for<I> S, class T>
inline constexpr auto gcd(I first, S last) noexcept(NO_EXCEPT) {
T res = T{0};
for(auto itr=first; itr!=last; ++itr) res = std::gcd(res, *itr);
return res;
}
template<std::input_iterator I, std::sentinel_for<I> S, class T>
inline constexpr auto lcm(I first, S last) noexcept(NO_EXCEPT) {
T res = T{1};
for(auto itr=first; itr!=last; ++itr) res = std::lcm(res, *itr);
return res;
}
template<std::ranges::input_range R, class T = std::ranges::range_value_t<R>>
auto mex(R&& range, const T& base) noexcept(NO_EXCEPT) {
return mex(ALL(range), base);
}
template<std::ranges::input_range R>
auto gcd(R&& range) noexcept(NO_EXCEPT) {
return gcd(ALL(range));
}
template<std::ranges::input_range R>
auto lcm(R&& range) noexcept(NO_EXCEPT) {
return lcm(ALL(range));
}
template<class R, std::input_iterator I, std::sentinel_for<I> S, class D>
requires
requires (R r, I itr) {
r.emplace_back(itr, itr);
}
auto split(I first, S last, const D& delim = ' ') noexcept(NO_EXCEPT) {
R res;
for(auto itr=first, fnd=first; ; itr=std::ranges::next(fnd)) {
fnd = std::find(itr, last, delim);
res.emplace_back(itr, fnd);
if(fnd == last) break;
}
return res;
}
template<class R, std::ranges::input_range V, class D>
requires (!std::ranges::input_range<D>)
auto split(V&& v, D&& d) noexcept(NO_EXCEPT) { return split<R>(ALL(v), d); }
template<class R, std::ranges::input_range V, std::ranges::input_range Ds>
auto split(V&& v, Ds&& ds) noexcept(NO_EXCEPT) {
R res = { v };
ITR(d, ds) {
R tmp;
ITR(p, res) tmp = concat(tmp, split<R>(p, d));
res = std::move(tmp);
}
return res;
}
template<class R, std::ranges::input_range V, class T>
auto split(V&& v, const std::initializer_list<T> ds) noexcept(NO_EXCEPT){
return split<R,V>(v, std::vector<T>(ALL(ds)));
}
template<std::ranges::sized_range Source, std::ranges::sized_range Qeury>
auto find(Source&& source, Qeury&& query) noexcept(NO_EXCEPT) {
z_array z_arr(views::concat(query, source));
const auto query_size = std::ranges::ssize(query);
vector<std::ranges::iterator_t<Source>> res;
{
auto itr = std::ranges::begin(source);
REP(i, query_size, std::ranges::size(z_arr)) {
if(z_arr[i] >= query_size) res.push_back(itr);
++itr;
}
}
return res;
}
template<
replacement_policy POLICY,
std::ranges::sized_range R,
std::ranges::sized_range From,
std::ranges::sized_range To
>
auto replaced(R&& source, From&& from, To&& to) noexcept(NO_EXCEPT) {
std::remove_cvref_t<R> res;
if constexpr(POLICY == replacement_policy::insert_sync) {
const auto found = find(source, from);
auto itr = std::ranges::begin(source);
ITRR(fn, found) {
std::ranges::copy(itr, fn, std::back_inserter(res));
std::ranges::copy(ALL(to), std::back_inserter(res));
itr = std::ranges::next(fn, std::ranges::size(from));
}
std::ranges::copy(itr, std::ranges::end(source), std::back_inserter(res));
}
else {
res = source;
res.resize(std::ranges::size(source) + std::ranges::size(to));
const auto found = find(res, from);
auto prev = std::ranges::begin(res);
ITRR(fn, found) {
if constexpr(POLICY == replacement_policy::overwrite_sync) {
if(prev <= fn) prev = std::ranges::copy(to, fn);
}
else {
std::ranges::copy(to, fn);
}
}
res.resize(std::ranges::size(source));
}
return res;
}
template<
std::ranges::sized_range R,
std::ranges::sized_range From,
std::ranges::sized_range To
>
inline auto replaced(R&& source, From&& from, To&& to) noexcept(NO_EXCEPT) {
return replaced<replacement_policy::insert_sync, R, From, To>(std::forward<R>(source), std::forward<From>(from), std::forward<To>(to));
}
template<alignment ALIGNMENT, internal::resizable_range R, class T = std::ranges::range_value_t<R>>
auto align(R&& source, const internal::size_t size, const T& v = T()) noexcept(NO_EXCEPT) {
if(std::ssize(source) >= size) return source;
if(ALIGNMENT == alignment::left) {
R left, right;
left = source;
right.resize(size - std::size(left), v);
return R(ALL(uni::views::concat(left, right)));
}
if(ALIGNMENT == alignment::center) {
R left, center, right;
center = source;
left.resize((size - std::size(center)) / 2, v);
right.resize(size - std::size(center) - std::size(left), v);
return R(ALL(uni::views::concat(left, center, right)));
}
if(ALIGNMENT == alignment::right) {
R left, right;
right = source;
left.resize(size - std::size(right), v);
return R(ALL(uni::views::concat(left, right)));
}
assert(false);
}
template<internal::resizable_range R, class T = std::ranges::range_value_t<R>>
auto ljust(R&& source, const internal::size_t size, const T& v = T()) noexcept(NO_EXCEPT) {
return align<alignment::left>(source, size, v);
}
template<internal::resizable_range R, class T = std::ranges::range_value_t<R>>
auto cjust(R&& source, const internal::size_t size, const T& v = T()) noexcept(NO_EXCEPT) {
return align<alignment::center>(source, size, v);
}
template<internal::resizable_range R, class T = std::ranges::range_value_t<R>>
auto rjust(R&& source, const internal::size_t size, const T& v = T()) noexcept(NO_EXCEPT) {
return align<alignment::right>(source, size, v);
}
template<
class Res,
std::ranges::random_access_range Target,
std::ranges::forward_range Order
>
requires std::ranges::output_range<Res, std::ranges::range_value_t<Target>>
Res ordered_by(Target&& target, Order&& order) noexcept(NO_EXCEPT) {
const auto target_size = std::ranges::ssize(target);
const auto order_size = std::ranges::ssize(order);
Res res(order_size);
{
auto res_itr = std::ranges::begin(res);
auto order_itr = std::ranges::begin(order);
const auto order_end = std::ranges::end(std::forward<Order>(order));
for(; order_itr != order_end; ++res_itr, ++order_itr) {
if constexpr(std::signed_integral<std::ranges::range_value_t<Order>>) assert(0 <= *order_itr);
assert(*order_itr < target_size);
*res_itr = target[*order_itr];
}
}
return res;
}
template<
std::ranges::random_access_range Target,
std::ranges::forward_range Order
>
auto ordered_by(Target&& target, Order&& order) noexcept(NO_EXCEPT) {
return ordered_by<std::remove_cvref_t<Target>, Target, Order>(std::forward<Target>(target), std::forward<Order>(order));
}
template<std::ranges::input_range Target, std::ranges::input_range Source>
requires std::equality_comparable_with<std::ranges::range_value_t<Target>, std::ranges::range_value_t<Source>>
auto is_subsequence_of(Target&& target, Source&& source) noexcept(NO_EXCEPT) {
auto target_itr = std::ranges::begin(source);
auto source_itr = std::ranges::begin(source);
const auto target_end = std::ranges::end(source);
const auto source_end = std::ranges::end(source);
for(; source_itr != source_end; ++source_itr) {
if(*target_itr == *source_itr) ++target_itr;
}
return target_itr == target_end;
}
template<std::ranges::input_range Target, std::ranges::input_range Source>
requires std::equality_comparable_with<std::ranges::range_value_t<Target>, std::ranges::range_value_t<Source>>
auto is_continuous_subsequence_of(Target&& target, Source&& source) noexcept(NO_EXCEPT) {
auto found = find(source, target);
return found.size() > 0;
}
} // namespace uni
#line 31 "numeric/arithmetic.hpp"
namespace uni {
template<class T>
inline constexpr T div_floor(const T& x, const T& d) noexcept(NO_EXCEPT) {
if constexpr(std::is_integral_v<T>) {
return x / d - (x % d && ((x < 0) ^ (d < 0)));
}
else {
return std::floor(x / d);
}
}
template<class T>
inline constexpr T div_ceil(const T& x, const T& d) noexcept(NO_EXCEPT) {
if constexpr(std::is_integral_v<T>) {
return div_floor(x + d - 1, d);
}
else {
return std::ceil(x / d);
}
}
template<class T>
inline constexpr T div_round(const T& x, const T& d) noexcept(NO_EXCEPT) {
if constexpr(std::is_integral_v<T>) {
return div_round<ld>(x, d);
}
else {
return std::round(x / d);
}
}
template<class T>
inline constexpr std::make_signed_t<T> to_signed(const T& x) noexcept(NO_EXCEPT) {
return std::bit_cast<std::make_signed_t<T>>(x);
}
template<class T>
inline constexpr std::make_unsigned_t<T> to_unsigned(const T& x) noexcept(NO_EXCEPT) {
return std::bit_cast<std::make_unsigned_t<T>>(x);
}
namespace internal {
template<class T>
inline constexpr auto perm(const T& n, const T& r) noexcept(NO_EXCEPT) {
T res = 1;
REP(i, r) res *= n - i;
return res;
}
template<class T>
inline constexpr auto comb(const T& n, T r) noexcept(NO_EXCEPT) {
if(n < 2 * r) r = n - r;
T p = 1, q = 1;
REP(i, r) p *= n - i, q *= r - i;
return p / q;
}
} // namespace internal
template<class T0, std::common_with<T0> T1>
inline constexpr auto perm(const T0& n, const T1& r) noexcept(NO_EXCEPT) {
assert(n >= 0), assert(r >= 0);
using T = std::common_type_t<T0, T1>;
if(n < r) return static_cast<T>(0);
return internal::perm<T>(n, r);
}
template<class T0, std::common_with<T0> T1>
inline constexpr auto comb(const T0& n, const T1& r) noexcept(NO_EXCEPT) {
assert(n >= 0), assert(r >= 0);
using T = std::common_type_t<T0, T1>;
if(n < r) return static_cast<T>(0);
if(n == r) return static_cast<T>(1);
return internal::comb<T>(n, r);
}
template<class T, class U, std::invocable<T, T> F = std::multiplies<>>
constexpr T pow(T x, U n, F mul = F(), T one = static_cast<T>(1)) noexcept(NO_EXCEPT) {
if(n == 0) return one;
if(n == 1 || x == one) return x;
T res = one;
while(true) {
if(n & 1) res = mul(res, x);
x = mul(x, x);
if(n == 0) return res;
n >>= 1;
}
assert(false);
}
using atcoder::pow_mod;
using atcoder::inv_mod;
using atcoder::crt;
template<class T> inline constexpr T sign(const T& x) noexcept(NO_EXCEPT) {
if(x == 0) return 0;
return (x > 0) ? 1 : -1;
}
template<class T, T FROM_MIN, T FROM_MAX, T TO_MIN, T TO_MAX> inline constexpr T mapping(const T x) {
return (x - FROM_MIN) * (TO_MAX - TO_MIN) / (FROM_MAX - FROM_MIN) + TO_MIN;
}
template<class T> inline constexpr T mapping(const T x, const T from_min, const T from_max, const T to_min, const T to_max) {
return (x - from_min) * (to_max - to_min) / (from_max - from_min) + to_min;
}
template<class... Args>
inline constexpr std::common_type_t<Args...> min(const Args&... args) noexcept(NO_EXCEPT) {
return std::min({ static_cast<std::common_type_t<Args...>>(args)... });
}
template<class... Args>
inline constexpr std::common_type_t<Args...> max(const Args&... args) noexcept(NO_EXCEPT) {
return std::max({ static_cast<std::common_type_t<Args...>>(args)... });
}
template<class T>
inline constexpr T gcd(const std::initializer_list<T> args) noexcept(NO_EXCEPT) {
return gcd(ALL(args));
}
template<class... Args>
inline constexpr std::common_type_t<Args...> gcd(const Args&... args) noexcept(NO_EXCEPT) {
return gcd({ static_cast<std::common_type_t<Args...>>(args)... });
}
template<class T>
inline constexpr T lcm(const std::initializer_list<T> args) noexcept(NO_EXCEPT) {
return lcm(ALL(args));
}
template<class... Args>
inline constexpr std::common_type_t<Args...> lcm(const Args&... args) noexcept(NO_EXCEPT) {
return lcm({ static_cast<std::common_type_t<Args...>>(args)... });
}
template<std::integral T0, std::integral T1>
inline constexpr std::optional<std::common_type_t<T0, T1>> add_overflow(const T0& a, const T1& b) noexcept(NO_EXCEPT) {
std::common_type_t<T0, T1> res;
if(__builtin_add_overflow(a, b, &res)) return {};
return res;
}
template<std::integral T0, std::integral T1>
inline constexpr std::optional<std::common_type_t<T0, T1>> sub_overflow(const T0& a, const T1& b) noexcept(NO_EXCEPT) {
std::common_type_t<T0, T1> res;
if(__builtin_sub_overflow(a, b, &res)) return {};
return res;
}
template<std::integral T0, std::integral T1>
inline constexpr std::optional<std::common_type_t<T0, T1>> mul_overflow(const T0& a, const T1& b) noexcept(NO_EXCEPT) {
std::common_type_t<T0, T1> res;
if(__builtin_mul_overflow(a, b, &res)) return {};
return res;
}
template<std::integral T0, std::integral T1, std::integral Limit>
inline auto add_clamp(const T0 x, const T1 y, const Limit inf, const Limit sup) noexcept(NO_EXCEPT) {
using Common = std::common_type_t<T0, T1, Limit>;
const auto res = add_overflow<Common>(x, y);
if(!res) {
if(x < 0 && y < 0) return inf;
if(x > 0 && y > 0) return sup;
assert(false);
}
return std::clamp<Common>(*res, inf, sup);
}
template<std::integral T0, std::integral T1, std::integral Limit>
inline auto sub_clamp(const T0 x, const T1 y, const Limit inf, const Limit sup) noexcept(NO_EXCEPT) {
using Common = std::common_type_t<T0, T1, Limit>;
const auto res = sub_overflow<Common>(x, y);
if(!res) {
if(x < 0 && y > 0) return inf;
if(x > 0 && y < 0) return sup;
assert(false);
}
return std::clamp<Common>(*res, inf, sup);
}
template<std::integral T0, std::integral T1, std::integral Limit>
inline auto mul_clamp(const T0 x, const T1 y, const Limit inf, const Limit sup) noexcept(NO_EXCEPT) {
using Common = std::common_type_t<T0, T1, Limit>;
const auto res = mul_overflow<Common>(x, y);
if(!res) {
if((x > 0) xor (y > 0)) return inf;
else return sup;
assert(false);
}
return std::clamp<Common>(*res, inf, sup);
}
template<class T>
inline constexpr T sqrt_floor(const T x) noexcept(NO_EXCEPT) {
return static_cast<T>(std::sqrt(static_cast<long double>(x)));
}
template<class T>
inline constexpr T sqrt_ceil(const T x) noexcept(NO_EXCEPT) {
T res = sqrt_floor(x);
if constexpr(std::is_floating_point_v<T>) {
while(res * res < x) res += 1;
}
else {
while(mul_overflow(res, res).value_or(std::numeric_limits<T>::max()) < x) ++res;
}
return res;
}
template<class T, std::integral K>
inline constexpr T kth_root_floor(T x, const K k) noexcept(NO_EXCEPT) {
assert(x >= 0);
if(std::signed_integral<K>) assert(k > 0);
if(x <= 1 or k == 1) return x;
constexpr auto DIGITS = std::numeric_limits<T>::digits;
if(k >= DIGITS) return T{1};
if(k == 2) return sqrt_floor(x);
constexpr auto MAX = std::numeric_limits<T>::max();
if(x == MAX) --x;
auto pow = [&](T t, i64 p) {
if(p == 0) return T{1};
T res = 1;
while(p) {
if(p & 1) {
res = mul_overflow(res, t).value_or(MAX);
}
t = mul_overflow(t, t).value_or(MAX);
p >>= 1;
}
return res;
};
auto res = static_cast<T>(std::pow(x, std::nextafter(1 / static_cast<double>(k), 0)));
while(pow(res + 1, k) <= x) ++res;
return res;
}
template<std::integral T>
T inline constexpr extended_gcd(const T& a, const T& b, T& x, T& y) noexcept {
if(b == 0) {
x = 1;
y = 0;
return a;
}
const T d = extended_gcd(b, a%b, y, x);
y -= a / b * x;
return d;
};
template<std::integral T>
std::pair<T, spair<T>> inline constexpr extended_gcd(const T& a, const T& b) noexcept {
T x, y;
const T d = extended_gcd(a, b, x, y);
return { d, spair<T>{ x, y } };
};
template<std::integral T>
std::optional<spair<T>> inline constexpr bezout_equation(const T& a, const T& b, const T& c) noexcept {
if(a == 0) {
if(b == 0) {
if(c == 0) return spair<T>{ 0, 0 };
else { };
}
if(c % b == 0) return spair<T>{ 0, c / b };
return {};
}
if(b == 0) {
const auto ans = bezout_equation(b, a, c);
if(ans.has_value()) return swapped(ans.value());
return {};
}
T x, y;
const T gcd = extended_gcd(a, b, x, y);
if(c % gcd != 0) return {};
const T p = c / gcd;
return spair<T>{ x * p, y * p };
};
} // namespace uni
#line 10 "algebraic/base.hpp"
namespace uni {
namespace algebraic {
template<class Derived>
struct scalar_multipliable {
struct identity {
template<std::integral Scalar>
friend inline Derived operator*(const Scalar, const Derived& val) noexcept(NO_EXCEPT) {
return val;
}
};
struct automatic {
template<std::integral Scalar>
friend inline Derived operator*(const Scalar k, const Derived& val) noexcept(NO_EXCEPT) {
return uni::pow<Derived, Scalar, std::plus<Derived>>(val, k, {}, {});
}
};
};
template<class T>
struct base {
using value_type = T;
protected:
value_type _value;
public:
template<class... Args>
requires std::constructible_from<value_type, Args...>
base(Args&&... args) noexcept(NO_EXCEPT) : _value(std::forward<Args>(args)...) {}
inline explicit operator value_type() const noexcept(NO_EXCEPT) { return this->_value; }
inline auto val() const noexcept(NO_EXCEPT) { return this->_value; };
inline const value_type* operator->() const noexcept(NO_EXCEPT) { return &this->_value; };
inline value_type* operator->() noexcept(NO_EXCEPT) { return &this->_value; };
friend inline auto operator<=>(const base& lhs, const base& rhs) noexcept(NO_EXCEPT) {
return lhs._value <=> rhs._value;
};
friend inline bool operator==(const base& lhs, const base& rhs) noexcept(NO_EXCEPT) {
return lhs._value == rhs._value;
}
};
struct associative {};
struct commutative {};
} // namespace algebraic
} // namespace uni
#line 11 "algebraic/internal/concepts.hpp"
namespace uni {
namespace algebraic {
namespace internal {
template<class T>
concept magma =
uni::internal::addable<T> &&
requires {
typename T::value_type;
};
template<class T>
concept associative = std::is_base_of_v<algebraic::associative, T>;
template<class T>
concept commutative = std::is_base_of_v<algebraic::commutative, T>;
template<class T>
concept invertible = uni::internal::unary_subtractable<T>;
template<class T>
concept semigroup = magma<T> && associative<T>;
template<class T>
concept monoid = semigroup<T> && std::default_initializable<T>;
template<class T>
concept group = monoid<T> && invertible<T>;
} // namespace internal
} // namespace algebraic
} // namespace uni
#line 13 "action/base.hpp"
namespace uni {
namespace actions {
template<class operation = uni::internal::dummy>
requires algebraic::internal::monoid<operation> || std::same_as<operation, uni::internal::dummy>
struct base {
static operation power(const operation& x, const uni::internal::size_t) noexcept(NO_EXCEPT) { return x; }
};
namespace internal {
template<class T>
concept operatable_action = algebraic::internal::magma<typename T::operand>;
template<class T>
concept effective_action =
algebraic::internal::magma<typename T::operation> &&
requires (const typename T::operation& f, const uni::internal::size_t length) {
{ T::power(f, length) } -> std::same_as<typename T::operation>;
};
template<class T>
concept operand_only_action = operatable_action<T> && (!effective_action<T>);
template<class T>
concept effect_only_action = effective_action<T> && (!operatable_action<T>);
template<class T>
concept full_action =
operatable_action<T> && effective_action<T> &&
requires (typename T::operation f, typename T::operand v) {
{ T::mapping(f, v) } -> std::same_as<typename T::operand>;
};
template<class T>
concept action = operatable_action<T> || effective_action<T>;
} // namespace internal
} // namespace actions
} // namespace uni
#line 2 "action/helpers.hpp"
#line 5 "action/helpers.hpp"
#line 2 "algebraic/null.hpp"
#line 5 "algebraic/null.hpp"
#line 9 "algebraic/null.hpp"
#line 12 "algebraic/null.hpp"
namespace uni {
namespace algebraic {
template<class T = uni::internal::dummy>
struct null : base<T>, scalar_multipliable<null<T>>::identity, associative, commutative {
using base<T>::base;
friend inline null operator+(const null& lhs, const null& rhs) noexcept(NO_EXCEPT) {
if(lhs == null()) return rhs;
return lhs;
}
inline null operator-() const noexcept(NO_EXCEPT)
requires internal::invertible<T>
{
return -*this;
}
};
} // namespace algebraic
} // namespace uni
#line 2 "algebraic/helper.hpp"
#line 7 "algebraic/helper.hpp"
namespace uni {
namespace algebraic {
template<class T, auto op, auto e, class... Tags>
struct helper : uni::algebraic::base<T>, uni::algebraic::scalar_multipliable<helper<T, op, e, Tags...>>::automatic, Tags... {
static_assert(std::same_as<std::invoke_result_t<decltype(op), T, T>, T>);
static_assert(std::same_as<std::invoke_result_t<decltype(e)>, T>);
using uni::algebraic::base<T>::base;
helper() : helper(e()) {}
friend inline helper operator+(const helper& lhs, const helper& rhs) noexcept(NO_EXCEPT) {
return op(lhs.val(), rhs.val());
}
};
template<class T, auto op, auto e>
using monoid_helper = helper<T, op, e, associative>;
template<class T>
struct make_magma {
using type = null<T>;
static_assert(internal::magma<type>);
};
template<internal::magma T>
struct make_magma<T> {
using type = T;
};
template<class T>
using make_magma_t = typename make_magma<T>::type;
} // namespace algebraic
} // namespace uni
#line 2 "action/null.hpp"
#line 6 "action/null.hpp"
#line 8 "action/null.hpp"
#line 2 "algebraic/addition.hpp"
#line 7 "algebraic/addition.hpp"
namespace uni {
namespace algebraic {
template<class T>
struct addition : base<T>, associative, commutative {
using base<T>::base;
friend inline addition operator+(const addition& lhs, const addition& rhs) noexcept(NO_EXCEPT) {
return lhs.val() + rhs.val();
}
template<std::integral Scalar>
friend inline addition operator*(const Scalar k, const addition& rhs) noexcept(NO_EXCEPT) {
return k * rhs.val();
}
inline addition operator-() const noexcept(NO_EXCEPT)
requires internal::invertible<T>
{
return -this->val();
}
};
} // namespace algebraic
} // namespace uni
#line 11 "action/null.hpp"
namespace uni {
namespace actions {
template<class T>
struct null : base<algebraic::null<T>> {
using operand = algebraic::null<T>;
using operation = algebraic::null<T>;
static operand mapping(const operation&, const operand& x) noexcept(NO_EXCEPT) { return x; }
};
} // namespace actions
} // namespace uni
#line 11 "action/helpers.hpp"
namespace uni {
namespace actions {
template<class S, auto op, auto e, class F, auto _mapping, auto composition, auto id, auto _power = nullptr>
struct helper {
static_assert(std::same_as<std::invoke_result_t<decltype(_mapping), F, S>, S>);
// static_assert(std::same_as<std::invoke_result_t<decltype(_power), F, uni::internal::size_t>, F>);
using operand = algebraic::monoid_helper<S, op, e>;
using operation = algebraic::monoid_helper<F, composition, id>;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return _mapping(f.val(), x.val());
}
static operation power(const operation& x, [[maybe_unused]] const uni::internal::size_t length) noexcept(NO_EXCEPT) {
if constexpr(_power == nullptr) return x;
else return _power(x.val(), length);
}
};
template<class S, class F, auto _mapping, auto _power = nullptr>
struct mixer {
static_assert(std::same_as<std::invoke_result_t<decltype(_mapping), F, S>, S>);
static_assert(std::same_as<std::invoke_result_t<decltype(_power), F, uni::internal::size_t>, F>);
using operand = S;
using operation = F;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return _mapping(f.val(), x.val());
}
static operation power(const operation& x, [[maybe_unused]] const uni::internal::size_t length) noexcept(NO_EXCEPT) {
if constexpr(_power == nullptr) return x;
return _power(x.val(), length);
}
};
template<class S>
struct amplifier {
using operand = S;
using operation = S;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return f + x;
}
static operation power(const operation& x, [[maybe_unused]] const uni::internal::size_t length) noexcept(NO_EXCEPT) {
return length * x;
}
};
template<algebraic::internal::magma Magma>
struct make_operatable {
struct type {
using operand = Magma;
};
static_assert(internal::operatable_action<type>);
};
template<class T>
using make_operatable_t = typename make_operatable<T>::type;
template<algebraic::internal::magma Magma>
struct make_effective {
struct type : base<Magma> {
using operation = Magma;
};
static_assert(internal::effective_action<type>);
};
template<class T>
using make_effective_t = typename make_effective<T>::type;
template<class T>
struct make_full {
using type = null<T>;
static_assert(internal::full_action<type>);
};
template<algebraic::internal::magma Magma>
struct make_full<Magma> {
using type = make_full<make_operatable_t<Magma>>::type;
};
template<internal::full_action Action>
struct make_full<Action> {
using type = Action;
};
template<internal::operand_only_action Action>
struct make_full<Action> {
using base = Action;
struct type : actions::base<algebraic::null<typename base::operand::value_type>> {
using operand = typename base::operand;
using operation = algebraic::null<typename base::operand::value_type>;
using actions::base<algebraic::null<typename base::operand::value_type>>::base;
static operand mapping(const operation&, const operand& x) noexcept(NO_EXCEPT) { return x; }
};
static_assert(internal::full_action<type>);
};
template<internal::effect_only_action Action>
struct make_full<Action> {
using base = Action;
struct type : base {
using operand = typename base::operation;
using operation = typename base::operation;
using base::base;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) { return f + x; }
};
static_assert(internal::full_action<type>);
};
template<class T>
using make_full_t = typename make_full<T>::type;
} // namespace actions
} // namespace uni
#line 2 "action/range_add.hpp"
#line 6 "action/range_add.hpp"
#line 8 "action/range_add.hpp"
namespace uni {
namespace actions {
template<class T>
struct range_add : base<algebraic::addition<T>> {
using operand = algebraic::null<T>;
using operation = algebraic::addition<T>;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return f.val() + x.val();
}
};
static_assert(internal::full_action<range_add<int>>);
} // namesapce actions
} // namespace uni
#line 2 "action/range_add_range_max.hpp"
#line 5 "action/range_add_range_max.hpp"
#line 7 "action/range_add_range_max.hpp"
#line 2 "algebraic/maximum.hpp"
#line 6 "algebraic/maximum.hpp"
#line 9 "algebraic/maximum.hpp"
namespace uni {
namespace algebraic {
template<class T>
struct maximum : base<T>, scalar_multipliable<maximum<T>>::identity, associative, commutative {
using base<T>::base;
maximum() noexcept(NO_EXCEPT) : maximum(std::numeric_limits<T>::lowest()) {};
friend inline maximum operator+(const maximum& lhs, const maximum& rhs) noexcept(NO_EXCEPT) {
return std::max(lhs.val(), rhs.val());
}
};
} // namespace algebraic
} // namespace uni
#line 10 "action/range_add_range_max.hpp"
namespace uni {
namespace actions {
template<class T>
struct range_add_range_max : base<algebraic::addition<T>> {
using operand = algebraic::maximum<T>;
using operation = algebraic::addition<T>;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return f.val() + x.val();
}
};
static_assert(internal::full_action<uni::actions::range_add_range_max<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_add_range_min.hpp"
#line 5 "action/range_add_range_min.hpp"
#line 7 "action/range_add_range_min.hpp"
#line 2 "algebraic/minimum.hpp"
#line 6 "algebraic/minimum.hpp"
#line 9 "algebraic/minimum.hpp"
namespace uni {
namespace algebraic {
template<class T>
struct minimum : base<T>, scalar_multipliable<minimum<T>>::identity, associative, commutative {
using base<T>::base;
minimum() noexcept(NO_EXCEPT) : minimum(std::numeric_limits<T>::max()) {};
friend inline minimum operator+(const minimum& lhs, const minimum& rhs) noexcept(NO_EXCEPT) {
return std::min(lhs.val(), rhs.val());
}
};
} // namespace algebraic
} // namespace uni
#line 10 "action/range_add_range_min.hpp"
namespace uni {
namespace actions {
template<class T>
struct range_add_range_min : base<algebraic::addition<T>> {
using operand = algebraic::minimum<T>;
using operation = algebraic::addition<T>;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return f.val() + x.val();
}
};
static_assert(internal::full_action<uni::actions::range_add_range_min<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_add_range_sum.hpp"
#line 5 "action/range_add_range_sum.hpp"
#line 7 "action/range_add_range_sum.hpp"
#line 9 "action/range_add_range_sum.hpp"
namespace uni {
namespace actions {
template<class T>
using range_add_range_sum = amplifier<algebraic::addition<T>>;
static_assert(internal::full_action<range_add_range_sum<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_affine_range_minmax.hpp"
#line 5 "action/range_affine_range_minmax.hpp"
#line 7 "action/range_affine_range_minmax.hpp"
#line 2 "algebraic/minmax.hpp"
#line 7 "algebraic/minmax.hpp"
#line 10 "algebraic/minmax.hpp"
namespace uni {
namespace algebraic {
template<class T>
struct minmax : base<std::pair<T, T>>, scalar_multipliable<minmax<T>>::identity, associative, commutative {
using base<std::pair<T, T>>::base;
minmax() noexcept(NO_EXCEPT)
: minmax(std::numeric_limits<T>::max(), std::numeric_limits<T>::lowest())
{};
minmax(const T& v) noexcept(NO_EXCEPT) : minmax(v, v) {};
friend inline minmax operator+(const minmax& lhs, const minmax& rhs) noexcept(NO_EXCEPT) {
return minmax({ std::min(lhs.val().first, rhs->first), std::max(lhs.val().second, rhs->second) });
}
};
} // namespace algebraic
} // namespace uni
#line 2 "algebraic/affine.hpp"
#line 4 "algebraic/affine.hpp"
#line 7 "algebraic/affine.hpp"
namespace uni {
namespace algebraic {
template<class T, bool REVERSE = false>
struct affine : base<std::pair<T, T>>, scalar_multipliable<affine<T, REVERSE>>::automatic, associative {
using base<std::pair<T, T>>::base;
affine() noexcept(NO_EXCEPT) : affine({ 1, 0 }) {};
friend inline affine operator+(const affine& lhs, const affine& rhs) noexcept(NO_EXCEPT) {
if constexpr(REVERSE) return affine({ lhs->first * rhs->first, lhs(rhs->second) });
return affine({ rhs->first * lhs->first, rhs(lhs->second) });
}
inline auto operator()(const T& x) const noexcept(NO_EXCEPT) {
return this->val().first * x + this->val().second;
}
};
} // namespace algebraic
} // namespace uni
#line 10 "action/range_affine_range_minmax.hpp"
namespace uni {
namespace actions {
template<class T, bool REVERSE = false>
struct range_affine_range_minmax : base<algebraic::affine<T, !REVERSE>> {
using operand = algebraic::minmax<T>;
using operation = algebraic::affine<T, !REVERSE>;
static auto mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
auto res = operand({ f(x->first), f(x->second) });
if (f->first < 0) std::swap(res->first, res->second);
return res;
}
};
static_assert(internal::full_action<range_affine_range_minmax<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_affine_range_sum.hpp"
#line 5 "action/range_affine_range_sum.hpp"
#line 7 "action/range_affine_range_sum.hpp"
#line 10 "action/range_affine_range_sum.hpp"
namespace uni {
namespace actions {
template<class T, bool REVERSE = false>
struct range_affine_range_sum {
using operand = algebraic::addition<T>;
using operation = algebraic::affine<T, !REVERSE>;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return f(x.val());
}
static auto power(const operation& f, const uni::internal::size_t length) noexcept(NO_EXCEPT) {
return operation({ f->first, f->second * length });
}
};
static_assert(internal::full_action<range_affine_range_sum<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_bitxor.hpp"
#line 5 "action/range_bitxor.hpp"
#line 8 "action/range_bitxor.hpp"
#line 2 "algebraic/bit_xor.hpp"
#line 5 "algebraic/bit_xor.hpp"
namespace uni {
namespace algebraic {
template<class T>
struct bit_xor : base<T>, associative, commutative {
using base<T>::base;
friend inline bit_xor operator+(const bit_xor& lhs, const bit_xor& rhs) noexcept(NO_EXCEPT) {
return lhs.val() xor rhs.val();
}
template<std::integral Scalar>
friend inline bit_xor operator*(const Scalar k, const bit_xor& val) noexcept(NO_EXCEPT) {
return k % 2 == 0 ? bit_xor{} : val;
}
inline bit_xor operator-() const noexcept(NO_EXCEPT) {
return this->val();
}
};
} // namespace algebraic
} // namespace uni
#line 10 "action/range_bitxor.hpp"
namespace uni {
namespace actions {
template<class T>
using range_bitxor = make_operatable_t<uni::algebraic::bit_xor<T>>;
static_assert(internal::operand_only_action<range_bitxor<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_chgcd_range_gcd.hpp"
#line 2 "algebraic/gcd.hpp"
#line 4 "algebraic/gcd.hpp"
#line 7 "algebraic/gcd.hpp"
namespace uni {
namespace algebraic {
template<class T>
struct gcd : base<T>, scalar_multipliable<gcd<T>>::identity, associative, commutative {
using base<T>::base;
gcd() noexcept(NO_EXCEPT) : gcd() {};
friend inline gcd operator+(const gcd& lhs, const gcd& rhs) noexcept(NO_EXCEPT) {
return std::gcd(lhs.val(), rhs.val());
}
};
} // namespace algebraic
} // namespace uni
#line 5 "action/range_chgcd_range_gcd.hpp"
#line 7 "action/range_chgcd_range_gcd.hpp"
namespace uni {
namespace actions {
template<class T>
using range_chgcd_range_gcd = amplifier<uni::algebraic::gcd<T>>;
static_assert(internal::full_action<range_chgcd_range_gcd<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_chmax_range_max.hpp"
#line 5 "action/range_chmax_range_max.hpp"
#line 7 "action/range_chmax_range_max.hpp"
namespace uni {
namespace actions {
template<class T>
using range_chmax_range_max = amplifier<algebraic::maximum<T>>;
static_assert(internal::full_action<range_chmax_range_max<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_chmin_range_min.hpp"
#line 5 "action/range_chmin_range_min.hpp"
#line 7 "action/range_chmin_range_min.hpp"
namespace uni {
namespace actions {
template<class T>
using range_chmin_range_min = amplifier<algebraic::maximum<T>>;
static_assert(internal::full_action<range_chmin_range_min<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_chminchmax_range_minmax.hpp"
#line 5 "action/range_chminchmax_range_minmax.hpp"
#line 7 "action/range_chminchmax_range_minmax.hpp"
namespace uni {
namespace actions {
template<class T>
using range_chminchmax_range_minmax = amplifier<algebraic::minmax<T>>;
static_assert(internal::full_action<range_chminchmax_range_minmax<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_composition.hpp"
#line 6 "action/range_composition.hpp"
#line 8 "action/range_composition.hpp"
namespace uni {
namespace actions {
template<class T, bool REVERSE = false>
using range_composition = make_operatable_t<uni::algebraic::affine<T, REVERSE>>;
static_assert(internal::operand_only_action<range_composition<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_flip_range_bitxor.hpp"
#line 5 "action/range_flip_range_bitxor.hpp"
#line 7 "action/range_flip_range_bitxor.hpp"
#line 9 "action/range_flip_range_bitxor.hpp"
namespace uni {
namespace actions {
template<class T>
using range_flip_range_bitxor = amplifier<uni::algebraic::bit_xor<T>>;
static_assert(internal::full_action<range_flip_range_bitxor<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_gcd.hpp"
#line 6 "action/range_gcd.hpp"
#line 8 "action/range_gcd.hpp"
namespace uni {
namespace actions {
template<class T>
using range_gcd = make_operatable_t<uni::algebraic::gcd<T>>;
static_assert(internal::operand_only_action<range_gcd<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_max.hpp"
#line 6 "action/range_max.hpp"
#line 8 "action/range_max.hpp"
namespace uni {
namespace actions {
template<class T>
using range_max = make_operatable_t<uni::algebraic::maximum<T>>;
static_assert(internal::operand_only_action<range_max<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_min.hpp"
#line 6 "action/range_min.hpp"
#line 8 "action/range_min.hpp"
namespace uni {
namespace actions {
template<class T>
using range_min = make_operatable_t<uni::algebraic::minimum<T>>;
static_assert(internal::operand_only_action<range_min<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_sequence_hash.hpp"
#line 5 "action/range_sequence_hash.hpp"
#line 8 "action/range_sequence_hash.hpp"
#line 2 "algebraic/rolling_hash.hpp"
#line 5 "algebraic/rolling_hash.hpp"
#line 8 "algebraic/rolling_hash.hpp"
#line 10 "algebraic/rolling_hash.hpp"
#line 12 "algebraic/rolling_hash.hpp"
#line 2 "numeric/fast_prime.hpp"
#line 6 "numeric/fast_prime.hpp"
#line 2 "adaptor/set.hpp"
#include <set>
#include <unordered_set>
#line 11 "adaptor/set.hpp"
#line 15 "adaptor/set.hpp"
#line 2 "utility/functional.hpp"
#line 8 "utility/functional.hpp"
#line 11 "utility/functional.hpp"
#line 13 "utility/functional.hpp"
#line 16 "utility/functional.hpp"
#line 18 "utility/functional.hpp"
namespace uni {
namespace internal {
template<class T> constexpr T plus(const T a, const T b) noexcept(NO_EXCEPT) { return std::plus<T>{}(a, b); }
template<class T> constexpr T minus(const T a, const T b) noexcept(NO_EXCEPT) { return std::minus<T>{}(a, b); }
template<class T> constexpr T bit_xor(const T a, const T b) noexcept(NO_EXCEPT) { return a xor b; }
} // namespace internal
template<class T, class U> inline auto to_optional_if_equal(const T& v, const U& ill) noexcept(NO_EXCEPT) -> std::optional<T> {
return v == ill ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class U> inline auto to_optional_if_over(const T& v, const U& ill) noexcept(NO_EXCEPT) -> std::optional<T> {
return v > ill ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class U> inline auto to_optional_if_or_over(const T& v, const U& ill) noexcept(NO_EXCEPT) -> std::optional<T> {
return v >= ill ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class U> inline auto to_optional_if_under(const T& v, const U& ill) noexcept(NO_EXCEPT) -> std::optional<T> {
return v < ill ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class U> inline auto to_optional_if_or_under(const T& v, const U& ill) noexcept(NO_EXCEPT) -> std::optional<T> {
return v <= ill ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class F> inline auto to_optional_if(const T& v, F&& f) noexcept(NO_EXCEPT) -> decltype(f(v), std::optional<T>{}){
return f(v) ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class U> inline bool chmin(T &a, const U& b) noexcept(NO_EXCEPT) { return (a>b ? a=b, true : false); }
template<class T, class U> inline bool chmax(T &a, const U& b) noexcept(NO_EXCEPT) { return (a<b ? a=b, true : false); }
template<class T, class... Ts> inline bool chmin(T &a, Ts... b) noexcept(NO_EXCEPT) { return chmin(a, min(b...)); }
template<class T, class... Ts> inline bool chmax(T &a, Ts... b) noexcept(NO_EXCEPT) { return chmax(a, max(b...)); }
template<class... Ts>
inline constexpr std::common_type_t<Ts...> tuple_sum(const std::tuple<Ts...>& tuple, const std::common_type_t<Ts...>& base = std::common_type_t<Ts...>()) noexcept(NO_EXCEPT) {
std::common_type_t<Ts...> res = base;
tuple_for_each(tuple, [&](const auto& v) constexpr { res += v; });
return res;
}
template<class... Ts>
inline constexpr std::common_type_t<Ts...> min_element(const std::tuple<Ts...>& tuple) noexcept(NO_EXCEPT) {
return std::apply([&](auto&&... v) constexpr { return min(v...); }, tuple);
}
template<class... Ts>
inline constexpr std::common_type_t<Ts...> max_element(const std::tuple<Ts...>& tuple) noexcept(NO_EXCEPT) {;
return std::apply([&](auto&&... v) constexpr { return max(v...); }, tuple);
}
template<interval_notation INTERVAL, class T0, class T1, class T2>
inline constexpr bool in_range(const T0& x, const T1& l, const T2& r) noexcept(NO_EXCEPT) {
if constexpr(INTERVAL == interval_notation::right_open) return l <= x and x < r;
else if constexpr(INTERVAL == interval_notation::left_open) return l < x and x <= r;
else if constexpr(INTERVAL == interval_notation::open) return l < x and x < r;
return l <= x and x <= r;
}
template<class F, class Tuple>
constexpr void tuple_for_each(F&& f, Tuple&& tuple) {
std::apply(
[&]<class... Ts>(Ts&&... elems) {
(std::invoke(f, std::forward<Ts>(elems)), ...);
},
std::forward<Tuple>(tuple)
);
}
template<class F, class Tuple>
constexpr auto tuple_transform(F&& f, Tuple&& tuple) {
return std::apply(
[&]<class...Ts>(Ts&&... elems) {
return internal::tuple_or_pair_t<std::invoke_result_t<F&,Ts>...>(
std::invoke(f, std::forward<Ts>(elems))...
);
},
std::forward<Tuple>(tuple)
);
}
} // namespace uni
#line 17 "adaptor/set.hpp"
namespace uni {
namespace internal {
template<class Set>
struct set_wrapper : Set {
using Set::Set;
using value_type = typename Set::value_type;
using size_type = internal::size_t;
template<class Key>
auto remove(Key&& key) noexcept(NO_EXCEPT) { return this->extract(std::forward<Key>(key)); }
inline auto ssize() const noexcept(NO_EXCEPT) { return std::ranges::ssize(*this); }
inline auto min_element() const noexcept(NO_EXCEPT) { return this->begin(); }
inline auto max_element() const noexcept(NO_EXCEPT) { return std::ranges::prev(this->end()); }
inline auto min() const noexcept(NO_EXCEPT) { return *this->begin(); }
inline auto max() const noexcept(NO_EXCEPT) { return *std::ranges::prev(this->end()); }
inline auto& pop_min() noexcept(NO_EXCEPT) { this->erase(this->begin()); return *this; }
inline auto& pop_max() noexcept(NO_EXCEPT) { this->erase(std::ranges::prev(this->end())); return *this; }
inline auto kth_smallest_element(const size_type k) const noexcept(NO_EXCEPT) {
return std::ranges::next(this->begin(), k);
}
inline auto kth_largest_element(const size_type k) const noexcept(NO_EXCEPT) {
return std::ranges::prev(this->end(), k + 1);
}
inline auto kth_smallest(const size_type k) const noexcept(NO_EXCEPT) {
return *std::ranges::next(this->begin(), k);
}
inline auto kth_largest(const size_type k) const noexcept(NO_EXCEPT) {
return *std::ranges::prev(this->end(), k + 1);
}
inline auto& pop_kth_smallest(const size_type k) const noexcept(NO_EXCEPT) {
return this->erase(std::ranges::next(this->begin(), k));
return *this;
}
inline auto& pop_kth_largest(const size_type k) const noexcept(NO_EXCEPT) {
return this->erase(std::ranges::prev(this->end(), k + 1));
return *this;
}
auto next_element(const typename Set::key_type& key, const size_type _count = 0) const noexcept(NO_EXCEPT) {
size_type count = std::abs(_count);
auto itr = this->lower_bound(key);
const auto begin = this->begin(), end = this->end();
if(itr == end) return this->end();
if(itr == begin) return this->begin();
while(count--) {
if(_count < 0) if(itr-- == begin) return this->begin();
if(_count > 0) if(++itr == end) return this->end();
}
return itr;
}
auto prev_element(const typename Set::key_type& key, const size_type _count = 0) const noexcept(NO_EXCEPT) {
size_type count = std::abs(_count);
auto itr = this->upper_bound(key);
const auto begin = this->begin(), end = this->end();
if(itr == end) return this->end();
if(itr-- == begin) return this->begin();
while(count--) {
if(_count < 0) if(itr-- == begin) return this->begin();
if(_count > 0) if(++itr == end) return this->end();
}
return itr;
}
std::optional<typename Set::value_type> next(const typename Set::key_type& key, size_type count = 0) const noexcept(NO_EXCEPT) {
if(this->empty()) return {};
auto itr = this->lower_bound(key);
const auto end = this->end();
if(itr == end) return {};
while(count--) if(++itr == end) return {};
return { *itr };
}
std::optional<typename Set::value_type> prev(const typename Set::key_type& key, size_type count = 0) const noexcept(NO_EXCEPT) {
if(this->empty()) return {};
auto itr = this->upper_bound(key);
const auto begin = this->begin();
if(itr-- == begin) return {};
while(count--) if(itr-- == begin) return {};
return { *itr };
}
template<class Rhs>
inline set_wrapper& operator|=(Rhs&& rhs) noexcept(NO_EXCEPT) {
set_wrapper res;
std::ranges::set_union(*this, std::forward<Rhs>(rhs), std::inserter(res, res.end()));
this->swap(res);
return *this;
}
template<class Rhs>
inline set_wrapper& operator&=(Rhs&& rhs) noexcept(NO_EXCEPT) {
set_wrapper res;
std::ranges::set_intersection(*this, std::forward<Rhs>(rhs), std::inserter(res, res.end()));
this->swap(res);
return *this;
}
template<class Rhs>
inline set_wrapper& operator^=(Rhs&& rhs) noexcept(NO_EXCEPT) {
set_wrapper res;
std::ranges::set_symmetric_difference(*this, std::forward<Rhs>(rhs), std::inserter(res, res.end()));
this->swap(res);
return *this;
}
template<class... Args>
inline set_wrapper operator|(set_wrapper<Args...> rhs) noexcept(NO_EXCEPT) {
return rhs |= *this;
}
template<class... Args>
inline set_wrapper operator&(set_wrapper<Args...> rhs) noexcept(NO_EXCEPT) {
return rhs &= *this;
}
template<class... Args>
inline set_wrapper operator^(set_wrapper<Args...> rhs) noexcept(NO_EXCEPT) {
return rhs ^= *this;
}
template<class... Args>
inline auto operator<=>(const set_wrapper<Args...>& rhs) const noexcept(NO_EXCEPT) {
const bool leq = this->size() <= rhs.size() && std::ranges::includes(rhs, *this);
const bool geq = rhs.size() <= this->size() && std::ranges::includes(*this, rhs);
if(leq) {
if(geq) return std::partial_ordering::equivalent;
return std::partial_ordering::less;
}
if(geq) return std::partial_ordering::greater;
return std::partial_ordering::unordered;
}
};
} //namespace internal
template<class... Args> using set = internal::set_wrapper<std::set<Args...>>;
template<class... Args> using unordered_set = internal::set_wrapper<std::unordered_set<Args...>>;
template<class... Args> using multiset = internal::set_wrapper<std::multiset<Args...>>;
template<class... Args> using unordered_multiset = internal::set_wrapper<std::unordered_multiset<Args...>>;
} // namespace uni
#line 2 "adaptor/map.hpp"
#include <map>
#include <unordered_map>
#line 7 "adaptor/map.hpp"
#line 11 "adaptor/map.hpp"
#line 2 "adaptor/gnu/hash_table.hpp"
#line 5 "adaptor/gnu/hash_table.hpp"
#include <stdexcept>
#include <ext/pb_ds/assoc_container.hpp>
#line 11 "adaptor/gnu/hash_table.hpp"
namespace uni {
namespace gnu {
template<class Base>
struct hash_table : Base {
using key_type = typename Base::key_type;
using value_type = typename Base::value_type;
using mapped_type = typename Base::mapped_type;
inline bool contains(const key_type& key) const noexcept(NO_EXCEPT) {
return this->Base::find(key) != this->Base::end();
}
template<class K, class T>
inline decltype(auto) emplace(K&& key, T&& val) noexcept(NO_EXCEPT) {
return this->Base::insert({ std::forward<K>(key), std::forward<T>(val) });
}
mapped_type& at(const key_type& key) {
auto itr = this->Base::find(key);
if(itr == this->Base::end()) throw std::out_of_range("hash_table::at()");
return itr->second;
};
const mapped_type& at(const key_type & key) const {
auto itr = this->Base::find(key);
if(itr == this->Base::end()) throw std::out_of_range("hash_table::at()");
return itr->second;
};
};
template<class Key, class T, class Hash = void>
struct cc_hash_table : hash_table<__gnu_pbds::cc_hash_table<Key, T, Hash>> {
using hash_table<__gnu_pbds::cc_hash_table<Key, T, Hash>>::hash_table;
};
template<class Key, class T>
struct cc_hash_table<Key, T, void> : hash_table<__gnu_pbds::cc_hash_table<Key, T>> {
using hash_table<__gnu_pbds::cc_hash_table<Key, T>>::hash_table;
};
template<class Key, class T, class Hash = void>
struct gp_hash_table : hash_table<__gnu_pbds::gp_hash_table<Key, T, Hash>> {
using hash_table<__gnu_pbds::gp_hash_table<Key, T, Hash>>::hash_table;
};
template<class Key, class T>
struct gp_hash_table<Key, T, void> : hash_table<__gnu_pbds::gp_hash_table<Key, T>> {
using hash_table<__gnu_pbds::gp_hash_table<Key, T>>::hash_table;
};
} // namespace gnu
} // namespace uni
#line 14 "adaptor/map.hpp"
namespace uni {
namespace internal {
template<class Map>
using map_wrapper_base = set_wrapper<Map>;
template<class Map> struct map_wrapper : map_wrapper_base<Map> {
private:
using base = map_wrapper_base<Map>;
public:
using base::base;
using mapped_type = typename base::mapped_type;
using key_type = typename base::key_type;
protected:
using default_func_noarg_type = std::function<mapped_type(void)>;
using default_func_type = std::function<mapped_type(key_type)>;
int _default_type = 0;
mapped_type _default_val = mapped_type();
default_func_noarg_type _default_func_noarg;
default_func_type _default_func;
inline mapped_type _get_default(const key_type& key) const noexcept(NO_EXCEPT) {
if(this->_default_type == 0) return this->_default_val;
if(this->_default_type == 1) return this->_default_func_noarg();
if(this->_default_type == 2) return this->_default_func(key);
else assert(false);
}
public:
inline auto& set_default(const mapped_type& val) noexcept(NO_EXCEPT) {
this->_default_val = val;
this->_default_type = 0;
return *this;
}
inline auto& set_default(const default_func_noarg_type func) noexcept(NO_EXCEPT) {
this->_default_func_noarg = func;
this->_default_type = 1;
return *this;
}
inline auto& set_default(const default_func_type func) noexcept(NO_EXCEPT) {
this->_default_func = func;
this->_default_type = 2;
return *this;
}
inline auto& operator[](const key_type& key) noexcept(NO_EXCEPT) {
auto found = this->base::find(key);
if(found == this->base::end()) return this->base::emplace(key, this->_get_default(key)).first->second;
return found->second;
}
inline auto& operator()(const key_type& key) noexcept(NO_EXCEPT) {
return this->base::operator[](key);
}
inline std::optional<mapped_type> get(const key_type& key) const noexcept(NO_EXCEPT) {
const auto found = this->base::find(key);
if(found == this->base::end()) return {};
return found->second;
}
};
} // namespace internal
template<class... Args> using map = internal::map_wrapper<std::map<Args...>>;
template<class... Args> using unordered_map = internal::map_wrapper<std::unordered_map<Args...>>;
template<class... Args> using multimap = internal::map_wrapper<std::multimap<Args...>>;
template<class... Args> using unordered_multimap = internal::map_wrapper<std::unordered_multimap<Args...>>;
template<class... Args> using cc_hash_table = internal::map_wrapper<gnu::cc_hash_table<Args...>>;
template<class... Args> using gp_hash_table = internal::map_wrapper<gnu::gp_hash_table<Args...>>;
} // namespace uni
#line 11 "numeric/fast_prime.hpp"
#line 2 "numeric/internal/primality_test.hpp"
#line 7 "numeric/internal/primality_test.hpp"
#line 10 "numeric/internal/primality_test.hpp"
#line 2 "numeric/modular/modint_interface.hpp"
#line 6 "numeric/modular/modint_interface.hpp"
#line 9 "numeric/modular/modint_interface.hpp"
#line 11 "numeric/modular/modint_interface.hpp"
#line 2 "numeric/modular/builtin_reduction.hpp"
#line 5 "numeric/modular/builtin_reduction.hpp"
#line 8 "numeric/modular/builtin_reduction.hpp"
#line 10 "numeric/modular/builtin_reduction.hpp"
#line 12 "numeric/modular/builtin_reduction.hpp"
namespace uni {
namespace internal {
template<std::unsigned_integral Value, std::unsigned_integral Large>
requires has_double_digits_of<Large, Value>
struct builtin_reduction {
using value_type = Value;
using large_type = Large;
private:
value_type _mod;
public:
static constexpr int digits = std::numeric_limits<value_type>::digits;
static constexpr value_type max() noexcept { return std::numeric_limits<value_type>::max(); }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mod; }
constexpr builtin_reduction() noexcept = default;
constexpr builtin_reduction(const value_type mod) noexcept(NO_EXCEPT) : _mod(mod) {
assert(0 < mod && mod < builtin_reduction::max());
}
inline constexpr value_type reduce(const large_type v) const noexcept(NO_EXCEPT) { return v % this->_mod; }
inline constexpr value_type add(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x >= this->_mod - y) x -= this->_mod;
x += y;
return x;
}
inline constexpr value_type subtract(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x < y) x += this->_mod;
x -= y;
return x;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->reduce(static_cast<large_type>(x) * static_cast<large_type>(y));
}
template<std::integral K>
inline constexpr value_type pow(const value_type v, const K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mod == 0) return 0;
return uni::pow(v, p, [this](const value_type x, const value_type y) { return this->multiply(x, y); });
}
inline constexpr auto compare(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return x <=> y;
}
constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) { return v; }
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
using common_type = std::common_type_t<T, value_type>;
const common_type mod = static_cast<common_type>(this->_mod);
if(std::is_constant_evaluated()) {
v %= mod;
if constexpr(std::signed_integral<T>) {
if(v < 0) v += mod;
}
}
else {
if(v > 0 && static_cast<common_type>(v) >= mod) {
v %= mod;
}
if constexpr(std::signed_integral<T>) {
if(v < 0) {
if(static_cast<common_type>(-v) <= mod) v += mod;
else {
v %= mod;
if(v != 0) v += mod;
}
}
}
}
return static_cast<value_type>(v);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) { return this->_mod == 1 ? 0 : v; }
};
} // namespace internal
using builtin_reduction_32bit = internal::builtin_reduction<u32, u64>;
using builtin_reduction_64bit = internal::builtin_reduction<u64, u128>;
} // namespace uni
#line 2 "numeric/modular/binary_reduction.hpp"
#line 7 "numeric/modular/binary_reduction.hpp"
#line 10 "numeric/modular/binary_reduction.hpp"
#line 13 "numeric/modular/binary_reduction.hpp"
#line 2 "numeric/bit.hpp"
#include <immintrin.h>
#line 13 "numeric/bit.hpp"
#line 16 "numeric/bit.hpp"
#line 18 "numeric/bit.hpp"
namespace uni {
template<std::unsigned_integral T>
constexpr T multiply_high(const T x, const T y) noexcept(NO_EXCEPT) {
constexpr int digits = std::numeric_limits<T>::digits;
if constexpr(digits <= 16) {
return static_cast<T>((static_cast<u32>(x) * static_cast<u32>(y)) >> digits);
}
else if constexpr(digits <= 32) {
return static_cast<T>((static_cast<u64>(x) * static_cast<u64>(y)) >> digits);
}
else if constexpr(digits <= 64) {
return static_cast<T>((static_cast<u128>(x) * static_cast<u128>(y)) >> digits);
}
else {
constexpr int h_digits = digits / 2;
constexpr T mask = (T{ 1 } << h_digits) - 1;
const T xh = x >> h_digits, yh = y >> h_digits;
const T xl = x & mask, yl = y & mask;
const T ph = xh * yh, pl = xl * yl;
return (((pl >> h_digits) + (xh + xl) * (yh + yl) - (ph + pl)) >> h_digits) + ph;
}
}
template<std::unsigned_integral T>
inline constexpr int highest_bit_pos(const T v) noexcept(NO_EXCEPT) {
return (int)std::bit_width(v) - 1; // cast to int for GCC12
}
template<std::unsigned_integral T>
inline constexpr int lowest_bit_pos(const T v) noexcept(NO_EXCEPT) {
if(v == 0) return -1;
return std::countr_zero(v);
}
template<std::unsigned_integral T, std::integral I = int>
__attribute__((target("bmi2")))
inline constexpr T clear_higher_bits(const T v, const I p) {
if constexpr(std::signed_integral<I>) assert(0 <= p);
constexpr int DIGITS = std::numeric_limits<T>::digits;
assert(p <= DIGITS);
if constexpr(DIGITS <= 32) return _bzhi_u32(v, static_cast<u32>(p));
if constexpr(DIGITS <= 64) return _bzhi_u64(v, static_cast<u64>(p));
else {
static_assert(DIGITS <= 128);
constexpr std::uint64_t MAX64 = std::numeric_limits<std::uint64_t>::max();
const std::uint64_t high = v >> 64;
const std::uint64_t low = v & MAX64;
if(p < 64) return _bzhi_u64(low, p);
return low | (T{_bzhi_u64(high, p - 64)} << 64);
}
}
template<std::unsigned_integral T, std::integral I = int> constexpr T shiftl(const T, const I = 1);
template<std::unsigned_integral T, std::integral I = int> constexpr T shiftr(const T, const I = 1);
template<std::unsigned_integral T, std::integral I>
constexpr T shiftl(const T x, const I n) {
constexpr int DIGITS = std::numeric_limits<T>::digits;
if constexpr(std::signed_integral<I>) {
if(n < 0) return shiftr(x, -n);
}
if(n >= DIGITS) return 0;
return x << n;
}
template<std::unsigned_integral T, std::integral I>
constexpr T shiftr(const T x, const I n) {
constexpr int DIGITS = std::numeric_limits<T>::digits;
if constexpr(std::signed_integral<I>) {
if(n < 0) return shiftl(x, -n);
}
if(n >= DIGITS) return 0;
return x >> n;
}
template<std::unsigned_integral T, std::integral I = int>
inline constexpr bool bit(const T x, const I p) {
if constexpr(std::signed_integral<I>) assert(0 <= p);
assert(p < std::numeric_limits<T>::digits);
return shiftr(x, p) & T{1};
}
template<std::unsigned_integral T, std::integral I = int>
inline constexpr auto reset_bit(const T x, const I p) {
if constexpr(std::signed_integral<I>) assert(0 <= p);
assert(p < std::numeric_limits<T>::digits);
return x & ~(T{1} << p);
}
template<std::unsigned_integral T, std::integral I = int>
inline constexpr auto set_bit(const T x, const I p, const bool bit = true) {
if constexpr(std::signed_integral<I>) assert(0 <= p);
assert(p < std::numeric_limits<T>::digits);
if(!bit) return reset_bit(x, p);
return x | (T{1} << p);
}
template<std::unsigned_integral T, std::integral I = int>
inline constexpr T lower_bits(const T x, const I digits) {
if constexpr(std::signed_integral<I>) assert(0 <= digits);
assert(digits <= std::numeric_limits<T>::digits);
return x & (uni::shiftl(x, digits) - 1);
}
// Thanks to: https://noshi91.github.io/Library/other/select64.cpp
constexpr int select64(const u64 x0, u32 k) {
const u64 x1 = (x0 & UINT64_C(0x5555555555555555)) + (x0 >> 1 & UINT64_C(0x5555555555555555));
const u64 x2 = (x1 & UINT64_C(0x3333333333333333)) + (x1 >> 2 & UINT64_C(0x3333333333333333));
const u64 x3 = (x2 & UINT64_C(0x0F0F0F0F0F0F0F0F)) + (x2 >> 4 & UINT64_C(0x0F0F0F0F0F0F0F0F));
const u64 x4 = (x3 & UINT64_C(0x00FF00FF00FF00FF)) + (x3 >> 8 & UINT64_C(0x00FF00FF00FF00FF));
const u64 x5 = (x4 & UINT64_C(0x0000FFFF0000FFFF)) + (x4 >> 16 & UINT64_C(0x0000FFFF0000FFFF));
int res = 0;
u32 t;
t = x5 & 0xFFFFFFFF;
if(t <= k) k -= t, res += 32;
t = x4 >> res & 0xFFFF;
if(t <= k) k -= t, res += 16;
t = x3 >> res & 0xFF;
if(t <= k) k -= t, res += 8;
t = x2 >> res & 0xF;
if(t <= k) k -= t, res += 4;
t = x1 >> res & 0x3;
if(t <= k) k -= t, res += 2;
t = x0 >> res & 0x1;
if(t <= k) k -= t, res += 1;
return res;
}
namespace internal {
template<std::unsigned_integral T>
constexpr T binary_gcd(T a, T b) noexcept(NO_EXCEPT) {
if(!a || !b) return a | b;
T t, s = std::countr_zero(a | b);
a >>= std::countr_zero(a);
do {
b >>= std::countr_zero(b);
if(a > b) t = a, a = b, b = t;
b -= a;
} while(b);
return a << s;
}
template<std::signed_integral T>
inline constexpr T binary_gcd(const T a, const T b) noexcept(NO_EXCEPT) {
return binary_gcd(a < 0 ? -a : a, b < 0 ? -b : b);
}
} // namespace internal
template<std::integral T0, std::integral T1>
inline constexpr auto binary_gcd(T0 v0, T1 v1) noexcept(NO_EXCEPT) {
using common_type = std::common_type_t<T0, T1>;
return internal::binary_gcd(static_cast<common_type>(v0), static_cast<common_type>(v1));
}
template<std::unsigned_integral T, std::unsigned_integral S>
inline constexpr bool is_subset_of(T target, S superset) noexcept(NO_EXCEPT) {
return (target & ~superset) == 0;
}
template<std::unsigned_integral T, std::unsigned_integral S>
inline constexpr bool is_superset_of(T target, S subset) noexcept(NO_EXCEPT) {
return (~target & subset) == 0;
}
template<std::unsigned_integral S0, std::unsigned_integral S1>
inline constexpr auto comapre_as_bitset(S0 s0, S1 s1) noexcept(NO_EXCEPT) {
if(s0 == s1) return std::partial_ordering::equivalent;
if(is_subset_of(s0, s1)) return std::partial_ordering::less;
if(is_superset_of(s0, s1)) return std::partial_ordering::greater;
return std::partial_ordering::unordered;
}
} // namespace uni
#line 16 "numeric/modular/binary_reduction.hpp"
namespace uni {
namespace internal {
template<std::unsigned_integral Value>
struct binary_reduction {
using value_type = Value;
private:
value_type _mask;
public:
static constexpr int digits = std::numeric_limits<value_type>::digits;
static constexpr value_type max() noexcept { return std::numeric_limits<value_type>::max(); }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mask + 1; }
constexpr binary_reduction() noexcept = default;
constexpr explicit inline binary_reduction(const value_type mod) noexcept(NO_EXCEPT) : _mask(mod - 1) {
assert(std::has_single_bit(mod));
}
inline constexpr value_type reduce(const value_type v) const noexcept(NO_EXCEPT) { return v; }
inline constexpr value_type add(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return x + y;
}
inline constexpr value_type subtract(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return x - y;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return x * y;
}
template<std::integral K>
inline constexpr value_type pow(const value_type v, const K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mask == 0) return 0;
return uni::pow(v, p);
}
inline constexpr auto compare(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->revert(x) <=> this->revert(y);
}
constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) {
return v;
}
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
return static_cast<value_type>(v);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) {
return v & this->_mask;
}
};
} // namespace internal
using binary_reduction_32bit = internal::binary_reduction<u32>;
using binary_reduction_64bit = internal::binary_reduction<u64>;
using binary_reduction_128bit = internal::binary_reduction<u128>;
} // namespace uni
#line 2 "numeric/modular/barrett_reduction.hpp"
#line 8 "numeric/modular/barrett_reduction.hpp"
#line 11 "numeric/modular/barrett_reduction.hpp"
#line 14 "numeric/modular/barrett_reduction.hpp"
#line 2 "template/debug.hpp"
#ifdef LOCAL_JUDGE
#define DEBUGGER_ENABLED
#define DEBUGGER_COLORED_OUTPUT 1
#endif
#line 2 "debugger/debug.hpp"
#line 9 "debugger/debug.hpp"
#include <array>
#line 13 "debugger/debug.hpp"
#include <bitset>
#include <deque>
#include <queue>
#include <stack>
#line 22 "debugger/debug.hpp"
#include <iomanip>
#line 26 "debugger/debug.hpp"
#line 2 "numeric/int128.hpp"
#include <cctype>
#line 9 "numeric/int128.hpp"
#line 12 "numeric/int128.hpp"
#line 14 "numeric/int128.hpp"
namespace std {
template<class C, class S>
auto& operator>>(std::basic_istream<C, S>& in, uni::i128& v) noexcept(NO_EXCEPT) {
std::string str; in >> str;
v = 0;
bool negative = (str[0] == '-');
REP(d, std::ranges::next(str.begin(), negative), str.end()) {
assert(std::isdigit(*d));
v = v * 10 + *d - '0';
}
if(negative) v *= -1;
return in;
}
template<class C, class S>
auto& operator>>(std::basic_istream<C, S>& in, uni::u128& v) noexcept(NO_EXCEPT) {
std::string str; in >> str;
v = 0U;
assert(str[0] != '-');
REP(d, str.begin(), str.end()) {
assert(std::isdigit(*d));
v = v * 10U + *d - '0';
}
return in;
}
template<class C, class S>
auto& operator<<(std::basic_ostream<C, S>& out, uni::i128 v) noexcept(NO_EXCEPT) {
if(v == 0) return out << 0;
if(v < 0) out << '-', v *= -1;
std::string str;
while(v > 0) str += static_cast<char>(v%10) + '0', v /= 10;
std::reverse(str.begin(), str.end());
return out << str;
}
template<class C, class S>
auto& operator<<(std::basic_ostream<C, S>& out, uni::u128 v) noexcept(NO_EXCEPT) {
if(v == 0) return out << 0U;
std::string str;
while(v > 0) str += static_cast<char>(v%10U) + '0', v /= 10U;
std::reverse(str.begin(), str.end());
return out << str;
}
}
#line 29 "debugger/debug.hpp"
#line 2 "internal/resolving_rank.hpp"
namespace uni {
namespace internal {
template<int P> struct resolving_rank : resolving_rank<P-1> {};
template<> struct resolving_rank<0> {};
} // namespace internal
} // namespace uni
#line 34 "debugger/debug.hpp"
#include <typeinfo>
#include <cxxabi.h>
namespace debugger {
template<class T>
auto _debug (T&& val) -> decltype(val._debug()) {
return val._debug();
}
std::ostream *cdebug = &std::clog;
#ifdef DEBUGGER_COLORED_OUTPUT
constexpr std::string COLOR_LINE = "\033[3;35m";
constexpr std::string COLOR_IDENTIFIER = "\033[32m";
constexpr std::string COLOR_INIT = "\033[m";
constexpr std::string COLOR_STRING = "\033[33m";
constexpr std::string COLOR_TYPE = "\033[34m";
constexpr std::string COLOR_NUMERIC = "\033[36m";
constexpr std::string COLOR_LITERAL_OPERATOR = "\033[31m";
#else
constexpr std::string COLOR_LINE = "";
constexpr std::string COLOR_IDENTIFIER = "";
constexpr std::string COLOR_INIT = "";
constexpr std::string COLOR_STRING = "";
constexpr std::string COLOR_TYPE = "";
constexpr std::string COLOR_NUMERIC = "";
constexpr std::string COLOR_LITERAL_OPERATOR = "";
#endif
using Brackets = std::pair<std::string, std::string>;
template<class T>
std::string dump(T&&);
template<class T>
const std::string get_type_name(T&& val) {
const char* const name = typeid(std::forward<T>(val)).name();
int status = -4;
char* const demangled_name = abi::__cxa_demangle(name, NULL, NULL, &status);
std::string res{name};
if (status == 0) {
res = std::string(demangled_name);
free(demangled_name);
}
return COLOR_TYPE + res + COLOR_INIT;
}
struct debug_t : std::string {
using std::string::string;
debug_t(const std::string& str) {
this->assign(str);
}
};
template<size_t N, class T>
void dump_tuple_impl([[maybe_unused]] T&& val, std::stringstream &res) {
if constexpr(N < std::tuple_size_v<std::remove_cvref_t<T>>) {
res << dump(std::get<N>(val));
if constexpr(N < std::tuple_size_v<std::remove_cvref_t<T>> - 1) res << ", ";
dump_tuple_impl<N + 1>(std::forward<T>(val), res);
}
}
template<std::ranges::input_range R>
std::string dump_range_impl(R&& range, const Brackets& brcs = { "[", "]" }, const std::string& spl = ", ") {
std::stringstream res;
res << brcs.first << " ";
auto itr = std::ranges::begin(range);
auto end = std::ranges::end(std::forward<R>(range));
while(itr != end) {
if(std::ranges::next(itr) == end) res << dump(*itr) << " ";
else res << dump(*itr) << spl;
++itr;
}
res << brcs.second ;
return res.str();
}
std::string dump_debug_t(debug_t info) {
return info;
}
struct dump_primitive_like {
std::string operator()(std::nullptr_t) const {
return COLOR_INIT;
}
template<uni::internal::pointer T>
std::string operator()(const T ptr) const {
return dump(*ptr);
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::basic_string>
std::string operator()(T&& val) const {
std::stringstream res;
res << COLOR_STRING << "`" << val << "`" << COLOR_INIT;
return res.str();
}
std::string operator()(const char val) const {
std::stringstream res;
res << COLOR_STRING << "\'" << val << "\'" << COLOR_INIT;
return res.str();
}
std::string operator()(const char val[]) const {
std::stringstream res;
res << COLOR_STRING << "\"" << val << "\"" << COLOR_INIT;
return res.str();
}
std::string operator()(const unsigned char val) const {
std::stringstream res;
res << COLOR_NUMERIC << static_cast<int>(val) << COLOR_INIT;
return res.str();
}
std::string operator()(const bool val) const {
std::stringstream res;
res << COLOR_NUMERIC << (val ? "true" : "false" ) << COLOR_INIT;
return res.str();
}
template<uni::internal::arithmetic T>
std::string operator()(const T val) const {
std::stringstream res;
res << std::setprecision(std::numeric_limits<T>::digits10) << val;
auto str = res.str();
std::string dst = "";
while(str.length() > 3) {
dst = ',' + str.substr(str.length() - 3, 3) + dst;
str = str.substr(0, str.length() - 3);
}
return COLOR_NUMERIC + str + dst + COLOR_LITERAL_OPERATOR + uni::internal::literal_operator_v<T> + COLOR_INIT;
};
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::optional>
std::string operator()(T&& val) const {
if(val.has_value()) return dump(*val);
return COLOR_TYPE + "invalid" + COLOR_INIT;
}
};
struct dump_bitset {
template<std::size_t N>
std::string operator()(const std::bitset<N>& val) const {
std::stringstream res;
res << COLOR_NUMERIC << val.to_string() << COLOR_INIT;
return res.str();
}
};
struct dump_has_val {
template<class T>
requires requires (T val) { val.val(); }
std::string operator()(T&& val) const {
return dump(val.val());
}
};
struct dump_iterator {
template<std::input_or_output_iterator I>
std::string operator()(I&& itr) const {
return COLOR_TYPE + "<iterator> " + COLOR_INIT+ dump(*itr);
}
};
struct dump_wrapper {
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::map>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::multimap>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::unordered_map>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::unordered_multimap>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::set>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::multiset>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::unordered_set>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::unordered_multiset>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::valarray>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("[", "]"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::vector>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("[", "]"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::deque>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("[", "]"));
}
template<uni::internal::derived_from_template<std::queue> T>
std::string operator()(T val) const {
std::vector<typename T::value_type> vec;
while(!val.empty()) vec.emplace_back(val.front()), val.pop();
return dump_range_impl(vec, Brackets("<", ">"));
}
template<uni::internal::derived_from_template<std::stack> T>
std::string operator()(T val) const {
std::vector<typename T::value_type> vec;
while(!val.empty()) vec.emplace_back(val.top()), val.pop();
std::ranges::reverse(vec);
return dump_range_impl(vec, Brackets("<", ">"));
}
template<uni::internal::derived_from_template<std::priority_queue> T>
std::string operator()(T val) const {
std::vector<typename T::value_type> vec;
while(!val.empty()) vec.emplace_back(val.top()), val.pop();
return dump_range_impl(vec, Brackets("<", ">"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::pair>
std::string operator()(T&& val) const {
std::stringstream res;
res << "( " << dump(val.first) << ", " << dump(val.second) << " )";
return res.str();
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::tuple>
std::string operator()(T&& val) const {
std::stringstream res;
res << "( ";
dump_tuple_impl<0>(val, res);
res << " )";
return res.str();
}
};
struct dump_range {
template<std::ranges::input_range T>
std::string operator()(T&& val) const {
return dump_range_impl(val);
}
};
struct dump_loggable {
template<uni::internal::loggable T>
std::string operator()(T&& val) const {
auto res = _debug(val);
if constexpr(std::same_as<decltype(res), debug_t>) {
return res;
}
else {
return dump(res);
}
}
};
template<class T>
std::string dump(T&& val) {
if constexpr(std::same_as<std::remove_cvref_t<T>, debug_t>) {
// return "debug_t";
return dump_debug_t(std::forward<T>(val));
}
if constexpr(std::invocable<dump_primitive_like, T>) {
// return "primitive";
return dump_primitive_like{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_loggable, T>) {
// return "loggable";
return dump_loggable{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_has_val, T>) {
// return "has val";
return dump_has_val{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_bitset, T>) {
// return "bitset";
return dump_bitset{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_iterator, T>) {
// return "iterator";
return dump_iterator{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_wrapper, T>) {
// return "wrapper";
return dump_wrapper{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_range, T>) {;
// return "range";
return dump_range{}(std::forward<T>(val));
}
return "== dump error ==";
}
template<class T> void debug(T&& val, const std::string& endl) {
*cdebug << dump(val) << endl << std::flush;
}
constexpr std::string_view WHITESPACES = " \n\r\t\f\v";
std::string ltrim(const std::string &s)
{
size_t start = s.find_first_not_of(WHITESPACES);
return (start == std::string::npos) ? "" : s.substr(start);
}
std::string rtrim(const std::string &s)
{
size_t end = s.find_last_not_of(WHITESPACES);
return (end == std::string::npos) ? "" : s.substr(0, end + 1);
}
std::string trim(const std::string &s) {
return rtrim(ltrim(s));
}
std::vector<std::string> split(const std::string& str) {
static constexpr char SEPARATOR = ',';
static constexpr char ESCAPE = '\\';
static constexpr std::string_view QUOTATIONS = "\"\'";
static constexpr std::string_view PARENTHESES = "()[]{}<>";
static constexpr auto PARENTHESES_KINDS = std::ranges::size(PARENTHESES);
static_assert(PARENTHESES_KINDS % 2 == 0);
std::vector<std::string> res = { "" };
bool quoted = false;
std::array<int,(PARENTHESES_KINDS / 2)> enclosed = { 0 };
for(auto itr = std::ranges::begin(str); itr != std::ranges::end(str); ++itr) {
if(std::ranges::find(QUOTATIONS, *itr) != std::ranges::end(QUOTATIONS)) {
if(itr == std::ranges::begin(str) or *std::ranges::prev(itr) != ESCAPE) {
quoted ^= true;
}
}
if(const auto found = std::ranges::find(PARENTHESES, *itr); found != std::ranges::end(PARENTHESES)) {
if(not quoted) {
auto& target = enclosed[std::ranges::distance(std::begin(PARENTHESES), found) / 2];
target = std::max(0, target - static_cast<int>((std::ranges::distance(std::begin(PARENTHESES), found) % 2) * 2) + 1);
}
}
if(
not quoted
and static_cast<std::size_t>(std::ranges::count(enclosed, 0)) == std::ranges::size(enclosed)
and *itr == SEPARATOR
) {
res.push_back("");
}
else {
res.back() += *itr;
}
}
for(auto&& v : res) v = trim(v);
return res;
}
template<class Arg> void raw(std::nullptr_t, Arg&& arg) { *cdebug << std::forward<Arg>(arg) << std::flush; }
template<class Arg> void raw(Arg&& arg) { *cdebug << dump(std::forward<Arg>(arg)) << std::flush; }
void debug(const std::vector<std::string>, const size_t, const int, const std::string) { debug(nullptr, COLOR_INIT + "\n"); }
std::map<std::pair<std::string, int>, int> count;
template<class Head, class... Tail>
void debug(
const std::vector<std::string> args, const size_t idx,
const int line, const std::string path,
Head&& H, Tail&&... T
) {
if(idx == 0) {
std::string file = path.substr(path.find_last_of("/") + 1);
debug(nullptr, COLOR_LINE + file + " #" + std::to_string(line) + " (" + std::to_string(count[{ file, line }]++) + ")" + COLOR_INIT);
}
debug(nullptr, "\n - ");
const std::string content = dump(H);
const std::string type_name = get_type_name(std::forward<Head>(H));
debug(nullptr, COLOR_IDENTIFIER + args[idx] + COLOR_INIT + " : ");
debug(nullptr, content);
if(type_name.size() + content.size() >= 300) debug(nullptr, "\n ");
debug(nullptr, " " + type_name);
debug(args, idx + 1, 0, path, std::forward<Tail>(T)...);
}
} // namespace debugger
#line 13 "template/debug.hpp"
#ifdef DEBUGGER_ENABLED
#define debug(...) debugger::debug(debugger::split(#__VA_ARGS__), 0, __LINE__, __FILE__, __VA_ARGS__)
#define debug_(...) do { const std::string file = __FILE__; debugger::raw(nullptr, debugger::COLOR_LINE + file.substr(file.find_last_of("/") + 1) + " #" + std::to_string(__LINE__) + debugger::COLOR_INIT + " "); debugger::raw(__VA_ARGS__); debugger::raw(nullptr, debugger::COLOR_INIT + "\n"); } while(0);
#define DEBUG if constexpr(true)
#else
#define debug(...) ({ ; })
#define debug_(...) ({ ; })
#define DEBUG if constexpr(false)
#endif
#line 18 "numeric/modular/barrett_reduction.hpp"
namespace uni {
namespace internal {
template<std::unsigned_integral Value, std::unsigned_integral Large>
requires has_double_digits_of<Large, Value>
struct barrett_reduction {
using value_type = Value;
using large_type = Large;
private:
large_type _mod = 0, _mi;
inline constexpr std::pair<large_type,value_type> _reduce(const large_type v) const noexcept(NO_EXCEPT) {
large_type x = multiply_high(v, this->_mi);
return { x, static_cast<value_type>(v - x * this->_mod) };
}
public:
static constexpr int digits = std::numeric_limits<value_type>::digits - 1;
static constexpr value_type max() noexcept { return (value_type{ 1 } << barrett_reduction::digits) - 1; }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mod; }
constexpr barrett_reduction() noexcept = default;
constexpr explicit inline barrett_reduction(const value_type mod)
: _mod(mod), _mi(std::numeric_limits<large_type>::max() / mod + 1)
{
assert(0 < mod && mod <= barrett_reduction::max());
}
inline constexpr large_type quotient(const large_type v) const noexcept(NO_EXCEPT) {
const auto [ x, r ] = this->_reduce(v);
return static_cast<large_type>(this->_mod <= r ? x - 1 : x);
}
inline constexpr value_type reduce(const large_type v) const noexcept(NO_EXCEPT) {
const auto [ x, r ] = this->_reduce(v);
return static_cast<value_type>(this->_mod <= r ? r + this->_mod : r);
}
inline constexpr std::pair<large_type,value_type> divide(const large_type v) const noexcept(NO_EXCEPT) {
const auto [ x, r ] = this->_reduce(v);
if(this->_mod <= r) return { static_cast<large_type>(x - 1), static_cast<value_type>(r + this->_mod) };
return { static_cast<large_type>(x), static_cast<value_type>(r) };
}
inline constexpr value_type add(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
x += y;
if(x >= this->_mod) x -= this->_mod;
return x;
}
inline constexpr value_type subtract(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x < y) x += this->_mod;
x -= y;
return x;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->reduce(static_cast<large_type>(x) * static_cast<large_type>(y));
}
template<std::integral K>
inline constexpr value_type pow(const large_type v, const K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mod == 1) return 0;
return uni::pow(
this->reduce(v), p,
[&](const value_type x, const value_type y) noexcept(NO_EXCEPT) { return this->multiply(x, y); }
);
}
inline constexpr auto compare(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return x <=> y;
}
constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) { return v; }
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
using common_type = std::common_type_t<T, value_type>;
const common_type mod = static_cast<common_type>(this->_mod);
if(v > 0 && static_cast<common_type>(v) >= mod) {
if(static_cast<common_type>(v) <= barrett_reduction::max()) v = this->reduce(v);
else v %= mod;
}
if constexpr(std::signed_integral<T>) {
if(v < 0) {
if(static_cast<common_type>(-v) <= mod) v += mod;
else if(static_cast<common_type>(-v) <= barrett_reduction::max()) {
v = mod - this->reduce(static_cast<value_type>(-v - 1)) - 1;
}
else {
v %= mod;
if(v != 0) v += mod;
}
}
}
return static_cast<value_type>(v);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) { return this->reduce(v); }
};
} // namespace internal
using barrett_reduction_32bit = internal::barrett_reduction<u32, u64>;
using barrett_reduction_64bit = internal::barrett_reduction<u64, u128>;
} // namespace uni
#line 2 "numeric/modular/montgomery_reduction.hpp"
#line 7 "numeric/modular/montgomery_reduction.hpp"
#line 10 "numeric/modular/montgomery_reduction.hpp"
#line 16 "numeric/modular/montgomery_reduction.hpp"
namespace uni {
namespace internal {
template<std::unsigned_integral Value, std::unsigned_integral Large>
requires has_double_digits_of<Large, Value>
struct montgomery_reduction {
using value_type = Value;
using large_type = Large;
private:
value_type _mod = 0, _r2, _mp;
constexpr value_type _inv() const noexcept(NO_EXCEPT) {
value_type res = this->_mod;
while(this->_mod * res != 1) res *= value_type{ 2 } - this->_mod * res;
return res;
}
public:
static constexpr int digits = std::numeric_limits<value_type>::digits - 2;
static constexpr value_type max() noexcept { return (value_type{ 1 } << montgomery_reduction::digits) - 1; }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mod; }
value_type zero = 0;
value_type one;
constexpr montgomery_reduction() noexcept = default;
constexpr montgomery_reduction(const value_type mod) noexcept(NO_EXCEPT)
: _mod(mod), _r2(static_cast<value_type>(-static_cast<large_type>(mod) % mod)),
_mp(-this->_inv()), one(this->reduce(this->_r2))
{
assert((mod & 1) == 1);
assert(mod <= montgomery_reduction::max());
}
constexpr value_type reduce(const large_type v) const noexcept(NO_EXCEPT) {
return
static_cast<value_type>(
(
v + static_cast<large_type>(static_cast<value_type>(v) * this->_mp) * this->_mod
) >> std::numeric_limits<value_type>::digits
);
}
inline constexpr value_type add(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
x += y;
if(x >= (this->_mod << 1)) x -= (this->_mod << 1);
return x;
}
inline constexpr value_type subtract(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x < y) x += (this->_mod << 1);
x -= y;
return x;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->reduce(static_cast<large_type>(x) * static_cast<large_type>(y));
}
template<std::integral K>
inline constexpr value_type pow(const large_type v, const K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mod == 1) return 0;
return uni::pow(
v, p,
[&](const value_type x, const value_type y) noexcept(NO_EXCEPT) { return this->multiply(x, y); },
static_cast<large_type>(this->one)
);
}
inline constexpr value_type normalize(const value_type v) const noexcept(NO_EXCEPT) {
assert(0 <= v && v < (this->_mod << 1));
if(v < this->_mod) return v;
return v - this->_mod;
}
inline constexpr auto compare(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->normalize(x) <=> this->normalize(y);
}
inline constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
return this->multiply(v, this->_r2);
}
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
using common_type = std::common_type_t<T, value_type>;
const common_type mod2 = static_cast<common_type>(this->_mod << 1);
if(v > 0 && static_cast<common_type>(v) >= mod2) {
v %= mod2;
}
if constexpr(std::is_signed_v<T>) {
if(v < 0 && static_cast<common_type>(-v) >= mod2) {
v %= mod2;
if(v != 0) v += mod2;
}
}
return this->multiply(v, this->_r2);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) {
return this->normalize(this->reduce(v));
}
};
// Thanks to: https://www.mathenachia.blog/even-mod-montgomery-impl/
template<std::unsigned_integral Value, std::unsigned_integral Large>
requires has_double_digits_of<Large, Value>
struct arbitrary_montgomery_reduction {
using value_type = Value;
using large_type = Large;
private:
using context = arbitrary_montgomery_reduction;
static constexpr int width = std::numeric_limits<value_type>::digits;
value_type _mod = 0;
int _tz;
value_type _m0;
large_type _m0i, _mask;
value_type _r2;
constexpr large_type _inv() const noexcept(NO_EXCEPT) {
large_type res = this->_m0;
while(((this->_m0 * res) & this->_mask) != 1) res *= large_type{ 2 } - this->_m0 * res;
return res & this->_mask;
}
constexpr value_type _m0ip() const noexcept(NO_EXCEPT) {
if(this->_tz == 0) return 0;
value_type res = this->_m0;
const value_type mask = (value_type{ 1 } << this->_tz) - 1;
while(((this->_m0 * res) & mask) != 1) res *= value_type{ 2 } - this->_m0 * res;
return res & mask;
}
public:
static constexpr int digits = std::numeric_limits<value_type>::digits - 2;
static constexpr value_type max() noexcept { return (value_type{ 1 } << context::digits) - 1; }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mod; }
value_type one;
constexpr arbitrary_montgomery_reduction() noexcept = default;
constexpr arbitrary_montgomery_reduction(value_type m) noexcept(NO_EXCEPT) {
assert(0 < m);
if(this->_mod == m) return;
this->_mod = m;
this->_tz = std::countr_zero(m);
this->_m0 = m >> this->_tz;
assert(this->_mod < context::max());
this->_mask = (large_type{ 1 } << (context::width + this->_tz)) - 1;
this->_m0i = this->_inv();
{
const value_type x = (std::numeric_limits<large_type>::max() % this->_m0) + 1;
const value_type mask = (value_type{ 1 } << this->_tz) - 1;
this->_r2 = (x + ((((large_type{ 1 } - x) * this->_m0ip()) & mask) * this->_m0));
}
this->one = this->reduce(this->_r2);
}
constexpr value_type reduce(const large_type v) const noexcept(NO_EXCEPT) {
const value_type res =
static_cast<value_type>(
(
v +
this->_m0 *
((((v << std::numeric_limits<value_type>::digits) - v) * this->_m0i) & this->_mask)
) >> std::numeric_limits<value_type>::digits
);
return res;
}
inline constexpr value_type add(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
x += y;
if(x >= (this->_mod << 1)) x -= (this->_mod << 1);
return x;
}
inline constexpr value_type subtract(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x < y) x += (this->_mod << 1);
x -= y;
return x;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->reduce(static_cast<large_type>(x) * static_cast<large_type>(y));
}
template<std::integral K>
inline constexpr value_type pow(const large_type v, K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mod == 1) return 0;
return uni::pow(
v, p,
[&](const value_type x, const value_type y) noexcept(NO_EXCEPT) { return this->multiply(x, y); },
static_cast<large_type>(this->one)
);
}
inline constexpr value_type normalize(const value_type v) const noexcept(NO_EXCEPT) {
assert(0 <= v && v < (this->_mod << 1));
if(v < this->_mod) return v;
return v - this->_mod;
}
inline constexpr auto compare(const large_type x, const large_type y) const noexcept(NO_EXCEPT) {
return this->normalize(x) <=> this->normalize(y);
}
inline constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
return this->multiply(v, this->_r2);
}
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
using common_type = std::common_type_t<T, value_type>;
const common_type mod2 = static_cast<common_type>(this->_mod << 1);
if(v > 0 && static_cast<common_type>(v) >= mod2) {
v %= mod2;
}
if constexpr(std::signed_integral<T>) {
if(v < 0) {
if(static_cast<common_type>(-v) >= mod2) v %= mod2;
if(v < 0) v += mod2;
}
}
return this->multiply(v, this->_r2);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) {
return this->normalize(this->reduce(v));
}
};
} // namespace internal
using montgomery_reduction_32bit = internal::montgomery_reduction<u32, u64>;
using montgomery_reduction_64bit = internal::montgomery_reduction<u64, u128>;
using arbitrary_montgomery_reduction_32bit = internal::arbitrary_montgomery_reduction<u32, u64>;
using arbitrary_montgomery_reduction_64bit = internal::arbitrary_montgomery_reduction<u64, u128>;
} // namespace uni
#line 16 "numeric/modular/modint_interface.hpp"
namespace uni {
namespace internal {
template<class T>
concept modint_family =
numeric<T> &&
has_static_one<T> && has_static_zero<T> &&
requires (T v, i64 p, typename T::value_type x) {
{ v.pow(p) } -> std::same_as<T>;
{ v.inv() } -> std::same_as<T>;
{ T::raw(x) } -> std::same_as<T>;
{ v.val() } -> std::same_as<typename T::value_type>;
{ T::mod() } -> std::same_as<typename T::value_type>;
{ T::max() } -> std::same_as<typename T::value_type>;
T::digits;
T::context::dynamic;
};
template<class T>
concept dynamic_modint_family =
modint_family<T> &&
T::context::dynamic &&
requires (typename T::value_type v) {
T::set_mod(v);
};
template<class T>
concept static_modint_family =
modint_family<T> &&
(!T::context::dynamic); //&&
// requires {
// T::is_prime;
// };
template<class T>
concept modular_reduction =
std::default_initializable<T> &&
std::constructible_from<T, typename T::value_type> &&
requires (T v, typename T::value_type x, i64 p) {
typename T::value_type;
T::digits;
{ T::max() } -> std::same_as<typename T::value_type>;
{ v.mod() } -> std::same_as<typename T::value_type>;
{ v.reduce(x) } -> std::same_as<typename T::value_type>;
{ v.add(x, x) } -> std::same_as<typename T::value_type>;
{ v.subtract(x, x) } -> std::same_as<typename T::value_type>;
{ v.multiply(x, x) } -> std::same_as<typename T::value_type>;
{ v.multiply(x, x) } -> std::same_as<typename T::value_type>;
{ v.pow(x, p) } -> std::same_as<typename T::value_type>;
{ v.convert_raw(x) } -> std::same_as<typename T::value_type>;
{ v.convert(x) } -> std::same_as<typename T::value_type>;
{ v.revert(x) } -> std::same_as<typename T::value_type>;
v.compare(x, x);
};
template<class T>
concept modular_context =
requires {
typename T::reductor;
typename T::value_type;
T::reduction;
};
} // namespace internal
template<internal::modular_reduction Reduction, typename Reduction::value_type Mod>
struct static_modular_context {
using reductor = Reduction;
using value_type = typename reductor::value_type;
static constexpr bool dynamic = false;
static constexpr reductor reduction = reductor(Mod);
private:
using context = static_modular_context;
};
template<internal::modular_reduction Reduction, i64 Id>
struct dynamic_modular_context {
using reductor = Reduction;
using value_type = typename reductor::value_type;
static constexpr bool dynamic = true;
static inline reductor reduction;
private:
using context = dynamic_modular_context;
public:
static constexpr void set_mod(const value_type mod) noexcept(NO_EXCEPT) { context::reduction = reductor(mod); }
};
template<internal::modular_context> struct modint;
template<u32 Mod> using static_builtin_modular_context_32bit = static_modular_context<builtin_reduction_32bit, Mod>;
template<u64 Mod> using static_builtin_modular_context_64bit = static_modular_context<builtin_reduction_64bit, Mod>;
template<u32 Mod> using static_barrett_modular_context_32bit = static_modular_context<barrett_reduction_32bit, Mod>;
template<u64 Mod> using static_barrett_modular_context_64bit = static_modular_context<barrett_reduction_64bit, Mod>;
template<u32 Mod> using static_montgomery_modular_context_32bit = static_modular_context<montgomery_reduction_32bit, Mod>;
template<u64 Mod> using static_montgomery_modular_context_64bit = static_modular_context<montgomery_reduction_64bit, Mod>;
template<u32 Mod> using static_arbitrary_montgomery_modular_context_32bit = static_modular_context<arbitrary_montgomery_reduction_32bit, Mod>;
template<u64 Mod> using static_arbitrary_montgomery_modular_context_64bit = static_modular_context<arbitrary_montgomery_reduction_64bit, Mod>;
template<u32 Mod> using static_binary_modular_context_32bit = static_modular_context<binary_reduction_32bit, Mod>;
template<u64 Mod> using static_binary_modular_context_64bit = static_modular_context<binary_reduction_64bit, Mod>;
template<u128 Mod> using static_binary_modular_context_128bit = static_modular_context<binary_reduction_128bit, Mod>;
template<u32 Mod> using static_builtin_modint_32bit = modint<static_builtin_modular_context_32bit<Mod>>;
template<u64 Mod> using static_builtin_modint_64bit = modint<static_builtin_modular_context_64bit<Mod>>;
template<u32 Mod> using static_barrett_modint_32bit = modint<static_barrett_modular_context_32bit<Mod>>;
template<u64 Mod> using static_barrett_modint_64bit = modint<static_barrett_modular_context_64bit<Mod>>;
template<u32 Mod> using static_montgomery_modint_32bit = modint<static_montgomery_modular_context_32bit<Mod>>;
template<u64 Mod> using static_montgomery_modint_64bit = modint<static_montgomery_modular_context_64bit<Mod>>;
template<u32 Mod> using static_arbitrary_montgomery_modint_32bit = modint<static_arbitrary_montgomery_modular_context_32bit<Mod>>;
template<u64 Mod> using static_arbitrary_montgomery_modint_64bit = modint<static_arbitrary_montgomery_modular_context_64bit<Mod>>;
template<u32 Mod> using static_binary_modint_32bit = modint<static_binary_modular_context_32bit<Mod>>;
template<u64 Mod> using static_binary_modint_64bit = modint<static_binary_modular_context_64bit<Mod>>;
template<u128 Mod> using static_binary_modint_128bit = modint<static_binary_modular_context_128bit<Mod>>;
template<i64 Id> using dynamic_builtin_modular_context_32bit = dynamic_modular_context<builtin_reduction_32bit, Id>;
template<i64 Id> using dynamic_builtin_modular_context_64bit = dynamic_modular_context<builtin_reduction_64bit, Id>;
template<i64 Id> using dynamic_barrett_modular_context_32bit = dynamic_modular_context<barrett_reduction_32bit, Id>;
template<i64 Id> using dynamic_barrett_modular_context_64bit = dynamic_modular_context<barrett_reduction_64bit, Id>;
template<i64 Id> using dynamic_montgomery_modular_context_32bit = dynamic_modular_context<montgomery_reduction_32bit, Id>;
template<i64 Id> using dynamic_montgomery_modular_context_64bit = dynamic_modular_context<montgomery_reduction_64bit, Id>;
template<i64 Id> using dynamic_arbitrary_montgomery_modular_context_32bit = dynamic_modular_context<arbitrary_montgomery_reduction_32bit, Id>;
template<i64 Id> using dynamic_arbitrary_montgomery_modular_context_64bit = dynamic_modular_context<arbitrary_montgomery_reduction_64bit, Id>;
template<i64 Id> using dynamic_binary_modular_context_32bit = dynamic_modular_context<binary_reduction_32bit, Id>;
template<i64 Id> using dynamic_binary_modular_context_64bit = dynamic_modular_context<binary_reduction_64bit, Id>;
template<i64 Id> using dynamic_binary_modular_context_128bit = dynamic_modular_context<binary_reduction_128bit, Id>;
template<i64 Id> using dynamic_builtin_modint_32bit = modint<dynamic_builtin_modular_context_32bit<Id>>;
template<i64 Id> using dynamic_builtin_modint_64bit = modint<dynamic_builtin_modular_context_64bit<Id>>;
template<i64 Id> using dynamic_barrett_modint_32bit = modint<dynamic_barrett_modular_context_32bit<Id>>;
template<i64 Id> using dynamic_barrett_modint_64bit = modint<dynamic_barrett_modular_context_64bit<Id>>;
template<i64 Id> using dynamic_montgomery_modint_32bit = modint<dynamic_montgomery_modular_context_32bit<Id>>;
template<i64 Id> using dynamic_montgomery_modint_64bit = modint<dynamic_montgomery_modular_context_64bit<Id>>;
template<i64 Id> using dynamic_arbitrary_montgomery_modint_32bit = modint<dynamic_arbitrary_montgomery_modular_context_32bit<Id>>;
template<i64 Id> using dynamic_arbitrary_montgomery_modint_64bit = modint<dynamic_arbitrary_montgomery_modular_context_64bit<Id>>;
template<i64 Id> using dynamic_binary_modint_32bit = modint<dynamic_binary_modular_context_32bit<Id>>;
template<i64 Id> using dynamic_binary_modint_64bit = modint<dynamic_binary_modular_context_64bit<Id>>;
template<i64 Id> using dynamic_binary_modint_128bit = modint<dynamic_binary_modular_context_128bit<Id>>;
template<u32 Mod> using static_modint_32bit = static_builtin_modint_32bit<Mod>;
template<u64 Mod> using static_modint_64bit = static_builtin_modint_64bit<Mod>;
using modint998244353 = static_modint_32bit<998244353>;
using modint1000000007 = static_modint_32bit<1000000007>;
using modint_32 = dynamic_barrett_modint_32bit<-1>;
using modint_64 = dynamic_barrett_modint_64bit<-1>;
template<const unsigned Val, const unsigned Mod = 998244353>
const uni::static_modint_32bit<Mod> MINT = Val;
template<const unsigned Val, const unsigned Mod = 998244353>
const unsigned INV = uni::static_modint_32bit<Mod>{ Val }.inv().val();
template<const unsigned Val, const unsigned Mod = 998244353>
const int SINV = uni::static_modint_32bit<Mod>{ Val }.inv().val();
} // namespace uni
#line 13 "numeric/internal/primality_test.hpp"
namespace uni {
namespace internal {
//Thanks to: https://github.com/NyaanNyaan/library/blob/master/prime/fast-factorize.hpp
namespace fast_factorize_impl {
namespace internal {
// Miller-Rabin primality test
template<modint_family Mint>
constexpr bool primality_test(const u64 n, const std::vector<u64>& ws) noexcept(NO_EXCEPT) {
if constexpr(dynamic_modint_family<Mint>) Mint::set_mod(n);
assert(Mint::mod() == n);
const u64 d = (n - 1) >> std::countr_zero(n - 1);
const Mint rev = n - 1;
for(u64 w : ws) {
Mint x = w;
if(x == Mint::zero) continue;
x = x.pow(d);
if(x == Mint::one || x == rev) continue;
u64 t = d;
while(t != n - 1 && x != Mint::one && x != rev) x *= x, t <<= 1;
if(x != rev) return false;
}
return true;
}
// Thanks to: https://miller-rabin.appspot.com/
template<modint_family Small, modint_family Large = Small>
inline constexpr bool is_prime(const u64 n) noexcept(NO_EXCEPT) {
if(n == 0 || n == 1) return false;
if(~n & 1UL) return n == 2UL;
auto bases = [&]() constexpr noexcept(NO_EXCEPT) -> vector<u64> {
if(n < 341531UL) return { 9345883071009581737UL };
else if(n < 1050535501UL) return { 336781006125UL, 9639812373923155UL };
else if(n < 350269456337UL) return { 4230279247111683200UL, 14694767155120705706UL, 16641139526367750375UL };
else if(n < 55245642489451UL) return { 2UL, 141889084524735UL, 1199124725622454117UL, 11096072698276303650UL };
else if(n < 7999252175582851UL) return { 2UL, 4130806001517UL, 149795463772692060UL, 186635894390467037UL, 3967304179347715805UL };
else if(n < 585226005592931977UL) return { 2UL, 123635709730000UL, 9233062284813009UL, 43835965440333360UL, 761179012939631437UL, 1263739024124850375UL };
else return { 2UL, 325UL, 9375UL, 28178UL, 450775UL, 9780504UL, 1795265022UL };
};
if(n <= Small::max()) return primality_test<Small>(n, bases());
else return primality_test<Large>(n, bases());
}
} // namespace internal
} // namespace fast_factorize_impl
using fast_factorize_impl::internal::is_prime;
} // namespace internal
} // namespace uni
#line 2 "numeric/internal/factorize.hpp"
#line 10 "numeric/internal/factorize.hpp"
#include <random>
#line 12 "numeric/internal/factorize.hpp"
#line 15 "numeric/internal/factorize.hpp"
#line 17 "numeric/internal/factorize.hpp"
#line 21 "numeric/internal/factorize.hpp"
#line 2 "random/engine.hpp"
#line 7 "random/engine.hpp"
#line 9 "random/engine.hpp"
#line 12 "random/engine.hpp"
#line 14 "random/engine.hpp"
#line 2 "hash/general_hasher.hpp"
#line 7 "hash/general_hasher.hpp"
#line 11 "hash/general_hasher.hpp"
#line 13 "hash/general_hasher.hpp"
namespace uni {
template<std::unsigned_integral R, std::integral T>
constexpr R shrink(T x) noexcept(NO_EXCEPT) {
constexpr int DIGITS_R = std::numeric_limits<R>::digits;
constexpr int DIGITS_T = std::numeric_limits<R>::digits;
REPD(digits, DIGITS_R, DIGITS_T, DIGITS_R) {
x = (x >> digits) ^ uni::lower_bits(x, digits);
}
return x;
}
// Thanks to: https://gist.github.com/badboy/6267743
template<class T>
constexpr u32 hash32(T x) {
if constexpr(std::integral<T>) {
if constexpr(std::signed_integral<T>) return hash32(to_unsigned(x));
constexpr int DIGITS_T = std::numeric_limits<T>::digits;
if constexpr(DIGITS_T <= 32) {
auto h = static_cast<u32>(x);
h = ~h + (h << 15);
h ^= (h >> 12);
h += (h << 2);
h ^= (h >> 4);
h *= 2057;
h ^= (h >> 16);
return h;
}
else if constexpr(DIGITS_T <= 64) {
auto h = static_cast<u64>(x);
h = (~h) + (h << 18);
h ^= (h >> 31);
h *= 21;
h ^= (h >> 11);
h += (h << 6);
h ^= (h >> 22);
return static_cast<u32>(h);
}
else {
return hash32(hash64(x));
}
}
else {
return hash32(std::hash<T>{}(x));
}
}
template<class T>
constexpr u64 hash64(T x) {
if constexpr(std::integral<T>) {
if constexpr(std::signed_integral<T>) return hash64(to_unsigned(x));
constexpr int DIGITS_T = std::numeric_limits<T>::digits;
if constexpr(DIGITS_T <= 64) {
auto h = static_cast<u64>(x);
h = (~h) + (h << 21);
h ^= (h >> 24);
h *= 265;
h ^= (h >> 14);
h *= 21;
h ^= (h >> 28);
h += h << 31;
return h;
}
else {
return hash64(shrink<u64>(x));
}
}
else {
return hash64(std::hash<T>{}(x));
}
}
template<class T>
struct hash {
inline constexpr auto operator()(const T& key) const noexcept(NO_EXCEPT) {
return static_cast<std::size_t>(uni::hash64(key));
}
};
} // namespace uni
#line 16 "random/engine.hpp"
// Thanks to: https://prng.di.unimi.it/
namespace uni {
namespace internal {
template<class Derived, class ResultType>
struct random_engine {
using result_type = ResultType;
static constexpr result_type MIN = std::numeric_limits<result_type>::min();
static constexpr result_type MAX = std::numeric_limits<result_type>::max();
static constexpr result_type min() noexcept(NO_EXCEPT) { return MIN; }
static constexpr result_type max() noexcept(NO_EXCEPT) { return MAX; }
template<std::unsigned_integral T = result_type>
constexpr random_engine(const T _seed = 0) noexcept(NO_EXCEPT) {
static_cast<Derived*>(this)->seed(_seed);
};
inline constexpr result_type operator()() noexcept(NO_EXCEPT) {
return static_cast<Derived*>(this)->next();
}
};
const i64 INTERNAL_RANDOM_GENERATOR_ID = -(1UL << 60);
}; // namespace internal
constexpr float to_float(const std::uint32_t x) noexcept(NO_EXCEPT) {
return float(x >> 8) * 0x1.0p-24f;
}
constexpr double to_double(const std::uint64_t x) noexcept(NO_EXCEPT) {
return double(x >> 11) * 0x1.0p-53;
}
struct mulberry32 : internal::random_engine<mulberry32, std::uint32_t> {
using internal::random_engine<mulberry32, std::uint32_t>::random_engine;
private:
std::uint32_t _x;
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T x) noexcept(NO_EXCEPT) { this->_x = x; }
inline constexpr std::uint32_t next() noexcept(NO_EXCEPT) {
std::uint32_t z = (this->_x += 0x6D2B79F5U);
z = (z ^ (z >> 15)) * (z | 1U);
z ^= z + (z ^ (z >> 7)) * (z | 61U);
return static_cast<std::uint32_t>(z ^ (z >> 14));
}
};
struct splitmix64 : internal::random_engine<splitmix64, std::uint64_t> {
using internal::random_engine<splitmix64, std::uint64_t>::random_engine;
private:
std::uint64_t _x;
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T x) noexcept(NO_EXCEPT) { this->_x = x; }
inline constexpr std::uint64_t next() noexcept(NO_EXCEPT) {
std::uint64_t z = (this->_x += 0x9e3779b97f4a7c15);
z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
return z ^ (z >> 31);
}
};
// xoroshiro64**
struct xoroshiro64ss : internal::random_engine<xoroshiro64ss, std::uint32_t> {
using internal::random_engine<xoroshiro64ss, std::uint32_t>::random_engine;
private:
std::uint32_t s[2];
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T _seed) noexcept(NO_EXCEPT) {
mulberry32 gen32(hash32(_seed));
this->s[0] = gen32();
this->s[1] = gen32();
}
inline constexpr std::uint32_t next() noexcept(NO_EXCEPT) {
const std::uint32_t s0 = this->s[0];
std::uint32_t s1 = this->s[1];
const std::uint32_t res = std::rotl(s0 * 0x9E3779BBU, 5) * 5;
s1 ^= s0;
this->s[0] = std::rotl(s0, 26) ^ s1 ^ (s1 << 9);
this->s[1] = std::rotl(s1, 13);
return res;
}
};
struct xoroshiro128ss : internal::random_engine<xoroshiro128ss, std::uint64_t> {
using internal::random_engine<xoroshiro128ss, std::uint64_t>::random_engine;
private:
std::uint64_t s[2];
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T _seed) noexcept(NO_EXCEPT) {
splitmix64 gen64(hash32(_seed));
this->s[0] = gen64();
this->s[1] = gen64();
}
inline constexpr std::uint64_t next() noexcept(NO_EXCEPT) {
const uint64_t s0 = this->s[0];
uint64_t s1 = this->s[1];
const uint64_t res = std::rotl(s0 * 5, 7) * 9;
s1 ^= s0;
this->s[0] = std::rotl(s0, 24) ^ s1 ^ (s1 << 16);
this->s[1] = std::rotl(s1, 37);
return res;
}
};
struct xoroshiro128pp : internal::random_engine<xoroshiro128pp, std::uint64_t> {
using internal::random_engine<xoroshiro128pp, std::uint64_t>::random_engine;
private:
std::uint64_t s[2];
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T _seed) noexcept(NO_EXCEPT) {
splitmix64 gen64(hash32(_seed));
this->s[0] = gen64();
this->s[1] = gen64();
}
inline constexpr std::uint64_t next() noexcept(NO_EXCEPT) {
const std::uint64_t s0 = this->s[0];
std::uint64_t s1 = this->s[1];
const std::uint64_t res = std::rotl(s0 + s1, 17) + s0;
s1 ^= s0;
this->s[0] = std::rotl(s0, 49) ^ s1 ^ (s1 << 21); // a, b
this->s[1] = std::rotl(s1, 28); // c
return res;
}
};
// xoroshiro128+
struct xoroshiro128p : internal::random_engine<xoroshiro128p, std::uint64_t> {
using internal::random_engine<xoroshiro128p, std::uint64_t>::random_engine;
private:
std::uint64_t s[2];
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T _seed) noexcept(NO_EXCEPT) {
splitmix64 gen64(hash64(_seed));
this->s[0] = gen64();
this->s[1] = gen64();
}
inline constexpr std::uint64_t next() noexcept(NO_EXCEPT) {
const std::uint64_t s0 = this->s[0];
std::uint64_t s1 = this->s[1];
const std::uint64_t res = s0 + s1;
s1 ^= s0;
this->s[0] = std::rotl(s0, 24) ^ s1 ^ (s1 << 16);
this->s[1] = std::rotl(s1, 37);
return res;
}
};
struct xoroshiro64s : internal::random_engine<xoroshiro64s, std::uint32_t> {
using internal::random_engine<xoroshiro64s, std::uint32_t>::random_engine;
private:
std::uint32_t s[2];
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T _seed) noexcept(NO_EXCEPT) {
mulberry32 gen32(hash32(_seed));
this->s[0] = gen32();
this->s[1] = gen32();
}
inline constexpr std::uint32_t next() noexcept(NO_EXCEPT) {
const std::uint32_t s0 = s[0];
std::uint32_t s1 = s[1];
const std::uint32_t res = s0 * 0x9E3779BB;
s1 ^= s0;
s[0] = std::rotl(s0, 26) ^ s1 ^ (s1 << 9);
s[1] = std::rotl(s1, 13);
return res;
}
};
using random_engine_32bit = xoroshiro64ss;
using random_engine_64bit = xoroshiro128pp;
using random_engine_float = xoroshiro64s;
using random_engine_double = xoroshiro128p;
random_engine_32bit randi32;
random_engine_64bit randi64;
float randf() {
static random_engine_float gen;
return to_float(gen());
}
double randd() {
static random_engine_double gen;
return to_double(gen());
}
} // namespace uni
#line 23 "numeric/internal/factorize.hpp"
namespace uni {
namespace internal {
//Thanks to: https://github.com/NyaanNyaan/library/blob/master/prime/fast-factorize.hpp
namespace fast_factorize_impl {
namespace internal {
// Pollard's rho algorithm
template<modint_family Mint, class T>
T find_factor(const T n) noexcept(NO_EXCEPT) {
if(~n & 1) return 2;
if(is_prime<Mint>(n)) return n;
assert(static_cast<u64>(Mint::mod()) == n);
Mint rr;
auto f = [&](const Mint& x) noexcept(NO_EXCEPT) { return x * x + rr; };
static random_engine_64bit rand(std::random_device{}());
auto rand_ = [&]() noexcept(NO_EXCEPT) { return rand() % (n - 2) + 2; };
while(true) {
Mint x, y, ys, q = Mint::one;
rr = rand_(), y = rand_();
T g = 1;
constexpr int m = 128;
for(int r = 1; g == 1; r <<= 1) {
x = y;
for(int i = 0; i < r; ++i) y = f(y);
for(int k = 0; g == 1 && k < r; k += m) {
ys = y;
for(int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
g = uni::binary_gcd(q.val(), n);
}
}
if(g == n) {
do {
g = uni::binary_gcd((x - (ys = f(ys))).val(), n);
} while(g == 1);
}
if(g != n) return g;
}
assert(false);
}
template<modint_family Small, modint_family Large, class R>
void factorize(const u64 n, R *const res) noexcept(NO_EXCEPT) {
if(n <= 1) return;
u64 p;
if constexpr(std::same_as<Small, Large>) p = find_factor<Small, typename Small::value_type>(n);
else {
if(n <= Small::max()) p = find_factor<Small, typename Small::value_type>(n);
else p = find_factor<Large, typename Large::value_type>(n);
}
if(p == static_cast<u64>(n)) {
res->emplace_back(p);
return;
}
factorize<Small, Large>(p, res);
factorize<Small, Large>(n / p, res);
}
} // namespace internal
} // namespace fast_factorize_impl
using fast_factorize_impl::internal::factorize;
} // namespace internal
} // namespace uni
#line 2 "numeric/internal/divisors.hpp"
#line 8 "numeric/internal/divisors.hpp"
#line 12 "numeric/internal/divisors.hpp"
namespace uni {
namespace internal {
//Thanks to: https://github.com/NyaanNyaan/library/blob/master/prime/fast-factorize.hpp
template<modint_family Small, modint_family Large, class R>
void divisors(const u64 n, R *const res) noexcept(NO_EXCEPT) {
if(n == 0) return;
std::vector<u64> facts; factorize<Small, Large>(n, &facts);
std::ranges::sort(facts);
std::vector<std::pair<u64, int>> v;
for(auto &p : facts) {
if(v.empty() || v.back().first != p) {
v.emplace_back(p, 1);
} else {
v.back().second++;
}
}
using value_type = std::ranges::range_value_t<R>;
const auto size = std::ranges::ssize(v);
auto f = [&](auto rc, int i, value_type x) noexcept(NO_EXCEPT) -> void {
if(i == size) {
res->push_back(x);
return;
}
for(int j = v[i].second; ; --j) {
rc(rc, i + 1, x);
if(j == 0) break;
x *= static_cast<value_type>(v[i].first);
}
};
f(f, 0, 1);
}
} // namespace internal
} // namespace uni
#line 2 "numeric/internal/primitive_root.hpp"
#line 8 "numeric/internal/primitive_root.hpp"
#line 11 "numeric/internal/primitive_root.hpp"
#line 13 "numeric/internal/primitive_root.hpp"
#line 16 "numeric/internal/primitive_root.hpp"
#line 18 "numeric/internal/primitive_root.hpp"
namespace uni {
namespace internal {
// Thanks to: https://37zigen.com/primitive-root/
template<modint_family Small, modint_family Large, modint_family Mint, std::unsigned_integral T>
T primitive_root(const T p) noexcept(NO_EXCEPT) {
std::vector<T> pows;
factorize<Small, Large>(p - 1, &pows);
{
std::ranges::sort(pows);
const auto rest = std::ranges::unique(pows);
pows.erase(ALL(rest));
}
ITRR(pow, pows) pow = (p - 1) / pow;
if constexpr(dynamic_modint_family<Mint>) Mint::set_mod(p);
assert(Mint::mod() == p);
static random_engine_64bit rand;
while(true) {
const Mint x = rand();
if(x == Mint::zero) continue;
bool ok = true;
ITR(pow, pows) {
if(x.pow(pow) == Mint::one) {
ok = false;
break;
}
}
if(ok) return x.val();
}
return 0;
}
// Thanks to: atcoder::internal::primitive_root_constexpr
template<static_modint_family Mint>
constexpr u32 primitive_root_constexpr(u32 m) {
assert(Mint::mod() == m);
u32 divs[20]{}; divs[0] = 2;
u32 cnt = 1;
u64 x = (m - 1) / 2;
while(x % 2 == 0) x /= 2;
for(u64 i = 3; i * i <= x; i += 2) {
if(x % i == 0) {
divs[cnt++] = i;
while(x % i == 0) x /= i;
}
}
if(x > 1) divs[cnt++] = x;
for(u32 g = 2; ; g++) {
bool ok = true;
REP(i, cnt) {
if(Mint{ g }.pow((m - 1) / divs[i]) == 1) {
ok = false;
break;
}
}
if(ok) return g;
}
}
template<modint_family Small, modint_family Large = Small, std::integral Res = u64, bool FORCE_RANDOM = false>
constexpr Res primitive_root(const u64 p) noexcept(NO_EXCEPT) {
if constexpr(!FORCE_RANDOM) {
if(p == 2) return 1;
if(p == 167772161) return 3;
if(p == 469762049) return 3;
if(p == 754974721) return 11;
if(p == 998244353) return 3;
if(p == (UINT64_C(1) << 61) - 1) return 37;
}
if(std::is_constant_evaluated()) {
if constexpr(static_modint_family<Small> && std::same_as<Small, Large> && Small::mod() < (1U << 31)) {
assert(p <= std::numeric_limits<u32>::max());
return primitive_root_constexpr<Small>(p);
}
assert(false);
}
else {
if(p <= Small::max()) return primitive_root<Small, Large, Small, typename Small::value_type>(p);
else return primitive_root<Small, Large, Large, typename Large::value_type>(p);
}
}
} // namespace internal
} // namespace uni
#line 2 "numeric/modular/modint.hpp"
#line 7 "numeric/modular/modint.hpp"
#line 10 "numeric/modular/modint.hpp"
#line 13 "numeric/modular/modint.hpp"
#line 15 "numeric/modular/modint.hpp"
#line 17 "numeric/modular/modint.hpp"
namespace uni {
namespace internal {
template<class, bool>
struct modint_base {};
template<class Mint>
struct modint_base<Mint, false> {
static constexpr Mint zero = Mint::_raw(0);
static constexpr Mint one = Mint::_one();
};
template<class Mint>
struct modint_base<Mint, true> {
static constexpr Mint zero = Mint::_raw(0);
static inline Mint one = Mint::_one();
};
} // internal
template<internal::modular_context Context>
struct modint : internal::modint_base<modint<Context>, Context::dynamic> {
using value_type = typename Context::value_type;
using context = Context;
private:
using base = internal::modint_base<modint, context::dynamic>;
friend base;
value_type _val = 0;
static constexpr auto _raw(const value_type v) noexcept(NO_EXCEPT) {
modint res;
res._val = v;
return res;
}
static constexpr auto _one() noexcept(NO_EXCEPT)
requires internal::has_static_one<typename modint::context::reductor>
{
return modint::_raw(modint::context::reduction.one);
}
static constexpr auto _one() noexcept(NO_EXCEPT)
requires (!internal::has_static_one<typename modint::context::reductor>)
{
return modint::_raw(1);
}
public:
static constexpr int digits = modint::context::reductor::digits;
static constexpr value_type max() noexcept { return modint::context::reductor::max(); }
static constexpr void set_mod(const value_type mod) noexcept(NO_EXCEPT)
requires requires(value_type mod) { modint::context::set_mod(mod); }
{
modint::context::set_mod(mod);
modint::one = modint::_one();
}
static constexpr auto mod() noexcept(NO_EXCEPT) { return modint::context::reduction.mod(); }
static constexpr auto raw(const value_type v) noexcept(NO_EXCEPT)
{
modint res;
res._val = modint::context::reduction.convert_raw(v);
return res;
};
constexpr modint() noexcept = default;
template<std::integral T>
constexpr modint(const T v) noexcept(NO_EXCEPT) : _val(modint::context::reduction.convert(v)) {}
inline constexpr auto val() const noexcept(NO_EXCEPT) {
return modint::context::reduction.revert(this->_val);
}
inline constexpr explicit operator value_type() const noexcept(NO_EXCEPT) { return this->_val; }
inline constexpr auto& operator+=(const modint& rhs) noexcept(NO_EXCEPT) {
this->_val = modint::context::reduction.add(this->_val, rhs._val);
return *this;
}
inline constexpr auto& operator-=(const modint& rhs) noexcept(NO_EXCEPT) {
this->_val = modint::context::reduction.subtract(this->_val, rhs._val);
return *this;
}
inline constexpr auto& operator*=(const modint& rhs) noexcept(NO_EXCEPT) {
this->_val = modint::context::reduction.multiply(this->_val, rhs._val);
return *this;
}
inline constexpr auto& operator/=(const modint& rhs) noexcept(NO_EXCEPT) { return *this *= rhs.inv(); }
template<std::integral K>
constexpr auto pow(const K n) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(n >= 0);
return modint::_raw(modint::context::reduction.pow(this->_val, n));
}
constexpr auto inv() const noexcept(NO_EXCEPT) {
using signed_value_type = std::make_signed_t<value_type>;
signed_value_type x = this->val(), y = modint::mod(), u = 1, v = 0;
while(y > 0) {
signed_value_type t = x / y;
std::swap(x -= t * y, y);
std::swap(u -= t * v, v);
}
assert(x == 1);
if(u < 0) u += v / x;
return modint::raw(u);
}
friend inline constexpr auto operator<=>(const modint& lhs, const modint& rhs) noexcept(NO_EXCEPT) {
return modint::context::reduction.compare(lhs._val, rhs._val);
}
friend inline constexpr bool operator==(const modint& lhs, const modint& rhs) noexcept(NO_EXCEPT) {
return lhs <=> rhs == 0;
}
inline constexpr auto& operator++() noexcept(NO_EXCEPT) { return *this += modint::one; }
inline constexpr auto& operator--() noexcept(NO_EXCEPT) { return *this -= modint::one; }
inline constexpr auto operator++(int) noexcept(NO_EXCEPT) { const modint res = *this; return ++*this, res; }
inline constexpr auto operator--(int) noexcept(NO_EXCEPT) { const modint res = *this; return --*this, res; }
inline constexpr auto operator+() const noexcept(NO_EXCEPT) { return *this; }
inline constexpr auto operator-() const noexcept(NO_EXCEPT) { return modint::zero - *this; }
friend inline constexpr auto operator+(modint lhs, const modint& rhs) noexcept(NO_EXCEPT) { return lhs += rhs; }
friend inline constexpr auto operator-(modint lhs, const modint& rhs) noexcept(NO_EXCEPT) { return lhs -= rhs; }
friend inline constexpr auto operator*(modint lhs, const modint& rhs) noexcept(NO_EXCEPT) { return lhs *= rhs; }
friend inline constexpr auto operator/(modint lhs, const modint& rhs) noexcept(NO_EXCEPT) { return lhs /= rhs; }
};
} // namespace uni
#line 17 "numeric/fast_prime.hpp"
namespace uni {
namespace internal {
constexpr i64 INTERNAL_MODINT_ID = -(1L << 62);
inline constexpr bool is_prime(const i64 n) noexcept(NO_EXCEPT) {
assert(n >= 0);
return is_prime<uni::dynamic_montgomery_modint_32bit<INTERNAL_MODINT_ID>, uni::dynamic_montgomery_modint_64bit<INTERNAL_MODINT_ID>>(n);
}
inline auto factorize(const i64 n) noexcept(NO_EXCEPT) {
assert(n >= 0);
vector<i64> res;
factorize<uni::dynamic_montgomery_modint_32bit<INTERNAL_MODINT_ID>, uni::dynamic_montgomery_modint_64bit<INTERNAL_MODINT_ID>>(n, &res);
return res;
}
inline auto divisors(const i64 n) noexcept(NO_EXCEPT) {
assert(n >= 0);
vector<i64> res;
divisors<uni::dynamic_montgomery_modint_32bit<INTERNAL_MODINT_ID>, uni::dynamic_montgomery_modint_64bit<INTERNAL_MODINT_ID>>(n, &res);
std::ranges::sort(res);
return res;
}
template<bool FORCE_RANDOM = false>
inline auto primitive_root(const i64 n) noexcept(NO_EXCEPT) {
assert(n >= 0);
return primitive_root<uni::dynamic_montgomery_modint_32bit<INTERNAL_MODINT_ID>, uni::dynamic_montgomery_modint_64bit<INTERNAL_MODINT_ID>, i64, FORCE_RANDOM>(n);
}
} // namespace internal
using internal::is_prime;
using internal::divisors;
using internal::primitive_root;
inline vector<i64> factorize(const i64 n) noexcept(NO_EXCEPT) {
assert(n >= 0);
auto res = internal::factorize(n);
std::ranges::sort(res);
return res;
}
inline set<i64> prime_factors(const i64 n) noexcept(NO_EXCEPT) {
assert(n >= 0);
const auto factors = factorize(n);
set<i64> res(ALL(factors));
return res;
}
inline map<i64,i64> count_factors(const i64 n) noexcept(NO_EXCEPT) {
assert(n >= 0);
map<i64,i64> mp;
for(auto &x : internal::factorize(n)) mp[x]++;
return mp;
}
} // namespace uni
#line 15 "algebraic/rolling_hash.hpp"
#line 17 "algebraic/rolling_hash.hpp"
namespace uni {
namespace algebraic {
template<uni::internal::modint_family ValueType, typename ValueType::value_type BASE>
struct rolling_hash_impl {
using value_type = ValueType;
inline static value_type base;
private:
value_type _value = 0, _power = 1;
public:
rolling_hash_impl(const value_type& value, const value_type& power) noexcept(NO_EXCEPT)
: _value(value), _power(power)
{
if(rolling_hash_impl::base == 0) {
if constexpr(BASE == 0) {
rolling_hash_impl::base = uni::primitive_root<true>(value_type::mod());
}
else if constexpr(BASE < 0) {
random_engine_64bit random(std::random_device{}());
rolling_hash_impl::base = static_cast<value_type>(random() % value_type::mod());
}
else {
rolling_hash_impl::base = BASE;
}
}
}
rolling_hash_impl(const value_type& value) noexcept(NO_EXCEPT) : rolling_hash_impl(value, 0) {
this->_power = rolling_hash_impl::base;
};
rolling_hash_impl() noexcept = default;
inline auto power() const noexcept(NO_EXCEPT) { return this->_power; }
inline auto val() const noexcept(NO_EXCEPT) { return this->_value; }
friend inline bool operator==(const rolling_hash_impl& lhs, const rolling_hash_impl& rhs) noexcept(NO_EXCEPT) {
return lhs._power == rhs._power && lhs._value == rhs._value;
}
friend inline auto operator<=>(const rolling_hash_impl& lhs, const rolling_hash_impl& rhs) noexcept(NO_EXCEPT) {
const auto comp_power = lhs._power <=> rhs._power;
if(comp_power != 0) return comp_power;
return lhs._value <=> rhs._value;
}
};
template<
bool REVERSE = false,
uni::internal::modint_family T = uni::static_modint_64bit<(1UL << 61) - 1>,
typename T::value_type BASE = 0
>
struct rolling_hash : base<rolling_hash_impl<T, BASE>>, scalar_multipliable<rolling_hash<REVERSE, T, BASE>>::automatic, associative {
using base<rolling_hash_impl<T, BASE>>::base;
rolling_hash(const T& v) : base<rolling_hash_impl<T, BASE>>(v) {}
template<class U>
requires (
(!std::same_as<std::remove_cvref_t<U>, T>) &&
(!std::constructible_from<rolling_hash_impl<T, BASE>, U>)
)
rolling_hash(U&& v) : base<rolling_hash_impl<T, BASE>>(hash64(std::forward<U>(v))) {}
friend inline auto operator+(const rolling_hash& lhs, const rolling_hash& rhs) noexcept(NO_EXCEPT) {
const auto power = lhs->power() * rhs->power();
if constexpr(REVERSE) return rolling_hash({ lhs->val() * rhs->power() + rhs->val(), power });
return rolling_hash({ lhs->val() + rhs->val() * lhs->power(), power });
}
inline auto operator-() noexcept(NO_EXCEPT) {
const auto power_inv = this->val().power().inv();
return rolling_hash({ -this->val().val() * power_inv, power_inv });
}
};
} // namespace algebraic
} // namespace uni
#line 10 "action/range_sequence_hash.hpp"
namespace uni {
namespace actions {
template<
bool REVERSE = false,
uni::internal::modint_family T = uni::static_modint_64bit<(1UL << 61) - 1>,
typename T::value_type BASE = 0
>
using range_sequence_hash = make_operatable_t<uni::algebraic::rolling_hash<REVERSE, T, BASE>>;
static_assert(internal::operand_only_action<range_sequence_hash<false>>);
static_assert(internal::operand_only_action<range_sequence_hash<true>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_set.hpp"
#line 6 "action/range_set.hpp"
#line 2 "algebraic/assignment.hpp"
#line 4 "algebraic/assignment.hpp"
#line 7 "algebraic/assignment.hpp"
namespace uni {
namespace algebraic {
template<class T>
struct assignment : base<std::optional<T>>, scalar_multipliable<assignment<T>>::identity, associative {
using base<std::optional<T>>::base;
friend inline assignment operator+(const assignment& lhs, const assignment& rhs) noexcept(NO_EXCEPT) {
if(lhs->has_value()) return lhs;
return rhs;
}
};
} // namespace algebraic
} // namespace uni
#line 9 "action/range_set.hpp"
namespace uni {
namespace actions {
template<class T>
struct range_set : base<algebraic::assignment<T>> {
using operand = algebraic::null<T>;
using operation = algebraic::assignment<T>;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return f->value_or(x.val());
}
};
static_assert(internal::full_action<range_set<int>>);
} // namesapce actions
} // namespace uni
#line 2 "action/range_set_range_composition.hpp"
#line 5 "action/range_set_range_composition.hpp"
#line 9 "action/range_set_range_composition.hpp"
#line 12 "action/range_set_range_composition.hpp"
namespace uni {
namespace actions {
template<class T, bool REVERSE = false>
struct range_set_range_composition : base<algebraic::assignment<std::pair<T, T>>> {
using base<algebraic::assignment<std::pair<T, T>>>::base;
using operand = algebraic::affine<T, REVERSE>;
using operation = algebraic::assignment<std::pair<T, T>>;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return f->value_or(std::make_pair(x->first, x->second));
}
};
static_assert(internal::full_action<range_set_range_composition<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_set_range_max.hpp"
#line 5 "action/range_set_range_max.hpp"
#line 7 "action/range_set_range_max.hpp"
#line 10 "action/range_set_range_max.hpp"
namespace uni {
namespace actions {
template<class T>
struct range_set_range_max : base<algebraic::assignment<T>> {
using operand = algebraic::maximum<T>;
using operation = algebraic::assignment<T>;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return f->value_or(x.val());
}
};
static_assert(internal::full_action<range_set_range_max<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_set_range_min.hpp"
#line 5 "action/range_set_range_min.hpp"
#line 7 "action/range_set_range_min.hpp"
#line 10 "action/range_set_range_min.hpp"
namespace uni {
namespace actions {
template<class T>
struct range_set_range_min : base<algebraic::assignment<T>> {
using operand = algebraic::minimum<T>;
using operation = algebraic::assignment<T>;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return f->value_or(x.val());
}
};
static_assert(internal::full_action<range_set_range_min<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_set_range_sum.hpp"
#line 5 "action/range_set_range_sum.hpp"
#line 7 "action/range_set_range_sum.hpp"
#line 10 "action/range_set_range_sum.hpp"
namespace uni {
namespace actions {
template<class T>
struct range_set_range_sum {
using operand = algebraic::addition<T>;
using operation = algebraic::assignment<T>;
static operand mapping(const operation& f, const operand& x) noexcept(NO_EXCEPT) {
return f->value_or(x.val());
}
static auto power(const operation& x, const uni::internal::size_t length) noexcept(NO_EXCEPT) {
if(x->has_value()) return operation(x->operator*() * length);
return x;
}
};
static_assert(internal::full_action<range_set_range_sum<int>>);
} // namespace actions
} // namespace uni
#line 2 "action/range_sum.hpp"
#line 6 "action/range_sum.hpp"
#line 8 "action/range_sum.hpp"
namespace uni {
namespace actions {
template<class T>
using range_sum = make_operatable_t<uni::algebraic::addition<T>>;
static_assert(internal::operand_only_action<range_sum<int>>);
} // namespace actions
} // namespace uni
#line 2 "include/adaptors.hpp"
#line 4 "include/adaptors.hpp"
#line 2 "adaptor/array.hpp"
#line 6 "adaptor/array.hpp"
#line 9 "adaptor/array.hpp"
namespace uni {
template<class T, int N>
using array = internal::advanced_container<std::array<T,N>>;
} // namespace uni
#line 2 "adaptor/auto_expander.hpp"
#line 7 "adaptor/auto_expander.hpp"
#line 11 "adaptor/auto_expander.hpp"
namespace uni {
template<class Container>
struct auto_expander : Container {
using size_type = Container::size_type;
public:
template<class... Args>
explicit auto_expander(Args&&... args) noexcept(NO_EXCEPT) : Container(std::forward<Args>(args)...) {}
inline auto& operator[](const size_type pos) noexcept(NO_EXCEPT) {
if(this->size() <= pos) this->Container::resize(pos + 1);
return this->Container::operator[](pos);
}
};
}
#line 2 "adaptor/deque_by_stack.hpp"
#line 9 "adaptor/deque_by_stack.hpp"
#line 12 "adaptor/deque_by_stack.hpp"
#line 14 "adaptor/deque_by_stack.hpp"
namespace uni {
template<class Front, class Back = Front>
struct deque_by_stack {
static_assert(std::same_as<typename Front::value_type, typename Back::value_type>);
static_assert(std::common_reference_with<typename Front::size_type, typename Back::size_type>);
using value_type = Front::value_type;
using size_type = std::common_type_t<typename Front::size_type, typename Back::size_type>;
protected:
Front _front;
Back _back;
private:
template<std::ptrdiff_t OFFSET>
inline void _distribute() noexcept(NO_EXCEPT) {
if(this->empty()) return;
std::vector<value_type> temp;
temp.reserve(this->size());
if(this->_front.empty()) {
while(!this->_back.empty()) {
temp.push_back(this->_back.top());
this->_back.pop();
}
std::ranges::reverse(temp);
}
else if(this->_back.empty()) {
while(!this->_front.empty()) {
temp.push_back(this->_front.top());
this->_front.pop();
}
}
else {
return;
}
assert(this->empty());
const auto size = std::ranges::ssize(temp);
const auto mid = (size + OFFSET) / 2;
REPD(i, mid) this->_front.push(temp[i]);
REP(i, mid, size) this->_back.push(temp[i]);
}
public:
deque_by_stack() noexcept = default;
inline bool empty() const noexcept(NO_EXCEPT) {
return this->_front.empty() && this->_back.empty();
}
inline auto size() const noexcept(NO_EXCEPT) {
return this->_front.size() + this->_back.size();
}
inline decltype(auto) front() const noexcept(NO_EXCEPT) {
this->_distribute<1>();
assert(!this->_front.empty());
return this->_front.top();
}
inline decltype(auto) back() const noexcept(NO_EXCEPT) {
this->_distribute<0>();
assert(!this->_back.empty());
return this->_back.top();
}
template<std::convertible_to<value_type> T = value_type>
requires std::is_move_constructible_v<T>
inline decltype(auto) front_or(T&& val) const noexcept(NO_EXCEPT) {
if(this->empty()) return static_cast<value_type>(std::forward<T>(val));
else return this->front();
}
template<std::convertible_to<value_type> T = value_type>
requires std::is_move_constructible_v<T>
inline decltype(auto) back_or(T&& val) const noexcept(NO_EXCEPT) {
if(this->empty()) return static_cast<value_type>(std::forward<T>(val));
else return this->back();
}
inline auto& clear() noexcept(NO_EXCEPT) {
this->_front.clear(), this->_back.clear();
return *this;
}
template<std::convertible_to<value_type> T = value_type>
inline auto& push_front(T&& val) noexcept(NO_EXCEPT) {
this->_front.push(std::forward<T>(val));
return *this;
}
template<std::convertible_to<value_type> T = value_type>
inline auto& push_back(T&& val) noexcept(NO_EXCEPT) {
this->_back.push(std::forward<T>(val));
return *this;
}
template<class... Args>
inline decltype(auto) emplace_front(Args&&... args) noexcept(NO_EXCEPT) {
return this->_front.emplace(std::forward<Args>(args)...);
}
template<class... Args>
inline decltype(auto) emplace_back(Args&&... args) noexcept(NO_EXCEPT) {
return this->_back.emplace(std::forward<Args>(args)...);
}
auto& pop_front() noexcept(NO_EXCEPT) {
this->_distribute<1>();
assert(!this->_front.empty());
this->_front.pop();
return *this;
}
auto& pop_back() noexcept(NO_EXCEPT) {
this->_distribute<0>();
assert(!this->_back.empty());
this->_back.pop();
return *this;
}
};
} // namespace uni
#line 2 "adaptor/io.hpp"
#include <regex>
#line 2 "adaptor/internal/input.hpp"
#line 12 "adaptor/internal/input.hpp"
#line 15 "adaptor/internal/input.hpp"
#line 18 "adaptor/internal/input.hpp"
#line 20 "adaptor/internal/input.hpp"
#line 22 "adaptor/internal/input.hpp"
#line 24 "adaptor/internal/input.hpp"
namespace uni {
template<std::derived_from<std::ios_base> Source = std::istream>
struct input_adaptor {
using source_type = Source;
private:
template<class T>
requires std::derived_from<T, std::valarray<typename T::value_type>>
auto _set(uni::internal::resolving_rank<6>, T& val) noexcept(NO_EXCEPT) -> int {
this->operator()(ALL(val));
return 0;
}
template<class T>
requires
requires (source_type& in, T& val) {
in >> val;
}
int _set(uni::internal::resolving_rank<5>, T& val) noexcept(NO_EXCEPT) {
*this->in >> val;
return 0;
}
template<std::ranges::range T>
int _set(uni::internal::resolving_rank<4>, T& val) noexcept(NO_EXCEPT) {
this->operator()(std::ranges::begin(val), std::ranges::end(val));
return 0;
}
template<class T>
requires
requires (T& val) {
val.first;
val.second;
}
int _set(uni::internal::resolving_rank<3>, T& val) noexcept(NO_EXCEPT) {
*this >> val.first >> val.second;
return 0;
}
template<class T>
requires
requires (T& val) {
std::get<0>(val);
}
int _set(uni::internal::resolving_rank<2>, T& val) noexcept(NO_EXCEPT) {
tuple_for_each([this](auto&& v) { *this >> v; }, val);
return 0;
}
template<uni::internal::modint_family T>
int _set(uni::internal::resolving_rank<1>, T& val) noexcept(NO_EXCEPT) {
std::int64_t v; std::cin >> v;
val = { v };
return 0;
}
template<class T>
requires
requires {
typename T::value_type;
}
int _set(uni::internal::resolving_rank<0>, T& val) noexcept(NO_EXCEPT) {
typename T::value_type v; *this >> v;
val = { v };
return 0;
}
protected:
template<class T>
source_type *set(T& val) noexcept(NO_EXCEPT) {
this->_set(uni::internal::resolving_rank<10>{}, val);
return this->in;
}
template<class T>
source_type *set(T&& _val) noexcept(NO_EXCEPT) {
T val = _val;
this->_set(uni::internal::resolving_rank<10>{}, val);
return this->in;
}
public:
using char_type = typename source_type::char_type;
source_type *in;
input_adaptor(source_type *_in = &std::cin) noexcept(NO_EXCEPT) : in(_in) {}
template<class T>
inline input_adaptor& operator>>(T&& s) noexcept(NO_EXCEPT) {
this->set(std::forward<T>(s));
return *this;
}
template<class T>
inline T one() noexcept(NO_EXCEPT) {
T val; *this >> val;
return val;
}
template<class T>
inline auto& operator()(T& val) noexcept(NO_EXCEPT) {
*this >> val;
return *this;
}
template<class T, class... Args>
inline auto& operator()(T& head, Args&... tail) noexcept(NO_EXCEPT) {
*this >> head;
this->operator()(tail...);
return *this;
}
template<std::input_or_output_iterator I, std::sentinel_for<I> S>
inline auto& operator()(I first, S last) noexcept(NO_EXCEPT) {
for(I itr=first; itr!=last; ++itr) *this >> *itr;
return *this;
}
explicit operator bool() const noexcept(NO_EXCEPT) { return (bool)*this->in; }
};
} // namespace uni
#line 2 "adaptor/internal/output.hpp"
#line 11 "adaptor/internal/output.hpp"
#line 15 "adaptor/internal/output.hpp"
namespace uni {
template<class Destination = std::ostream>
struct output_adaptor {
using destination_type = Destination;
private:
template<class T>
requires
requires (destination_type& out, T val) {
out << val;
}
int _put(uni::internal::resolving_rank<5>, T&& val) noexcept(NO_EXCEPT) {
*this->out << std::forward<T>(val);
return 0;
}
template<class T>
requires
requires (T&& val) {
val.val();
}
int _put(uni::internal::resolving_rank<4>, T&& val) noexcept(NO_EXCEPT) {
this->put(val.val());
return 0;
}
template<std::ranges::input_range T>
int _put(uni::internal::resolving_rank<3>, T&& val) noexcept(NO_EXCEPT) {
(*this)(std::ranges::begin(val), std::ranges::end(val), false);
return 0;
}
template<class T>
requires
requires (T&& val) {
val.first;
val.second;
}
int _put(uni::internal::resolving_rank<2>, T&& val) noexcept(NO_EXCEPT) {
*this << val.first, this->put_separator();
*this << val.second;
return 0;
}
template<class T>
requires
requires (T&& val) {
std::get<0>(val);
}
auto _put(uni::internal::resolving_rank<1>, T&& val) noexcept(NO_EXCEPT) {
std::apply([this](const auto&... args) constexpr { ((*this << args, this->put_separator()), ...); }, std::forward<T>(val));
return 0;
}
template<std::input_or_output_iterator T>
int _put(uni::internal::resolving_rank<0>, T&& val) noexcept(NO_EXCEPT) {
(*this)(*std::forward<T>(val));
return 0;
}
protected:
template<class T>
destination_type* put(T&& val) noexcept(NO_EXCEPT){
this->_put(uni::internal::resolving_rank<10>{}, std::forward<T>(val));
return this->out;
}
public:
using char_type = typename destination_type::char_type;
static constexpr auto sendl = std::endl<char_type,std::char_traits<char_type>>;
static constexpr auto sflush = std::flush<char_type,std::char_traits<char_type>>;
protected:
using sfunc_type = std::remove_const_t<decltype(output_adaptor::sendl)>;
public:
using separator_type = std::variant<std::string,sfunc_type>;
destination_type *out;
separator_type endline;
separator_type separator;
protected:
void put_separator() noexcept(NO_EXCEPT) {
if(this->separator.index() == 0) *this->out << std::get<std::string>(this->separator);
if(this->separator.index() == 1) *this->out << std::get<sfunc_type>(this->separator);
}
void put_endline() noexcept(NO_EXCEPT) {
if(this->endline.index() == 0) *this->out << std::get<std::string>(this->endline);
if(this->endline.index() == 1) *this->out << std::get<sfunc_type>(this->endline);
}
public:
template<class Terminator = std::string, class Separator = std::string>
output_adaptor(destination_type *des = &std::cout, Terminator endl = "\n", Separator sep = " ") noexcept(NO_EXCEPT)
: out(des), endline(endl), separator(sep)
{
*this << std::fixed << std::setprecision(20);
}
inline auto& seekp(const typename destination_type::off_type off, const std::ios_base::seekdir dir = std::ios_base::cur) noexcept(NO_EXCEPT) {
this->out->seekp(off, dir); return *this;
};
template<class T> inline output_adaptor& operator<<(T&& s) noexcept(NO_EXCEPT){
this->put(std::forward<T>(s));
return *this;
}
template<class T = std::string>
inline auto& operator()(T&& val = "") noexcept(NO_EXCEPT){
*this << std::forward<T>(val), this->put_endline();
return *this;
}
template<class T, class ...Args>
inline auto& operator()(T&& head, Args&& ...tail) noexcept(NO_EXCEPT){
*this << std::forward<T>(head), this->put_separator();
(*this)(std::forward<Args>(tail)...);
return *this;
}
template<std::forward_iterator I, std::sentinel_for<I> S>
inline auto& operator()(I first, S last, const bool terminate = true) noexcept(NO_EXCEPT) {
for(I itr=first; itr!=last;) {
*this << *itr;
if(++itr == last) {
if(terminate) this->put_endline();
}
else this->put_separator();
}
return *this;
}
template<class T>
inline auto& operator()(const std::initializer_list<T> vals) noexcept(NO_EXCEPT) {
std::vector wrapped(vals.begin(), vals.end());
(*this)(wrapped.begin(), wrapped.end());
return *this;
}
template<class T0, class T1>
inline auto& conditional(const bool cond, const T0& a, const T1& b) noexcept(NO_EXCEPT) {
if(cond) (*this)(a);
else (*this)(b);
return *this;
}
inline auto& yesno(const bool cond) noexcept(NO_EXCEPT) {
if(cond) this->yes();
else this->no();
return *this;
}
inline auto yes() noexcept(NO_EXCEPT) {
*this->out << "Yes";
this->put_endline();
return *this;
}
inline auto no() noexcept(NO_EXCEPT) {
*this->out << "No";
this->put_endline();
return *this;
}
inline auto flush() noexcept(NO_EXCEPT) {
*this->out << std::flush;
return *this;
}
};
} // namespace uni
#line 7 "adaptor/io.hpp"
namespace uni {
uni::input_adaptor _input;
uni::output_adaptor _print;
}
#define input uni::_input
#define print uni::_print
#line 2 "adaptor/multi_container.hpp"
#line 7 "adaptor/multi_container.hpp"
#line 9 "adaptor/multi_container.hpp"
#line 12 "adaptor/multi_container.hpp"
#line 15 "adaptor/multi_container.hpp"
#line 18 "adaptor/multi_container.hpp"
namespace uni {
namespace internal {
namespace multi_container_impl {
template<class Holder> struct base : Holder {
using Holder::Holder;
protected:
template<std::integral T>
constexpr auto _positivize_index(const T _x) const noexcept(NO_EXCEPT) {
auto x = static_cast<internal::size_t>(_x);
return x < 0 ? this->size() + x : x;
}
};
} // namespace multi_contatiner_impl
} // namespace internal
template<class T, unsigned int RANK, template<class...> class Holder = vector, template<class...> class Container = vector>
struct multi_container : internal::multi_container_impl::base<Holder<multi_container<T, RANK - 1, Holder, Container>>> {
private:
using base = internal::multi_container_impl::base<Holder<multi_container<T, RANK - 1, Holder, Container>>>;
public:
using base::base;
template<std::integral Head, class... Tail>
constexpr multi_container(const Head head, Tail&&... tail) noexcept(NO_EXCEPT)
: base(head, multi_container<T, RANK - 1, Holder, Container>(std::forward<Tail>(tail)...))
{
assert(head >= 0);
}
template<std::integral Head, class... Tail>
constexpr T& operator()(Head _head, Tail&&... tail) noexcept(NO_EXCEPT) {
static_assert(std::is_integral_v<Head>, "index must be integral");
const auto index = this->_positivize_index(_head);
assert(0 <= index && index < std::ranges::ssize(*this));
return (*this)[index](std::forward<Tail>(tail)...);
}
template<std::integral Head, class... Tail>
constexpr T& operator()(Head _head, Tail&&... tail) const noexcept(NO_EXCEPT) {
static_assert(std::is_integral_v<Head>, "index must be integral");
const auto index = this->_positivize_index(_head);
assert(0 <= index && index < std::ranges::ssize(*this));
return (*this)[index](std::forward<Tail>(tail)...);
}
};
template<class T, template<class...> class Holder, template<class...> class Container>
struct multi_container<T, 1, Holder, Container> : internal::multi_container_impl::base<Container<T>> {
using internal::multi_container_impl::base<Container<T>>::base;
template<class... Args>
constexpr multi_container(const Args&... args) noexcept(NO_EXCEPT) : internal::multi_container_impl::base<Container<T>>(args...)
{}
template<class Index>
constexpr T& operator()(Index&& _index) noexcept(NO_EXCEPT) {
const auto index = this->_positivize_index(std::forward<T>(_index));
assert(0 <= index && index < std::ranges::ssize(*this));
return (*this)[index];
}
template<class Index>
constexpr T& operator()(Index&& _index) const noexcept(NO_EXCEPT) {
const auto index = this->_positivize_index(std::forward<T>(_index));
assert(0 <= index && index < std::ranges::ssize(*this));
return (*this)[index];
}
};
template<class T, template<class...> class Holder, template<class...> class Container>
struct multi_container<T, 0, Holder, Container> {
static_assert(internal::EXCEPTION_ON_TYPE<T>, "invalid rank: 0, should be 1 or more");
};
} // namespace uni
#line 2 "adaptor/queue_by_stack.hpp"
#line 6 "adaptor/queue_by_stack.hpp"
#line 9 "adaptor/queue_by_stack.hpp"
namespace uni {
template<class In, class Out = In>
struct queue_by_stack {
static_assert(std::same_as<typename In::value_type, typename Out::value_type>);
static_assert(std::common_reference_with<typename In::size_type, typename Out::size_type>);
using value_type = In::value_type;
using size_type = std::common_type_t<typename In::size_type, typename Out::size_type>;
protected:
In _in;
Out _out;
private:
inline void _shift() noexcept(NO_EXCEPT) {
if(!this->_out.empty()) return;
while(!this->_in.empty()) {
this->_out.push(this->_in.top());
this->_in.pop();
}
}
public:
queue_by_stack() noexcept = default;
inline bool empty() const noexcept(NO_EXCEPT) {
return this->_in.empty() && this->_out.empty();
}
inline auto size() const noexcept(NO_EXCEPT) {
return this->_in.size() + this->_out.size();
}
inline decltype(auto) front() noexcept(NO_EXCEPT) {
this->_shift();
assert(!this->_out.empty());
return this->_out.top();
}
template<std::convertible_to<value_type> T = value_type>
requires std::is_move_constructible_v<T>
inline decltype(auto) front_or(T&& val) const noexcept(NO_EXCEPT) {
if(this->empty()) return static_cast<value_type>(std::forward<T>(val));
else return this->front();
}
inline auto& clear() noexcept(NO_EXCEPT) {
this->_in.clear(), this->_out.clear();
return *this;
}
template<std::convertible_to<value_type> T = value_type>
inline auto& push(T&& val) noexcept(NO_EXCEPT) {
this->_in.push(std::forward<T>(val));
return *this;
}
template<class... Args>
inline decltype(auto) emplace(Args&&... args) noexcept(NO_EXCEPT) {
return this->_in.emplace(std::forward<Args>(args)...);
}
auto& pop() noexcept(NO_EXCEPT) {
this->_shift();
assert(!this->_out.empty());
this->_out.pop();
return *this;
}
};
} // namespace uni
#line 2 "adaptor/range_extractor.hpp"
#line 7 "adaptor/range_extractor.hpp"
#line 10 "adaptor/range_extractor.hpp"
namespace uni {
template<class Container>
struct range_extractor : Container {
using size_type = typename Container::size_type;
using value_type = typename Container::value_type;
protected:
using default_func_noarg_type = std::function<value_type(void)>;
using default_func_type = std::function<value_type(size_type)>;
size_type _begin = 0;
size_type _end;
int _default_type = 0;
value_type _default_val = value_type();
default_func_noarg_type _default_func_noarg;
default_func_type _default_func;
inline static value_type _tmp;
inline value_type _get_default(const size_type key) const noexcept(NO_EXCEPT) {
if(this->_default_type == 0) return this->_default_val;
if(this->_default_type == 1) return this->_default_func_noarg();
if(this->_default_type == 2) return this->_default_func(key);
else assert(false);
}
public:
template<class... Args>
explicit range_extractor(Args&&... args) noexcept(NO_EXCEPT) : Container(std::forward<Args>(args)...) {
this->_begin = 0;
this->_end = this->size();
}
inline auto& extract(const size_type begin, const size_type end) noexcept(NO_EXCEPT) {
assert(begin <= end);
this->_begin = begin, this->_end = end;
return *this;
}
inline auto& set_default(const value_type& val) noexcept(NO_EXCEPT) {
this->_default_val = val;
this->_default_type = 0;
return *this;
}
inline auto& set_default(const default_func_noarg_type func) noexcept(NO_EXCEPT) {
this->_default_func_noarg = func;
this->_default_type = 1;
return *this;
}
inline auto& set_default(const default_func_type func) noexcept(NO_EXCEPT) {
this->_default_func = func;
this->_default_type = 2;
return *this;
}
inline auto& operator[](const size_type pos) noexcept(NO_EXCEPT) {
if(pos < this->_begin or this->_end <= pos) return range_extractor::_tmp = this->_get_default(pos);
return this->Container::operator[](pos);
}
inline const auto& operator[](const size_type pos) const noexcept(NO_EXCEPT) {
if(pos < this->_begin or this->_end <= pos) return range_extractor::_tmp = this->_get_default(pos);
return this->Container::operator[](pos);
}
inline auto& operator()(const size_type pos) noexcept(NO_EXCEPT) {
return this->Container::operator[](pos);
}
inline const auto& operator()(const size_type pos) const noexcept(NO_EXCEPT) {
return this->Container::operator[](pos);
}
inline std::optional<value_type> get(const size_type pos) const noexcept(NO_EXCEPT) {
if(pos < this->_begin or this->_end <= pos) return {};
return this->Container::operator[](pos);
}
};
}
#line 2 "adaptor/stack.hpp"
#line 6 "adaptor/stack.hpp"
namespace uni {
template<class T, class Allocator = std::allocator<T>>
using stack = std::stack<T, std::vector<T, Allocator>>;
} // namespace uni
#line 2 "adaptor/virtual_map.hpp"
#line 5 "adaptor/virtual_map.hpp"
#line 7 "adaptor/virtual_map.hpp"
namespace uni {
template<class> struct virtual_combined_map {};
template<class Mapped, class... Keys>
struct virtual_combined_map<Mapped(Keys...)> {
using key_type = std::tuple<Keys...>;
using mapped_type = Mapped;
using value_type = std::pair<key_type,mapped_type>;
protected:
std::function<Mapped(Keys...)> _f;
public:
virtual_combined_map() = default;
template<class F>
explicit virtual_combined_map(F&& f) noexcept(NO_EXCEPT) : _f(f) {};
inline const auto* get_functor() const noexcept(NO_EXCEPT) { return this->_f; }
inline auto* get_functor() noexcept(NO_EXCEPT) { return this->_f; }
template<class F>
inline auto& set_functor(F&& f) const noexcept(NO_EXCEPT) { return this->_f = f; }
inline mapped_type operator()(const Keys&... key) const noexcept(NO_EXCEPT) {
return this->_f(key...);
}
inline mapped_type operator[](const key_type& key) const noexcept(NO_EXCEPT) {
return std::apply(this->_f, key);
}
};
template<class Key, class Mapped>
struct virtual_map : virtual_combined_map<Mapped(Key)> {
using key_type = Key;
using mapped_type = Mapped;
using value_type = std::pair<key_type,mapped_type>;
using virtual_combined_map<mapped_type(key_type)>::virtual_combined_map;
inline mapped_type operator[](const key_type& key) const noexcept(NO_EXCEPT) {
return this->_f(key);
}
};
}; // namesapce uni
#line 2 "include/algebraic.hpp"
#line 2 "algebraic/bit_and.hpp"
#line 6 "algebraic/bit_and.hpp"
namespace uni {
namespace algebraic {
template<class T>
struct bit_and : base<T>, associative, scalar_multipliable<bit_and<T>>::identity, commutative {
using base<T>::base;
bit_and() noexcept(NO_EXCEPT) : base<T>(uni::numeric_limits<T>::max()) {};
friend inline bit_and operator+(const bit_and& lhs, const bit_and& rhs) noexcept(NO_EXCEPT) {
return lhs.val() bitand rhs.val();
}
};
} // namespace algebraic
} // namespace uni
#line 2 "algebraic/bit_or.hpp"
#line 5 "algebraic/bit_or.hpp"
namespace uni {
namespace algebraic {
template<class T>
struct bit_or : base<T>, scalar_multipliable<bit_or<T>>::identity, associative, commutative {
using base<T>::base;
friend inline bit_or operator+(const bit_or& lhs, const bit_or& rhs) noexcept(NO_EXCEPT) {
return lhs.val() bitor rhs.val();
}
};
} // namespace algebraic
} // namespace uni
#line 2 "algebraic/combined.hpp"
#line 6 "algebraic/combined.hpp"
#line 9 "algebraic/combined.hpp"
#line 12 "algebraic/combined.hpp"
namespace uni {
namespace algebraic {
template<
internal::magma M0,
internal::magma M1
>
struct combined
: base<std::pair<M0, M1>>,
std::conditional_t<internal::associative<M0> && internal::associative<M1>, associative, uni::internal::dummy>,
std::conditional_t<internal::commutative<M0> && internal::commutative<M1>, commutative, uni::internal::dummy>
{
using base<std::pair<M0, M1>>::base;
template<class T>
requires std::convertible_to<T, M0> && std::convertible_to<T, M1>
combined(const T& v) : combined(v, v) {};
friend inline combined operator+(const combined& lhs, const combined& rhs) noexcept(NO_EXCEPT) {
return { lhs->first + rhs->first, lhs->second + rhs->second };
}
template<std::integral Scalar>
friend inline combined&& operator*(const Scalar k, const combined& val) noexcept(NO_EXCEPT) {
return { k * val->first, k * val->second };
}
friend inline combined operator-(const combined& val) noexcept(NO_EXCEPT)
requires internal::invertible<M0> && internal::invertible<M1>
{
return { -val->first, -val->second };
}
};
} // namespace algebraic
} // namespace uni
#line 2 "algebraic/opposite.hpp"
#line 6 "algebraic/opposite.hpp"
#line 9 "algebraic/opposite.hpp"
#line 12 "algebraic/opposite.hpp"
namespace uni {
namespace algebraic {
template<internal::magma M>
struct opposite
:
std::conditional_t<internal::associative<M>, associative, uni::internal::dummy>,
std::conditional_t<internal::commutative<M>, commutative, uni::internal::dummy>
{
using value_type = M::value_type;
private:
M _value;
public:
template<std::convertible_to<M> T>
opposite(const T& v) : _value(v) {};
template<class... Args>
requires std::constructible_from<value_type, Args...>
opposite(Args&&... args) noexcept(NO_EXCEPT) : _value(std::forward<Args>(args)...) {}
inline explicit operator value_type() const noexcept(NO_EXCEPT) { return this->_value.val(); }
inline auto val() const noexcept(NO_EXCEPT) { return this->_value.val(); };
inline const value_type* operator->() const noexcept(NO_EXCEPT) { return this->_value.operator->(); };
inline value_type* operator->() noexcept(NO_EXCEPT) { return this->_value.operator->(); };
friend inline auto operator<=>(const opposite& lhs, const opposite& rhs) noexcept(NO_EXCEPT) {
return lhs._value <=> rhs._value;
};
friend inline bool operator==(const opposite& lhs, const opposite& rhs) noexcept(NO_EXCEPT) {
return lhs._value == rhs._value;
}
friend inline opposite operator+(const opposite& lhs, const opposite& rhs) noexcept(NO_EXCEPT) {
return rhs._value + lhs._value;
}
friend inline opposite operator-(const opposite& val) noexcept(NO_EXCEPT)
requires internal::invertible<M>
{
return -val._value;
}
};
template<internal::magma M>
struct make_opposite;
template<internal::magma M>
struct make_opposite<opposite<M>> {
using type = M;
};
template<internal::magma M>
requires internal::commutative<M>
struct make_opposite<M> {
using type = M;
};
template<internal::magma M>
requires (!internal::commutative<M>)
struct make_opposite<M> {
using type = opposite<M>;
};
template<internal::magma M>
using make_opposite_t = make_opposite<M>::type;
} // namespace algebraic
} // namespace uni
#line 2 "include/convolutions.hpp"
#line 2 "convolution/gcd.hpp"
#line 6 "convolution/gcd.hpp"
#line 9 "convolution/gcd.hpp"
#line 2 "numeric/divisor_multiple_transform.hpp"
#line 5 "numeric/divisor_multiple_transform.hpp"
#line 2 "numeric/prime_enumerator.hpp"
#line 10 "numeric/prime_enumerator.hpp"
#line 13 "numeric/prime_enumerator.hpp"
#line 15 "numeric/prime_enumerator.hpp"
#line 18 "numeric/prime_enumerator.hpp"
#line 22 "numeric/prime_enumerator.hpp"
namespace uni {
// Thanks to: https://qiita.com/peria/items/e0ab38f95d16a5f7cc58
template<class T>
struct prime_enumerator : std::ranges::view_interface<prime_enumerator<T>> {
using value_type = T;
using size_type = internal::size_t;
protected:
using impl_type = std::uint32_t;
impl_type _n = 0;
using small_bit_type = std::uint8_t;
using large_bit_type = std::uint64_t;
static constexpr impl_type SEGMENT_SIZE = 1'000'000;
static constexpr impl_type MOD30[8] = { 1, 7, 11, 13, 17, 19, 23, 29 };
static constexpr small_bit_type MASK[8][8] = {
{ 0xfe, 0xfd, 0xfb, 0xf7, 0xef, 0xdf, 0xbf, 0x7f },
{ 0xfd, 0xdf, 0xef, 0xfe, 0x7f, 0xf7, 0xfb, 0xbf },
{ 0xfb, 0xef, 0xfe, 0xbf, 0xfd, 0x7f, 0xf7, 0xdf },
{ 0xf7, 0xfe, 0xbf, 0xdf, 0xfb, 0xfd, 0x7f, 0xef },
{ 0xef, 0x7f, 0xfd, 0xfb, 0xdf, 0xbf, 0xfe, 0xf7 },
{ 0xdf, 0xf7, 0x7f, 0xfd, 0xbf, 0xfe, 0xef, 0xfb },
{ 0xbf, 0xfb, 0xf7, 0x7f, 0xfe, 0xef, 0xdf, 0xfd },
{ 0x7f, 0xbf, 0xdf, 0xef, 0xf7, 0xfb, 0xfd, 0xfe },
};
static constexpr impl_type C1[8] = { 6, 4, 2, 4, 2, 4, 6, 2 };
static constexpr impl_type C0[8][8] = {
{ 0, 0, 0, 0, 0, 0, 0, 1 }, { 1, 1, 1, 0, 1, 1, 1, 1 },
{ 2, 2, 0, 2, 0, 2, 2, 1 }, { 3, 1, 1, 2, 1, 1, 3, 1 },
{ 3, 3, 1, 2, 1, 3, 3, 1 }, { 4, 2, 2, 2, 2, 2, 4, 1 },
{ 5, 3, 1, 4, 1, 3, 5, 1 }, { 6, 4, 2, 4, 2, 4, 6, 1 },
};
size_type _size;
impl_type _sqrt_n = 0, _sqrt_ni = 0, _quart_n = 0;
std::valarray<small_bit_type> _small;
std::valarray<large_bit_type> _large;
std::vector<impl_type> _indecies;
small_bit_type* _flag = nullptr;
inline void _init(const value_type n, const impl_type size) noexcept(NO_EXCEPT) {
const size_type blocks = (size + 7) >> 3;
this->_large.resize(blocks + 1, ~0UL);
this->_flag = reinterpret_cast<small_bit_type*>(&(this->_large[0]));
this->_flag[0] = 0xfe;
value_type r = n % 30;
if(r <= 1) this->_flag[size - 1] = 0x0;
else if(r <= 7) this->_flag[size - 1] = 0x1;
else if(r <= 11) this->_flag[size - 1] = 0x3;
else if(r <= 13) this->_flag[size - 1] = 0x7;
else if(r <= 17) this->_flag[size - 1] = 0xf;
else if(r <= 19) this->_flag[size - 1] = 0x1f;
else if(r <= 23) this->_flag[size - 1] = 0x3f;
else if(r <= 29) this->_flag[size - 1] = 0x7f;
if(n < 30) this->_flag[0] &= 0xfe;
this->_large[blocks - 1] <<= 64 - ((size & 7) << 3);
this->_large[blocks - 1] >>= 64 - ((size & 7) << 3);
this->_large[blocks] = 0;
// for(auto x : this->_large) debug(std::bitset<64>(x));
}
inline void _gen_small() noexcept(NO_EXCEPT) {
const impl_type quart_ni = this->_quart_n / 30 + 1;
this->_small.resize(this->_sqrt_ni, 0xff);
this->_small[0] = 0xfe;
REP(i, quart_ni) {
for(small_bit_type flags = this->_small[i]; flags; flags &= flags - 1) {
const int ibit = lowest_bit_pos(flags);
const impl_type m = prime_enumerator::MOD30[ibit];
const impl_type pm = 30 * i + 2 * m;
for(
impl_type j = i * pm + (m * m) / 30, k = ibit;
j < this->_sqrt_ni;
j += i * prime_enumerator::C1[k] + prime_enumerator::C0[ibit][k], k = (k + 1) & 7
) {
this->_small[j] &= prime_enumerator::MASK[ibit][k];
}
}
}
REP(i, this->_sqrt_ni) {
for(small_bit_type flags = this->_small[i]; flags; flags &= flags - 1) {
const int ibit = lowest_bit_pos(flags);
const impl_type m = prime_enumerator::MOD30[ibit];
impl_type j = i * (30 * i + 2 * m) + (m * m) / 30;
this->_indecies.emplace_back(((j + prime_enumerator::SEGMENT_SIZE) << 3) | ibit);
}
}
}
inline void _gen_core(small_bit_type *const flags, const impl_type size) noexcept(NO_EXCEPT) {
auto p_index = this->_indecies.begin();
REP(i, this->_sqrt_ni) {
for(small_bit_type primes = this->_small[i]; primes; primes &= primes - 1) {
const int ibit = lowest_bit_pos(primes);
impl_type j = (*p_index >> 3) - prime_enumerator::SEGMENT_SIZE;
impl_type k = *p_index & 7;
for(; j < size; j += i * prime_enumerator::C1[k] + prime_enumerator::C0[ibit][k], k = (k + 1) & 7) {
flags[j] &= prime_enumerator::MASK[ibit][k];
}
*p_index = ((j << 3) | k);
++p_index;
}
}
}
using iterator_interface = internal::bidirectional_iterator_interface<const value_type>;
public:
struct iterator;
using const_iterator = iterator;
prime_enumerator() noexcept {};
prime_enumerator(const value_type n) noexcept(NO_EXCEPT) : _n(n) {
assert(n >= 0);
assert(std::endian::native == std::endian::little);
this->_sqrt_n = static_cast<impl_type>(sqrt_ceil(this->_n + 1));
this->_sqrt_ni = this->_sqrt_n / 30 + 1;
this->_quart_n = static_cast<impl_type>(sqrt_ceil(this->_sqrt_n));
this->_gen_small();
impl_type size = (this->_n + 1) / 30 + 1;
this->_init(this->_n + 1, size);
for(small_bit_type* seg = this->_flag; ; seg += prime_enumerator::SEGMENT_SIZE) {
if(size < prime_enumerator::SEGMENT_SIZE) {
this->_gen_core(seg, size);
break;
};
this->_gen_core(seg, prime_enumerator::SEGMENT_SIZE);
size -= prime_enumerator::SEGMENT_SIZE;
}
this->_size = (this->_n >= 2) + (this->_n >= 3) + (this->_n >= 5);
for(const large_bit_type f : this->_large) this->_size += std::popcount(f);
}
inline size_type size() const noexcept(NO_EXCEPT) { return this->_size; }
inline size_type count(const T x) const noexcept(NO_EXCEPT) {
assert(0 <= x and x <= this->_n);
size_type res = (x >= 2) + (x >= 3) + (x >= 5);
T count = 0;
constexpr int large_bit_width = std::numeric_limits<large_bit_type>::digits;
constexpr int large_bit_size = (30 * large_bit_width) >> 3;
for(const large_bit_type f : this->_large) {
if(count + large_bit_size > x) {
REP(i, large_bit_width) {
if(count + prime_enumerator::MOD30[i & 7] > x) break;
if((f >> i) & 1) res++;
if(((i + 1) & 7) == 0) count += 30;
}
break;
}
res += std::popcount(f);
count += large_bit_size;
}
return res;
}
inline size_type count(const T l, const T r) const noexcept(NO_EXCEPT) {
assert(l <= r);
return this->count(r) - this->count(l - 1);
}
inline bool is_prime(const T v) const noexcept(NO_EXCEPT) {
assert(0 <= v and v <= this->_n);
if(v == 0 or v == 1) return false;
if(v == 2 or v == 3 or v == 5) return true;
if((v & 1) == 0 or v % 3 == 0 or v % 5 == 0) return false;
REP(i, 8) {
if(prime_enumerator::MOD30[i] == v % 30) {
return static_cast<bool>((this->_flag[v / 30] >> i) & 1);
}
}
assert(false);
}
inline auto begin() const noexcept(NO_EXCEPT) { return iterator(this, 0); }
inline auto end() const noexcept(NO_EXCEPT) { return iterator(this, -1); }
inline auto rbegin() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
struct iterator : iterator_interface {
protected:
value_type _n = 0;
size_type _index = 0;
const std::valarray<large_bit_type>* _flags = nullptr;
size_type _block = -1, _flag_size;
int _bit = 0;
inline value_type _value() const noexcept(NO_EXCEPT) {
if(this->_bit < 0) return numeric_limits<value_type>::arithmetic_infinity();
if(this->_block < 0) {
if(this->_bit == 0) return 2;
if(this->_bit == 1) return 3;
if(this->_bit == 2) return 5;
}
return (
value_type{30} * ((this->_block << 3) + (this->_bit >> 3)) +
prime_enumerator::MOD30[this->_bit & 7]
);
}
public:
iterator() noexcept = default;
iterator(const prime_enumerator *const super, const int bit) noexcept(NO_EXCEPT)
: _n(super->_n), _flags(&super->_large), _flag_size(static_cast<size_type>(super->_large.size())), _bit(bit) {
if(bit < 0) {
this->_index = super->size();
this->_block = static_cast<size_type>(super->_large.size()) - 1;
}
}
inline size_type index() const noexcept(NO_EXCEPT) { return this->_index; }
inline value_type operator*() const noexcept(NO_EXCEPT) {
const value_type res = this->_value();
return (res > this->_n ? -1 : res);
}
inline iterator& operator++() noexcept(NO_EXCEPT) {
if(this->_value() > this->_n) return *this;
++this->_index;
if(this->_block < 0) {
++this->_bit;
if(this->_bit > 2) this->_block = 0, this->_bit = 1;
return *this;
}
int next;
while(true) {
const large_bit_type mask = this->_bit >= 63 ? 0UL : ~((1UL << (this->_bit + 1)) - 1);
next = lowest_bit_pos(this->_flags->operator[](this->_block) & mask);
if(next >= 0) break;
this->_block++;
this->_bit = -1;
if(this->_block >= this->_flag_size) break;
}
this->_bit = next;
return *this;
}
inline iterator& operator--() noexcept(NO_EXCEPT) {
if(this->_block < 0) {
if(this->_bit > 0) --this->_bit, --this->_index;
return *this;
}
--this->_index;
int prev = -1;
while(true) {
if(0 < this->_bit) {
const large_bit_type mask = this->_bit >= 64 ? ~0UL : ((1UL << this->_bit) - 1);
prev = highest_bit_pos(this->_flags->operator[](this->_block) & mask);
}
if(prev >= 0) break;
--this->_block;
this->_bit = 64;
if(this->_block < 0) {
this->_bit = (this->_n >= 3) + (this->_n >= 5);
return *this;
}
}
this->_bit = prev;
return *this;
}
inline iterator operator++(int) noexcept(NO_EXCEPT) { const auto res = *this; ++(*this); return res; }
inline iterator operator--(int) noexcept(NO_EXCEPT) { const auto res = *this; --(*this); return res; }
friend inline bool operator==(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT) { return lhs._index == rhs._index; }
friend inline auto operator<=>(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT) { return lhs._index <=> rhs._index; }
friend inline auto operator-(const iterator& lhs, const iterator& rhs) { return lhs._index - rhs._index; }
};
};
} // namespace uni
namespace std::ranges {
template<class T>
inline constexpr bool enable_borrowed_range<uni::prime_enumerator<T>> = true;
} // namespace std::ranges
#line 10 "numeric/divisor_multiple_transform.hpp"
// Thanks to: https://nyaannyaan.github.io/library/multiplicative-function/divisor-multiple-transform.hpp.html
namespace uni {
namespace divisor_transform {
using size_type = internal::size_t;
template<std::size_t OFFSET, std::ranges::sized_range R>
requires (!requires { typename R::mapped_type; })
auto zeta(R&& range) noexcept(NO_EXCEPT) {
const auto n = std::ranges::ssize(range) + OFFSET - 1;
ITR(p, uni::prime_enumerator(n)) {
for(size_type k=1; k*p <= n; ++k) range[k*p - OFFSET] += range[k - OFFSET];
}
}
template<std::size_t OFFSET, std::ranges::sized_range R>
requires (!requires { typename R::mapped_type; })
auto mobius(R&& range) noexcept(NO_EXCEPT) {
const auto n = std::ranges::ssize(range) + OFFSET - 1;
ITR(p, uni::prime_enumerator(n)) {
for(size_type k=n/p; k>0; --k) range[k*p - OFFSET] -= range[k - OFFSET];
}
}
template<std::ranges::sized_range R>
auto zeta(R&& range) noexcept(NO_EXCEPT) { return zeta<0>(range); }
template<std::ranges::sized_range R>
auto mobius(R&& range) noexcept(NO_EXCEPT) { return mobius<0>(range); }
template<std::ranges::input_range R>
requires requires { typename R::mapped_type; }
auto zeta(R&& range) noexcept(NO_EXCEPT) {
auto begin = std::ranges::begin(range);
auto end = std::ranges::end(range);
for(auto itr1 = end; itr1-- != begin; ) {
for(auto itr2 = begin; itr2 != end; ++itr2) {
if(itr1->first == itr2->first) break;
if(itr1->first % itr2->first == 0) itr1->second += itr2->second;
}
}
}
template<std::ranges::input_range R>
requires requires { typename R::mapped_type; }
auto mobius(R&& range) noexcept(NO_EXCEPT) {
auto begin = std::ranges::begin(range);
auto end = std::ranges::end(range);
for(auto itr2 = begin; itr2 != end; ++itr2) {
for(auto itr1 = end; (itr1--) != begin; ) {
if(itr1->first == itr2->first) break;
if(itr1->first % itr2->first == 0) itr1->second -= itr2->second;
}
}
}
} // namespace divisor_transform
namespace multiple_transform {
using size_type = internal::size_t;
template<std::size_t OFFSET, std::ranges::sized_range R>
requires (!requires { typename R::mapped_type; })
auto zeta(R&& range) noexcept(NO_EXCEPT) {
const auto n = std::ranges::ssize(range) + OFFSET - 1;
ITR(p, uni::prime_enumerator(n)) {
for(size_type k=n/p; k>0; --k) range[k - OFFSET] += range[k*p - OFFSET];
}
}
template<std::size_t OFFSET, std::ranges::sized_range R>
requires (!requires { typename R::mapped_type; })
auto mobius(R&& range) noexcept(NO_EXCEPT) {
const auto n = std::ranges::ssize(range) + OFFSET - 1;
ITR(p, uni::prime_enumerator(n)) {
for(size_type k=1; k*p <= n; ++k) range[k - OFFSET] -= range[k*p - OFFSET];
}
}
template<std::ranges::sized_range R>
auto zeta(R&& range) noexcept(NO_EXCEPT) { return zeta<0>(range); }
template<std::ranges::sized_range R>
auto mobius(R&& range) noexcept(NO_EXCEPT) { return mobius<0>(range); }
template<std::ranges::input_range R>
requires requires { typename R::mapped_type; }
auto zeta(R&& range) noexcept(NO_EXCEPT) {
auto begin = std::ranges::begin(range);
auto end = std::ranges::end(range);
for(auto itr2 = begin; itr2 != end; ++itr2) {
for(auto itr1 = end; --itr1 != itr2; ) {
if(itr1->first % itr2->first == 0) itr2->second += itr1->second;
}
}
}
template<std::ranges::input_range R>
requires requires { typename R::mapped_type; }
auto mobius(R&& range) noexcept(NO_EXCEPT) {
auto begin = std::ranges::begin(range);
auto end = std::ranges::end(range);
for(auto itr2 = end; itr2-- != begin; ) {
for(auto itr1 = end; --itr1 != itr2; ) {
if(itr1->first % itr2->first == 0) itr2->second -= itr1->second;
}
}
}
} // namespace multiple_transform
} // namespace uni
#line 11 "convolution/gcd.hpp"
#line 13 "convolution/gcd.hpp"
namespace uni {
template<std::ranges::range Res, std::size_t OFFSET, std::ranges::sized_range R0, std::ranges::sized_range R1>
Res gcd_convolution(R0 v0, R1 v1) {
assert(std::ranges::size(v0) == std::ranges::size(v1));
multiple_transform::zeta<OFFSET>(v0), multiple_transform::zeta<OFFSET>(v1);
REP(i, std::ranges::size(v0)) v0[i] *= v1[i];
multiple_transform::mobius<OFFSET>(v0);
if constexpr(std::convertible_to<R0, Res>) return v0;
else return Res(ALL(v0));
}
template<std::size_t OFFSET, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>
auto gcd_convolution(R0&& v0, R1&& v1) {
using common_type = std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>;
return gcd_convolution<valarray<common_type>, OFFSET>(v0, v1);
}
template<std::ranges::range Res, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>
auto gcd_convolution(R0&& v0, R1&& v1) { return gcd_convolution<Res, 0>(v0, v1); }
template<std::ranges::sized_range R0, std::ranges::sized_range R1>
requires std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>
auto gcd_convolution(R0&& v0, R1&& v1) { return gcd_convolution<0>(v0, v1); }
} // namespace uni
#line 2 "convolution/lcm.hpp"
#line 6 "convolution/lcm.hpp"
#line 9 "convolution/lcm.hpp"
#line 11 "convolution/lcm.hpp"
#line 13 "convolution/lcm.hpp"
namespace uni {
template<std::ranges::range Res, std::size_t OFFSET, std::ranges::sized_range R0, std::ranges::sized_range R1>
Res lcm_convolution(R0 v0, R1 v1) {
assert(std::ranges::size(v0) == std::ranges::size(v1));
divisor_transform::zeta<OFFSET>(v0), divisor_transform::zeta<OFFSET>(v1);
REP(i, std::ranges::size(v0)) v0[i] *= v1[i];
divisor_transform::mobius<OFFSET>(v0);
if constexpr(std::convertible_to<R0, Res>) return v0;
else return Res(ALL(v0));
}
template<std::size_t OFFSET, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>
auto lcm_convolution(R0&& v0, R1&& v1) {
using common_type = std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>;
return lcm_convolution<valarray<common_type>, OFFSET>(v0, v1);
}
template<std::ranges::range Res, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>
auto lcm_convolution(R0&& v0, R1&& v1) { return lcm_convolution<Res, 0>(v0, v1); }
template<std::ranges::sized_range R0, std::ranges::sized_range R1>
requires std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>
auto lcm_convolution(R0&& v0, R1&& v1) { return lcm_convolution<0>(v0, v1); }
} // namespace uni
#line 2 "convolution/sum.hpp"
#line 7 "convolution/sum.hpp"
#line 2 "convolution/internal/butterfly.hpp"
#line 13 "convolution/internal/butterfly.hpp"
#line 16 "convolution/internal/butterfly.hpp"
#line 19 "convolution/internal/butterfly.hpp"
#line 21 "convolution/internal/butterfly.hpp"
#line 23 "convolution/internal/butterfly.hpp"
namespace uni {
namespace internal {
// Thanks to: atocder/convolution
template<uni::internal::modint_family mint>
struct fft_info {
static constexpr mint g = primitive_root<mint>(mint::mod());
static constexpr auto rank2 = std::countr_zero(mint::mod() - 1);
std::array<mint, rank2 + 1> root;
std::array<mint, rank2 + 1> iroot;
std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
consteval fft_info() {
this->root[rank2] = g.pow((mint::mod() - 1) >> this->rank2);
this->iroot[rank2] = this->root[this->rank2].inv();
REPD(i, rank2) {
this->root[i] = this->root[i + 1] * this->root[i + 1];
this->iroot[i] = this->iroot[i + 1] * this->iroot[i + 1];
}
{
mint prod = mint::one, iprod = mint::one;
REP(i, rank2 - 1) {
this->rate2[i] = this->root[i + 2] * prod;
this->irate2[i] = this->iroot[i + 2] * iprod;
prod *= this->iroot[i + 2];
iprod *= this->root[i + 2];
}
}
{
mint prod = mint::one, iprod = mint::one;
REP(i, rank2 - 2) {
this->rate3[i] = this->root[i + 3] * prod;
this->irate3[i] = this->iroot[i + 3] * iprod;
prod *= this->iroot[i + 3];
iprod *= this->root[i + 3];
}
}
}
};
} // namespace internal
template<std::ranges::sized_range R>
requires internal::static_modint_family<std::ranges::range_value_t<R>>
void butterfly(R& v1) {
using mint = std::ranges::range_value_t<R>;
const auto n = std::ranges::ssize(v1);
const auto h = to_signed(std::countr_zero(to_unsigned(n)));
static constexpr internal::fft_info<mint> info;
internal::size_t len = 0;
while(len < h) {
if(h - len == 1) {
const internal::size_t p = 1 << (h - len - 1);
mint rot = mint::one;
REP(s, 1 << len) {
const internal::size_t offset = s << (h - len);
REP(i, p) {
const auto l = v1[i + offset];
const auto r = v1[i + offset + p] * rot;
v1[i + offset] = l + r;
v1[i + offset + p] = l - r;
}
if(s + 1 != (1 << len)) {
rot *= info.rate2[std::countr_zero(~to_unsigned(s))];
}
}
++len;
}
else {
const internal::size_t p = 1 << (h - len - 2);
const mint imag = info.root[2];
mint rot = mint::one;
REP(s, 1 << len) {
const mint rot2 = rot * rot;
const mint rot3 = rot2 * rot;
const internal::size_t offset = s << (h - len);
REP(i, p) {
const auto mod2 = 1ULL * mint::mod() * mint::mod();
const auto a0 = 1ULL * v1[i + offset].val();
const auto a1 = 1ULL * v1[i + offset + p].val() * rot.val();
const auto a2 = 1ULL * v1[i + offset + 2 * p].val() * rot2.val();
const auto a3 = 1ULL * v1[i + offset + 3 * p].val() * rot3.val();
const auto a1na3imag = 1ULL * mint{ a1 + mod2 - a3 }.val() * imag.val();
const auto na2 = mod2 - a2;
v1[i + offset] = a0 + a2 + a1 + a3;
v1[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
v1[i + offset + 2 * p] = a0 + na2 + a1na3imag;
v1[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
if(s + 1 != (1 << len)) rot *= info.rate3[std::countr_zero(~to_unsigned(s))];
}
len += 2;
}
}
}
template<std::ranges::sized_range R>
requires internal::static_modint_family<std::ranges::range_value_t<R>>
void butterfly_inv(R& v1) {
using mint = std::ranges::range_value_t<R>;
const auto n = std::ranges::ssize(v1);
const auto h = std::countr_zero(to_unsigned(n));
static constinit internal::fft_info<mint> info;
internal::size_t len = h;
while(len > 0) {
if(len == 1) {
const internal::size_t p = 1 << (h - len);
mint irot = mint::one;
REP(s, 1 << (len - 1)) {
const internal::size_t offset = s << (h - len + 1);
REP(i, p) {
const auto l = v1[i + offset];
const auto r = v1[i + offset + p];
v1[i + offset] = l + r;
v1[i + offset + p] = to_unsigned(mint::mod() + l.val() - r.val()) * irot.val();
}
if(s + 1 != (1 << (len - 1))) irot *= info.irate2[std::countr_zero(~to_unsigned(s))];
}
--len;
}
else {
const auto p = 1 << (h - len);
const mint iimag = info.iroot[2];
mint irot = mint::one;
REP(s, 1 << (len - 2)) {
const mint irot2 = irot * irot;
const mint irot3 = irot2 * irot;
const internal::size_t offset = s << (h - len + 2);
REP(i, p) {
const auto a0 = 1ULL * v1[i + offset + 0 * p].val();
const auto a1 = 1ULL * v1[i + offset + 1 * p].val();
const auto a2 = 1ULL * v1[i + offset + 2 * p].val();
const auto a3 = 1ULL * v1[i + offset + 3 * p].val();
const auto a2na3iimag = 1ULL * mint{ (mint::mod() + a2 - a3) * iimag.val() }.val();
v1[i + offset] = a0 + a1 + a2 + a3;
v1[i + offset + 1 * p] = (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
v1[i + offset + 2 * p] = (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) * irot2.val();
v1[i + offset + 3 * p] = (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) * irot3.val();
}
if(s + 1 != (1 << (len - 2))) irot *= info.irate3[std::countr_zero(~to_unsigned(s))];
}
len -= 2;
}
}
}
template<class Res, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires
std::same_as<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
internal::static_modint_family<std::ranges::range_value_t<R0>>
Res convolution_naive(R0&& v0, R1&& v1) {
const auto n = std::ranges::ssize(v0);
const auto m = std::ranges::ssize(v1);
Res ans(n + m - 1);
if(n < m) {
REP(j, m) REP(i, n) ans[i + j] += v0[i] * v1[j];
}
else {
REP(i, n) REP(j, m) ans[i + j] += v0[i] * v1[j];
}
return ans;
}
template<class Res, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires
std::same_as<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
internal::static_modint_family<std::ranges::range_value_t<R0>> &&
internal::resizable_range<R0> && internal::resizable_range<R1> &&
std::convertible_to<std::ranges::range_value_t<R0>, std::ranges::range_value_t<Res>>
Res convolution_fft(R0 v0, R1 v1) {
using mint = std::ranges::range_value_t<R0>;
const auto n = std::ranges::ssize(v0);
const auto m = std::ranges::ssize(v1);
const auto z = to_signed(std::bit_ceil(to_unsigned(n + m - 1)));
v0.resize(z);
butterfly(v0);
v1.resize(z);
butterfly(v1);
REP(i, z) v0[i] *= v1[i];
butterfly_inv(v0);
v0.resize(n + m - 1);
const mint iz = mint{ z }.inv();
REP(i, n + m - 1) v0[i] *= iz;
if constexpr(std::convertible_to<R0, Res>) return v0;
else return Res(ALL(v0));
}
} // namespace uni
#line 10 "convolution/sum.hpp"
#line 12 "convolution/sum.hpp"
namespace uni {
template<class Res, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires
std::same_as<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
internal::static_modint_family<std::ranges::range_value_t<R0>> &&
std::convertible_to<std::ranges::range_value_t<R0>, std::ranges::range_value_t<Res>>
Res convolution(R0&& v0, R1&& v1) {
using mint = std::ranges::range_value_t<R0>;
const auto n = std::ranges::ssize(v0);
const auto m = std::ranges::ssize(v1);
if(!n || !m) return {};
const auto z = to_signed(std::bit_ceil(to_unsigned(n + m - 1)));
assert((mint::mod() - 1) % z == 0);
// if(uni::min(n, m) <= 60) return convolution_naive<Res>(v0, v1);
return convolution_fft<Res>(v0, v1);
}
template<
u32 Mod = 998244353,
class Res,
std::ranges::sized_range R0, std::ranges::sized_range R1
>
requires
std::convertible_to<std::ranges::range_value_t<R0>, static_modint_32bit<Mod>> &&
std::convertible_to<std::ranges::range_value_t<R1>, static_modint_32bit<Mod>> &&
std::convertible_to<std::ranges::range_value_t<R0>, std::ranges::range_value_t<Res>>
Res convolution(R0&& v0, R1&& v1) {
using mint = static_modint_32bit<Mod>;
const auto n = std::ranges::ssize(v0);
const auto m = std::ranges::ssize(v1);
if(!n || !m) return {};
const auto z = to_signed(std::bit_ceil(to_unsigned(n + m - 1)));
assert((mint::mod() - 1) % z == 0);
std::vector<mint> a2(n), b2(m);
REP(i, n) a2[i] = mint{ v0[i] };
REP(i, m) b2[i] = mint{ v1[i] };
const auto c1 = convolution(a2, b2);
Res c(n + m - 1);
REP(i, n + m - 1) c[i] = c1[i].val();
return c;
}
template<class Res, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires
std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
std::integral<std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>> &&
(
std::integral<std::ranges::range_value_t<Res>> ||
internal::modint_family<std::ranges::range_value_t<Res>>
) &&
std::convertible_to<std::ranges::range_value_t<R0>, std::ranges::range_value_t<Res>>
Res convolution(R0&& v0, R1&& v1) {
using res_value_type = std::ranges::range_value_t<Res>;
const auto n = std::ranges::ssize(v0);
const auto m = std::ranges::ssize(v1);
if(!n || !m) return {};
static constexpr i64 MOD0 = 167772161;
static constexpr i64 MOD1 = 469762049;
static constexpr i64 MOD2 = 754974721;
static constexpr auto M0 = res_value_type{ MOD0 };
static constexpr auto M1 = res_value_type{ MOD1 };
static constexpr auto M2 = res_value_type{ MOD2 };
static constexpr auto M0M1 = M0 * M1;
static constexpr auto M0M2 = M0 * M2;
static constexpr auto M1M2 = M1 * M2;
static constexpr auto M0M1M2 = M0 * M1 * M2;
static constexpr u64 r0 = atcoder::internal::inv_gcd(MOD1 * MOD2, MOD0).second;
static constexpr u64 r1 = atcoder::internal::inv_gcd(MOD0 * MOD2, MOD1).second;
static constexpr u64 r2 = atcoder::internal::inv_gcd(MOD0 * MOD1, MOD2).second;
static constexpr i64 i01 = atcoder::internal::inv_gcd(MOD0, MOD1).second;
static constexpr i64 i02 = atcoder::internal::inv_gcd(MOD0, MOD2).second;
static constexpr i64 i12 = atcoder::internal::inv_gcd(MOD1, MOD2).second;
static constexpr i64 i02i12 = (i02 * i12) % MOD2;
static constexpr size_t MAX_AB_BIT = 24;
static_assert(MOD0 % (1ull << MAX_AB_BIT) == 1, "MOD0 isn't enough to support an array length of 2^24.");
static_assert(MOD1 % (1ull << MAX_AB_BIT) == 1, "MOD1 isn't enough to support an array length of 2^24.");
static_assert(MOD2 % (1ull << MAX_AB_BIT) == 1, "MOD2 isn't enough to support an array length of 2^24.");
assert(n + m - 1 <= (1 << MAX_AB_BIT));
const auto c0 = convolution<MOD0, std::remove_cvref_t<R0>>(v0, v1);
const auto c1 = convolution<MOD1, std::remove_cvref_t<R0>>(v0, v1);
const auto c2 = convolution<MOD2, std::remove_cvref_t<R0>>(v0, v1);
Res c(n + m - 1);
REP(i, n + m - 1) {
if constexpr(internal::modint_family<res_value_type>) {
const auto c01 = ((c1[i] + MOD1 - c0[i]) * i01) % MOD1;
const auto c012 = ((c2[i] + MOD2 - c0[i]) * i02i12 + (MOD2 - c01) * i12) % MOD2;
c[i] = c0[i] + c01 * M0 + c012 * M0M1;
}
else {
res_value_type x = 0;
x += (c0[i] * r0) % MOD0 * M1M2;
x += (c1[i] * r1) % MOD1 * M0M2;
x += (c2[i] * r2) % MOD2 * M0M1;
auto diff = c2[i] - uni::mod(to_signed(x), to_signed(MOD2));
if (diff < 0) diff += MOD2;
static constexpr res_value_type offset[5] = { 0, 0, M0M1M2, 2 * M0M1M2, 3 * M0M1M2 };
x -= offset[diff % 5];
c[i] = x;
}
}
return c;
}
template<std::ranges::range R0, std::ranges::range R1>
requires
std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
internal::modint_family<std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>>
auto convolution(R0&& v0, R1&& v1) {
using common_type = std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>;
return convolution<valarray<common_type>>(v0, v1);
}
template<u32 Mod = 998244353, std::ranges::range R0, std::ranges::range R1>
requires
std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
std::integral<std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>> &&
(
std::numeric_limits<
std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>
>::digits <= 64
)
auto convolution(R0&& v0, R1&& v1) {
using common_type = std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>;
return convolution<Mod, valarray<common_type>>(v0, v1);
}
} // namespace uni
#line 2 "include/data_structures.hpp"
#line 2 "data_structure/adaptor/set.hpp"
#line 10 "data_structure/adaptor/set.hpp"
#line 15 "data_structure/adaptor/set.hpp"
#line 17 "data_structure/adaptor/set.hpp"
#line 2 "data_structure/segment_tree.hpp"
#line 11 "data_structure/segment_tree.hpp"
#line 14 "data_structure/segment_tree.hpp"
#line 2 "internal/point_reference.hpp"
#line 6 "internal/point_reference.hpp"
#line 9 "internal/point_reference.hpp"
#line 11 "internal/point_reference.hpp"
namespace uni {
namespace internal {
template<class Super, std::integral SizeType = typename Super::size_type>
struct point_reference {
using size_type = SizeType;
using iterator = typename Super::iterator;
protected:
Super *const _super;
const size_type _pos;
point_reference(Super *const super, const size_type pos) noexcept(NO_EXCEPT) : _super(super), _pos(pos) {}
inline auto index() noexcept(NO_EXCEPT) { return this->_pos; }
};
} // namespace internal
} // namespace uni
#line 2 "internal/range_reference.hpp"
#line 8 "internal/range_reference.hpp"
#line 11 "internal/range_reference.hpp"
#line 13 "internal/range_reference.hpp"
namespace uni {
namespace internal {
template<class Super, std::integral SizeType = typename Super::size_type>
struct range_reference {
using size_type = SizeType;
using iterator = Super::iterator;
protected:
Super *const _super;
const size_type _begin, _end;
range_reference(Super *const super, const size_type begin, const size_type end) noexcept(NO_EXCEPT) : _super(super), _begin(begin), _end(end) {}
public:
inline auto begin() const noexcept(NO_EXCEPT) { return std::ranges::next(std::ranges::begin(*this->_super), this->_begin); }
inline auto end() const noexcept(NO_EXCEPT) { return std::ranges::next(std::ranges::begin(*this->_super), this->_end); }
inline auto size() const noexcept(NO_EXCEPT) { return this->_end - this->_begin; }
inline auto interval() const noexcept(NO_EXCEPT) { return std::make_pair(this->_begin, this->_end); }
protected:
inline auto sub_range(size_type l, size_type r) const noexcept(NO_EXCEPT) {
l = _super->_positivize_index(l), r = _super->_positivize_index(r);
assert(0 <= l and l <= r and r <= this->size());
return range_reference(_super, this->_begin + l, this->_begin + r);
}
public:
template<uni::interval_notation rng = uni::interval_notation::right_open>
inline auto range(const size_type l, const size_type r) const noexcept(NO_EXCEPT) {
if constexpr(rng == uni::interval_notation::right_open) return this->sub_range(l, r);
if constexpr(rng == uni::interval_notation::left_open) return this->sub_range(l+1, r+1);
if constexpr(rng == uni::interval_notation::open) return this->sub_range(l+1, r);
if constexpr(rng == uni::interval_notation::closed) return this->sub_range(l, r+1);
}
inline auto range() const noexcept(NO_EXCEPT) { return range_reference(this->_begin, this->_end); }
inline auto operator()(const size_type l, const size_type r) const noexcept(NO_EXCEPT) { return this->sub_range(l, r); }
inline auto subseq(const size_type p, const size_type c) const noexcept(NO_EXCEPT) { return this->sub_range(p, p+c); }
inline auto subseq(const size_type p) const noexcept(NO_EXCEPT) { return this->sub_range(p, this->size()); }
};
} // namespace internal
} // namespace uni
#line 2 "internal/unconstructible.hpp"
namespace uni {
namespace internal {
struct unconstructible {
private:
template<class... Args>
unconstructible(Args...) = delete;
};
} // namespace internal
} // namespace uni
#line 21 "data_structure/segment_tree.hpp"
#line 25 "data_structure/segment_tree.hpp"
namespace uni {
namespace internal {
namespace segment_tree_impl {
// Thanks to: atcoder::segtree
template<algebraic::internal::monoid Monoid>
struct core {
using size_type = internal::size_t;
using operand = Monoid;
protected:
size_type _n = 0, _size = 0, _depth = 0;
std::valarray<operand> _data;
inline void _pull(const size_type k) noexcept(NO_EXCEPT) {
this->_data[k] = this->_data[k << 1] + this->_data[k << 1 | 1];
}
public:
core() noexcept = default;
explicit core(const size_type n) noexcept(NO_EXCEPT)
: _n(n), _size(std::bit_ceil(uni::to_unsigned(n))), _depth(std::countr_zero(uni::to_unsigned(this->_size))),
_data(this->_size << 1)
{}
inline size_type size() const noexcept(NO_EXCEPT) { return this->_n; }
inline size_type allocated() const noexcept(NO_EXCEPT) { return this->_values.size(); }
inline size_type depth() const noexcept(NO_EXCEPT) { return this->_depth; }
inline operand fold_all() const noexcept(NO_EXCEPT) { return this->_data[1]; }
template<std::input_iterator I, std::sentinel_for<I> S>
inline void assign(I first, S last) noexcept(NO_EXCEPT) {
if constexpr(std::sized_sentinel_for<S, I>) {
assert(std::ranges::distance(first, last) == this->_n);
}
{
size_type p = 0;
for(auto itr=first; itr!=last; ++itr, ++p) this->_data[this->_size + p] = static_cast<operand>(*itr);
}
REPD(p, 1, this->_size) this->_pull(p);
}
inline void fill(const operand& v = operand()) noexcept(NO_EXCEPT) {
REP(p, this->_n) this->_data[this->_size + p] = v;
REPD(p, 1, this->_size) this->_pull(p);
}
inline void add(size_type p, const operand& x) noexcept(NO_EXCEPT) {
this->set(p, this->_data[p + this->_size] + x);
}
inline void set(size_type p, const operand& x) noexcept(NO_EXCEPT) {
p += this->_size;
this->_data[p] = x;
FOR(i, 1, this->_depth) this->_pull(p >> i);
}
inline operand get(size_type p) const noexcept(NO_EXCEPT) {
return this->_data[p + this->_size];
}
inline operand fold(size_type l, size_type r) const noexcept(NO_EXCEPT) {
operand sml, smr;
l += this->_size;
r += this->_size;
while(l < r) {
if(l & 1) sml = sml + this->_data[l++];
if(r & 1) smr = this->_data[--r] + smr;
l >>= 1;
r >>= 1;
}
return sml + smr;
}
template<class F>
inline size_type max_right(size_type l, F&& f) const noexcept(NO_EXCEPT) {
assert(0 <= l && l <= this->_n);
assert(f(operand{}));
if(l == this->_n) return this->_n;
l += this->_size;
operand acc;
do {
while((l & 1) == 0) l >>= 1;
if(!f(acc + this->_data[l])) {
while(l < this->_size) {
l <<= 1;
if(f(acc + this->_data[l])) {
acc = acc + this->_data[l];
++l;
}
}
return l - this->_size;
}
acc = acc + this->_data[l];
++l;
} while((l & -l) != l);
return this->_n;
}
template<class F>
inline size_type min_left(size_type r, F&& f) const noexcept(NO_EXCEPT) {
assert(0 <= r && r <= this->_n);
assert(f(operand{}));
if (r == 0) return 0;
r += this->_size;
operand acc;
do {
--r;
while(r > 1 && (r & 1)) r >>= 1;
if(!f(this->_data[r] + acc)) {
while(r < this->_size) {
r = (r << 1 | 1);
if(f(this->_data[r] + acc)) {
acc = this->_data[r] + acc;
--r;
}
}
return r + 1 - this->_size;
}
acc = this->_data[r] + acc;
} while((r & -r) != r);
return 0;
}
};
} // namespace segment_tree_impl
} // namespace internal
template<class T>
struct segment_tree : internal::unconstructible {};
template<algebraic::internal::monoid Monoid>
struct segment_tree<Monoid> {
private:
using core = typename internal::segment_tree_impl::core<Monoid>;
core _impl;
public:
using value_type = Monoid;
using size_type = typename core::size_type;
private:
inline auto _positivize_index(const size_type p) const noexcept(NO_EXCEPT) {
return p < 0 ? this->_impl.size() + p : p;
}
public:
segment_tree() noexcept(NO_EXCEPT) : _impl() {};
explicit segment_tree(const size_type n, const value_type& v = value_type()) noexcept(NO_EXCEPT) : _impl(n) { this->_impl.fill(v); }
template<std::convertible_to<value_type> T>
segment_tree(const std::initializer_list<T>& init_list) noexcept(NO_EXCEPT) : segment_tree(ALL(init_list)) {}
template<std::input_iterator I, std::sized_sentinel_for<I> S>
segment_tree(I first, S last) noexcept(NO_EXCEPT)
: segment_tree(static_cast<size_type>(std::ranges::distance(first, last)))
{ this->assign(first, last); }
template<std::ranges::input_range R>
explicit segment_tree(R&& range) noexcept(NO_EXCEPT) : segment_tree(ALL(range)) {}
inline auto size() const noexcept(NO_EXCEPT) { return this->_impl.size(); }
inline auto allocated() const noexcept(NO_EXCEPT) { return this->_impl.allocated(); }
inline auto depth() const noexcept(NO_EXCEPT) { return this->_impl.depth(); }
template<std::convertible_to<value_type> T>
inline auto& assign(const std::initializer_list<T>& init_list) noexcept(NO_EXCEPT) { return this->assign(ALL(init_list)); }
template<std::input_iterator I, std::sentinel_for<I> S>
inline auto& assign(I first, S last) noexcept(NO_EXCEPT) {
this->_impl.assign(first, last);
return *this;
}
template<std::ranges::input_range R>
inline auto& assign(R&& range) noexcept(NO_EXCEPT) { return this->assign(ALL(range)); }
inline auto& fill(const value_type& v = value_type()) noexcept(NO_EXCEPT) {
this->_impl.fill(v);
return *this;
}
inline bool empty() const noexcept(NO_EXCEPT) { return this->_impl.size() == 0; }
struct point_reference : internal::point_reference<segment_tree> {
point_reference(segment_tree *const super, const size_type p) noexcept(NO_EXCEPT)
: internal::point_reference<segment_tree>(super, super->_positivize_index(p))
{
assert(0 <= this->_pos && this->_pos < this->_super->size());
}
operator value_type() const noexcept(NO_EXCEPT) { return this->_super->get(this->_pos); }
auto val() const noexcept(NO_EXCEPT) { return this->_super->get(this->_pos); }
inline auto& operator=(const value_type& v) noexcept(NO_EXCEPT) {
this->_super->set(this->_pos, v);
return *this;
}
inline auto& operator+=(const value_type& v) noexcept(NO_EXCEPT) {
this->_super->add(this->_pos, v);
return *this;
}
};
struct range_reference : internal::range_reference<segment_tree> {
range_reference(segment_tree *const super, const size_type l, const size_type r) noexcept(NO_EXCEPT)
: internal::range_reference<segment_tree>(super, super->_positivize_index(l), super->_positivize_index(r))
{
assert(0 <= this->_begin && this->_begin <= this->_end && this->_end <= this->_super->size());
}
inline auto fold() noexcept(NO_EXCEPT) {
if(this->_begin == 0 and this->_end == this->_super->size()) return this->_super->fold();
return this->_super->fold(this->_begin, this->_end);
}
};
inline auto& add(const size_type p, const value_type& x) noexcept(NO_EXCEPT) {
assert(0 <= p && p < this->_impl.size());
this->_impl.add(p, x);
return *this;
}
inline auto& set(const size_type p, const value_type& x) noexcept(NO_EXCEPT) {
assert(0 <= p && p < this->_impl.size());
this->_impl.set(p, x);
return *this;
}
inline auto get(const size_type p) const noexcept(NO_EXCEPT) {
assert(0 <= p && p < this->_impl.size());
return this->_impl.fold(p, p+1);
}
inline auto operator[](const size_type p) noexcept(NO_EXCEPT) { return point_reference(this, p); }
inline auto operator()(const size_type l, const size_type r) noexcept(NO_EXCEPT) { return range_reference(this, l, r); }
inline auto fold(const size_type l, const size_type r) const noexcept(NO_EXCEPT) {
assert(0 <= l && l <= r && r <= this->_impl.size());
return this->_impl.fold(l, r);
}
inline auto fold(const size_type r) const noexcept(NO_EXCEPT) {
assert(0 <= r && r <= this->_impl.size());
return this->_impl.fold(0, r);
}
inline auto fold() const noexcept(NO_EXCEPT) {
return this->_impl.fold_all();
}
template<bool (*f)(value_type)>
inline auto max_right(const size_type l) const noexcept(NO_EXCEPT) {
return this->_impl.max_right(l, [](value_type x) { return f(x); });
}
template<class F>
inline auto max_right(const size_type l, F&& f) const noexcept(NO_EXCEPT) {
return this->_impl.max_right(l, std::forward<F>(f));
}
template<bool (*f)(value_type)>
inline auto min_left(const size_type r) const noexcept(NO_EXCEPT) {
return this->_impl.min_left(r, [](value_type x) { return f(x); });
}
template<class F>
inline auto min_left(const size_type r, F&& f) const noexcept(NO_EXCEPT) {
return this->_impl.min_left(r, std::forward<F>(f));
}
struct iterator;
protected:
using iterator_interface = internal::container_iterator_interface<value_type, const segment_tree, iterator>;
public:
struct iterator : iterator_interface {
using iterator_interface::iterator_interface;
};
inline auto begin() const noexcept(NO_EXCEPT) { return iterator(this, 0); }
inline auto end() const noexcept(NO_EXCEPT) { return iterator(this, this->_impl.size()); }
inline auto rbegin() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
};
template<actions::internal::operatable_action Action>
struct segment_tree<Action> : segment_tree<typename Action::operand> {
using segment_tree<typename Action::operand>::segment_tree;
};
} // namespace uni
#line 26 "data_structure/adaptor/set.hpp"
namespace uni {
namespace internal {
template<
template<class...> class Tree,
template<class...> class Action
>
requires actions::internal::action<Action<internal::size_t>>
struct set_adaptor_impl {
using size_type = internal::size_t;
using key_type = internal::size_t;
using value_type = internal::size_t;
protected:
using impl_data_type = algebraic::combined<algebraic::addition<value_type>, algebraic::minimum<value_type>>;
using impl_tree =
Tree<
std::conditional_t<
internal::available_with<
Tree,
Action<impl_data_type>
>,
Action<impl_data_type>,
actions::range_sum<impl_data_type>
>
>;
impl_tree _data;
size_type _elem = 0;
public:
set_adaptor_impl(const size_type sup) noexcept(NO_EXCEPT) : _data(sup) {};
inline size_type size() const noexcept(NO_EXCEPT) { return this->_data.fold(); }
inline bool empty() const noexcept(NO_EXCEPT) { return this->size() == 0; }
inline size_type count(const key_type& k) const noexcept(NO_EXCEPT) { return this->_data.get(k).val()->first.val(); }
inline bool contains(const key_type& k) const noexcept(NO_EXCEPT) { return this->_data.get(k).val()->first.val() > 0; }
inline value_type mex(const key_type& base = 0) const noexcept(NO_EXCEPT) {
return this->_data.max_right(base, [](const auto& p) { return p.val()->second.val() > 0; });
}
inline std::optional<value_type> next(const key_type& k, const size_type count = 0) const noexcept(NO_EXCEPT) {
const auto v = this->_data.max_right(k, [count](const auto& p) { return p.val()->first.val() <= count; });
if(v == this->_data.size()) return {};
return { v };
}
inline std::optional<value_type> prev(const key_type& k, const size_type count = 0) const noexcept(NO_EXCEPT) {
const auto v = this->_data.min_left(k + 1, [count](const auto& p) { return p.val()->first.val() <= count; });
if(v == 0) return {};
return { v - 1 };
}
inline auto kth_smallest(const size_type k) const noexcept(NO_EXCEPT) { return this->next(0, k); }
inline auto kth_largest(const size_type k) const noexcept(NO_EXCEPT) { return this->prev(this->_data.size()-1, k); }
inline value_type min() const noexcept(NO_EXCEPT) { return this->kth_smallest(0); }
inline value_type max() const noexcept(NO_EXCEPT) { return this->kth_largest(0); }
inline size_type count_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->_data.fold(0, v).val()->first.val(); }
inline size_type count_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->_data.fold(v+1, this->_data.size()).val()->first.val(); }
inline size_type count_or_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->_data.fold(0, v+1).val()->first.val(); }
inline size_type count_or_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->_data.fold(v, this->_data.size()).val()->first.val(); }
template<comparison com = comparison::equal_to>
inline size_type count(const value_type& v) const noexcept(NO_EXCEPT) {
if constexpr(com == comparison::eq) return this->count(v);
if constexpr(com == comparison::under) return this->count_under(v);
if constexpr(com == comparison::over) return this->count_over(v);
if constexpr(com == comparison::or_under) return this->count_or_under(v);
if constexpr(com == comparison::or_over) return this->count_or_over(v);
assert(false);
}
inline const auto& _debug() const noexcept(NO_EXCEPT) { return this->_data; }
};
};
template<template<class...> class Tree = uni::segment_tree>
struct set_adaptor : internal::set_adaptor_impl<Tree, actions::range_set_range_sum> {
using size_type = internal::size_t;
using key_type = internal::size_t;
using value_type = size_type;
protected:
using Base = internal::set_adaptor_impl<Tree, actions::range_set_range_sum>;
using impl_data_type = typename Base::impl_data_type;
public:
set_adaptor() noexcept(NO_EXCEPT) = default;
set_adaptor(const size_type sup) noexcept(NO_EXCEPT) : Base(sup) {};
template<std::input_iterator I, std::sentinel_for<I> S>
set_adaptor(I first, S last) noexcept(NO_EXCEPT) : set_adaptor(*std::ranges::max_element(first, last) + 1) {
valarray<bool> bits(this->_data.size());
REP(itr, first, last) {
assert(0 <= *itr && *itr < this->_data.size());
bits[*itr] = true;
}
this->build_from_bits(ALL(bits));
};
template<std::ranges::input_range R>
set_adaptor(R&& range) noexcept(NO_EXCEPT) : set_adaptor(ALL(range)) {}
template<std::input_iterator I, std::sentinel_for<I> S>
inline auto& build_from_bits(I first, S last) noexcept(NO_EXCEPT) {
if constexpr(std::sized_sentinel_for<S, I>) {
assert(std::ranges::distance(first, last) == this->_data.size());
}
this->_data.assign(first, last);
return *this;
};
template<std::ranges::input_range R>
inline auto& build_from_bits(R&& range) noexcept(NO_EXCEPT) {
return this->build_from_bits(ALL(range));
}
inline bool insert(const key_type& k) noexcept(NO_EXCEPT) {
assert(0 <= k && k < this->_data.size());
const bool res = !this->_data.get(k).val()->first.val();
if(res) this->_data.set(k, impl_data_type{ 1 });
return res;
}
inline bool remove(const key_type& k) noexcept(NO_EXCEPT) {
assert(0 <= k && k < this->_data.size());
const bool res = this->_data.get(k).val()->first.val();
if(res) this->_data.set(k, impl_data_type{ 0 });
return res;
}
};
template<template<class...> class Tree = uni::segment_tree, std::integral Size = std::int64_t>
struct multiset_adaptor : internal::set_adaptor_impl<Tree, actions::range_add_range_sum> {
using size_type = Size;
using key_type = internal::size_t;
using value_type = key_type;
private:
using Base = internal::set_adaptor_impl<Tree, actions::range_add_range_sum>;
using impl_data_type = typename Base::impl_data_type;
public:
multiset_adaptor(const size_type sup) noexcept(NO_EXCEPT) : Base(sup) {};
template<std::input_iterator I, std::sentinel_for<I> S>
multiset_adaptor(I first, S last) noexcept(NO_EXCEPT) : Base(*std::ranges::max_element(first, last) + 1) {
vector<size_type> cnts(this->_data.size());
REP(itr, first, last) {
assert(0 <= *itr && *itr < this->_data.size());
cnts[*itr]++;
}
this->build_from_histogram(ALL(cnts));
};
template<std::ranges::input_range R>
multiset_adaptor(R&& range) noexcept(NO_EXCEPT) : multiset_adaptor(ALL(range)) {}
template<std::input_iterator I, std::sentinel_for<I> S>
inline auto& build_from_histogram(I first, S last) noexcept(NO_EXCEPT) {
if constexpr(std::sized_sentinel_for<S, I>) {
assert(std::ranges::distance(first, last) == this->_data.size());
}
this->_data.assign(first, last);
return *this;
};
template<std::ranges::input_range R>
inline auto& build_from_histogram(R&& range) noexcept(NO_EXCEPT) {
return this->build_from_histogram(ALL(range));
}
inline void insert(const key_type& k, const size_type count = 1) noexcept(NO_EXCEPT) {
assert(0 <= k && k < this->_data.size());
assert(0 <= count);
const auto cur = this->_data.get(k);
const auto num = cur.val()->first.val();
this->_data.set(k, impl_data_type{ num + count });
this->_elem += count;
}
inline void remove(const key_type& k, const size_type count = 1) noexcept(NO_EXCEPT) {
assert(0 <= k && k < this->_data.size());
const auto cur = this->_data.get(k);
const auto num = cur.val()->first.val();
assert(0 <= count && count <= num);
this->_data.set(k, impl_data_type{ num - count });
}
};
} // namespace uni
#line 4 "include/data_structures.hpp"
#line 2 "data_structure/bit_vector.hpp"
#line 9 "data_structure/bit_vector.hpp"
#line 14 "data_structure/bit_vector.hpp"
#line 16 "data_structure/bit_vector.hpp"
namespace uni {
// Thanks to: https://github.com/NyaanNyaan/library/blob/master/data-structure-2d/wavelet-matrix.hpp
struct bit_vector {
using size_type = std::uint_fast32_t;
private:
static constexpr size_type WORDSIZE = 64;
std::vector<std::uint64_t> _block;
std::vector<size_type> _count;
size_type _n, _zeros;
public:
bit_vector(const size_type n = 0) noexcept(NO_EXCEPT) { this->init(n); }
template<std::input_iterator I, std::sentinel_for<I> S>
bit_vector(I first, S last) noexcept(NO_EXCEPT)
: bit_vector(std::ranges::distance(first, last))
{
size_type pos = 0;
for(auto itr=first; itr != last; ++pos, ++itr) if(*itr) this->set(pos);
}
template<std::ranges::input_range R>
bit_vector(R&& range) noexcept(NO_EXCEPT) : bit_vector(ALL(range)) {}
template<class T> bit_vector(const std::initializer_list<T>& init_list) noexcept(NO_EXCEPT)
: bit_vector(ALL(init_list))
{}
inline constexpr size_type size() const noexcept(NO_EXCEPT) { return this->_n; }
inline constexpr size_type zeros() const noexcept(NO_EXCEPT) { return this->_zeros; }
inline constexpr size_type ones() const noexcept(NO_EXCEPT) { return this->_n - this->_zeros; }
inline void set(const size_type k) noexcept(NO_EXCEPT) { this->_block[k / WORDSIZE] |= (1LL << (k % WORDSIZE)); }
inline bool get(const size_type k) const noexcept(NO_EXCEPT) {
return 1U & static_cast<std::uint32_t>(this->_block[k / WORDSIZE] >> (k % WORDSIZE));
}
__attribute__((optimize("O3", "unroll-loops")))
inline void init(const size_type n) noexcept(NO_EXCEPT) {
this->_n = this->_zeros = n;
this->_block.resize(this->_n / WORDSIZE + 1, 0);
this->_count.resize(this->_block.size(), 0);
}
inline void build() noexcept(NO_EXCEPT) {
for(auto k = 1UL; k < this->_block.size(); ++k) {
this->_count[k] = this->_count[k-1] + static_cast<size_type>(std::popcount(this->_block[k-1]));
}
this->_zeros = this->rank0(this->_n);
}
inline size_type rank1(const size_type k) const noexcept(NO_EXCEPT) {
return
this->_count[k / WORDSIZE] +
static_cast<size_type>(std::popcount(uni::clear_higher_bits(this->_block[k / WORDSIZE], k % WORDSIZE)));
}
inline size_type rank0(const size_type k) const noexcept(NO_EXCEPT) { return k - this->rank1(k); }
template<bool BIT>
inline size_type rank(const size_type k) const noexcept(NO_EXCEPT) {
if constexpr(BIT) return this->rank0(k);
else return this->rank1(k);
}
template<bool BIT>
inline size_type select(const size_type rank) const noexcept(NO_EXCEPT) {
if constexpr(BIT) {
if(rank >= this->ones()) return this->_n;
}
else {
if(rank >= this->zeros()) return this->_n;
}
size_type index = 0;
{
size_type ng = static_cast<size_type>(this->_count.size());
while(ng - index > 1) {
size_type mid = (ng + index) / 2;
size_type cnt = this->_count[mid];
if constexpr(!BIT) cnt = mid * WORDSIZE - cnt;
(cnt <= rank ? index : ng) = mid;
}
}
const size_type base = index * WORDSIZE;
if constexpr(BIT) {
return base + select64(this->_block[index], rank - this->_count[index]);
}
else {
return base + select64(~this->_block[index], rank - (base - this->_count[index]));
}
}
inline size_type select0(const size_type k) const noexcept(NO_EXCEPT) { return this->select<false>(k); }
inline size_type select1(const size_type k) const noexcept(NO_EXCEPT) { return this->select<true>(k); }
struct iterator;
private:
using iterator_interface = internal::container_iterator_interface<bool, const bit_vector, iterator>;
public:
struct iterator : iterator_interface {
iterator() noexcept = default;
iterator(const bit_vector *const ref, const size_type pos) noexcept(NO_EXCEPT) : bit_vector::iterator_interface(ref, static_cast<difference_type>(pos)) {}
inline bool operator*() const noexcept(NO_EXCEPT) { return this->ref()->get(this->pos()); }
};
inline auto begin() const noexcept(NO_EXCEPT) { return iterator(this, 0); }
inline auto end() const noexcept(NO_EXCEPT) { return iterator(this, this->size()); }
};
} // namespace uni
#line 2 "data_structure/disjoint_set.hpp"
#line 8 "data_structure/disjoint_set.hpp"
#line 12 "data_structure/disjoint_set.hpp"
#line 15 "data_structure/disjoint_set.hpp"
#line 17 "data_structure/disjoint_set.hpp"
namespace uni {
//Thanks to: atcoder::disjoint_set
struct disjoint_set {
using size_type = internal::size_t;
private:
size_type _n = 0, _group_count = 0;
// root node: -1 * component size
// otherwise: parent
std::vector<size_type> _parent_or_size;
public:
disjoint_set() noexcept = default;
explicit disjoint_set(const size_type n) noexcept(NO_EXCEPT) : _n(n), _group_count(n), _parent_or_size(n, -1) {}
inline auto size() const noexcept(NO_EXCEPT) { return this->_n; }
inline auto group_count() const noexcept(NO_EXCEPT) { return this->_group_count; }
inline auto merge(const size_type a, const size_type b) noexcept(NO_EXCEPT) {
assert(0 <= a && a < _n);
assert(0 <= b && b < _n);
size_type x = this->leader(a), y = this->leader(b);
if (x == y) return x;
--this->_group_count;
if (-this->_parent_or_size[x] < -this->_parent_or_size[y]) std::swap(x, y);
this->_parent_or_size[x] += this->_parent_or_size[y];
this->_parent_or_size[y] = x;
return x;
}
inline bool same(const size_type a, const size_type b) noexcept(NO_EXCEPT) {
assert(0 <= a && a < _n);
assert(0 <= b && b < _n);
return this->leader(a) == this->leader(b);
}
inline size_type leader(const size_type a) noexcept(NO_EXCEPT) {
assert(0 <= a && a < _n);
if(this->_parent_or_size[a] < 0) return a;
return this->_parent_or_size[a] = this->leader(this->_parent_or_size[a]);
}
inline auto size(const size_type a) noexcept(NO_EXCEPT) {
assert(0 <= a && a < _n);
return -this->_parent_or_size[this->leader(a)];
}
inline auto groups() noexcept(NO_EXCEPT) {
vector<size_type> leader_buf(_n), group_size(_n);
REP(i, this->_n) {
leader_buf[i] = this->leader(i);
group_size[leader_buf[i]]++;
}
vector<vector<size_type>> result(_n);
REP(i, this->_n) result[i].reserve(group_size[i]);
REP(i, this->_n) result[leader_buf[i]].push_back(i);
{
const auto range = std::ranges::remove_if(result, [&](const auto& v) { return v.empty(); });
result.erase(ALL(range));
}
return result;
}
};
} // namespace uni
#line 2 "data_structure/disjoint_sparse_table.hpp"
#line 12 "data_structure/disjoint_sparse_table.hpp"
#line 19 "data_structure/disjoint_sparse_table.hpp"
#line 21 "data_structure/disjoint_sparse_table.hpp"
#line 24 "data_structure/disjoint_sparse_table.hpp"
namespace uni {
namespace internal {
namespace disjoint_sparse_table_impl {
// Thanks to: https://noshi91.hatenablog.com/entry/2018/05/08/183946
template<algebraic::internal::semigroup Operand>
struct core {
using size_type = internal::size_t;
using operand = Operand;
using iterator = std::vector<std::vector<Operand>>;
size_type _n = 0, _depth = 0;
bool _built = false;
protected:
std::vector<std::vector<operand>> _table = {};
public:
explicit core(const size_type n = 0) noexcept(NO_EXCEPT) : _n(n) {
this->_depth = std::bit_width<std::make_unsigned_t<size_type>>(n);
this->_table.resize(this->_depth+1, std::vector<operand>(n));
}
template<std::input_iterator I, std::sized_sentinel_for<I> S>
core(I first, S last) noexcept(NO_EXCEPT)
: core(static_cast<size_type>(std::ranges::distance(first, last)))
{
std::ranges::copy(first, last, this->_table.begin()->begin());
}
template<bool FORCE = false>
inline auto& build() noexcept(NO_EXCEPT) {
if(!FORCE and this->_built) return *this;
FOR(i, 2, this->_depth) {
const size_type len = 1 << i;
for(size_type l = 0, m = (len >> 1); m < this->_n; l += len, m = l + (len >> 1)) {
this->_table[i - 1][m - 1] = this->_table.front()[m - 1];
REPD(j, l, m-1) {
this->_table[i - 1][j] = this->_table.front()[j] + this->_table[i - 1][j + 1];
}
this->_table[i - 1][m] = this->_table.front()[m];
REP(j, m + 1, std::min(l + len, this->_n)) {
this->_table[i - 1][j] = this->_table[i - 1][j - 1] + this->_table.front()[j];
}
}
}
this->_built = true;
return *this;
}
inline auto& raw() noexcept(NO_EXCEPT) {
this->_built = false;
return this->_table.front();
}
inline const auto& raw() const noexcept(NO_EXCEPT) { return this->_table.front(); }
inline auto& data() noexcept(NO_EXCEPT) { return this->_table; }
inline const auto& data() const noexcept(NO_EXCEPT) { return this->_table; }
size_type size() const noexcept(NO_EXCEPT) { return this->_n; }
operand fold(const size_type l, size_type r) {
if(l == r) return operand{};
if(l == --r) return this->_table.front()[l];
this->build();
const size_type p = highest_bit_pos<std::make_unsigned_t<size_type>>(l ^ r);
return this->_table[p][l] + this->_table[p][r];
}
};
} // namespace disjoint_sparse_table_impl
} // namespace internal
template<class> struct disjoint_sparse_table : internal::unconstructible {};
template<algebraic::internal::semigroup Semigroup>
struct disjoint_sparse_table<Semigroup> {
private:
using core = internal::disjoint_sparse_table_impl::core<Semigroup>;
using iterator = core::iterator;
core _impl;
public:
using value_type = Semigroup;
using size_type = core::size_type;
protected:
inline auto _positivize_index(const size_type p) const noexcept(NO_EXCEPT) {
return p < 0 ? this->_impl.size() + p : p;
}
public:
explicit disjoint_sparse_table(const size_type n, const value_type& val = value_type()) noexcept(NO_EXCEPT) : _impl(n) {
this->_impl.data().begin()->assign(n, val);
}
template<std::input_iterator I, std::sized_sentinel_for<I> S>
disjoint_sparse_table(I first, S last) noexcept(NO_EXCEPT) : _impl(first, last) {}
template<std::ranges::input_range R>
explicit disjoint_sparse_table(R&& range) noexcept(NO_EXCEPT)
: _impl(std::ranges::begin(range), std::ranges::end(range))
{}
inline auto& raw() noexcept(NO_EXCEPT) { return this->_impl.raw(); }
inline const auto& raw() const noexcept(NO_EXCEPT) { return this->_impl.raw(); }
inline const auto& data() const noexcept(NO_EXCEPT) { return this->impl.data(); }
inline auto size() const noexcept(NO_EXCEPT) { return this->_impl.size(); }
friend internal::range_reference<disjoint_sparse_table>;
struct range_reference : internal::range_reference<disjoint_sparse_table> {
range_reference(disjoint_sparse_table *const super, const size_type l, const size_type r) noexcept(NO_EXCEPT)
: internal::range_reference<disjoint_sparse_table>(super, super->_positivize_index(l), super->_positivize_index(r))
{
assert(0 <= this->_begin && this->_begin <= this->_end && this->_end <= this->_super->size());
}
inline auto fold() noexcept(NO_EXCEPT) {
return this->_super->fold(this->_begin, this->_end);
}
};
inline auto fold(size_type l, size_type r) noexcept(NO_EXCEPT) {
l = this->_positivize_index(l), r = this->_positivize_index(r);
assert(0 <= l && l <= r && r <= this->size());
return this->_impl.fold(l, r);
}
inline auto fold() noexcept(NO_EXCEPT) { return this->fold(0, this->size()); }
inline auto operator[](const size_type index) const noexcept(NO_EXCEPT) { return this->_impl.data().front()[index]; }
inline auto operator()(const size_type l, const size_type r) noexcept(NO_EXCEPT) { return range_reference(this, l, r); }
inline auto begin() const noexcept(NO_EXCEPT) { return this->_impl.data().begin()->begin(); }
inline auto end() const noexcept(NO_EXCEPT) { return this->_impl.data().begin()->end(); }
inline auto rbegin() const noexcept(NO_EXCEPT) { return this->_impl.data().begin()->rbegin(); }
inline auto rend() const noexcept(NO_EXCEPT) { return this->_impl.data().begin()->rend(); }
};
template<actions::internal::operatable_action Action>
struct disjoint_sparse_table<Action> : disjoint_sparse_table<typename Action::operand> {
using disjoint_sparse_table<typename Action::operand>::disjoint_sparse_table;
};
} // namespace uni
#line 2 "data_structure/dynamic_segment_tree.hpp"
#include <memory_resource>
#line 6 "data_structure/dynamic_segment_tree.hpp"
#include <memory>
#line 13 "data_structure/dynamic_segment_tree.hpp"
#line 16 "data_structure/dynamic_segment_tree.hpp"
#line 23 "data_structure/dynamic_segment_tree.hpp"
#line 2 "data_structure/internal/node_handler.hpp"
#line 5 "data_structure/internal/node_handler.hpp"
#line 7 "data_structure/internal/node_handler.hpp"
namespace uni {
namespace node_handlers {
namespace internal {
template<class Allocator, class NodeType>
struct base_handler {
using allocator_type = Allocator;
protected:
using allocator_traits = std::allocator_traits<allocator_type>;
using node_allocator_type = allocator_traits::template rebind_alloc<NodeType>;
using node_allocator_traits = std::allocator_traits<node_allocator_type>;
[[no_unique_address]] node_allocator_type _allocator;
public:
base_handler(const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: _allocator(allocator)
{}
base_handler(const base_handler& source) noexcept(NO_EXCEPT)
: _allocator(node_allocator_traits::select_on_container_copy_construction(source._allocator))
{}
base_handler(base_handler&& source) noexcept = default;
auto& operator=(const base_handler& source) noexcept(NO_EXCEPT) {
if(&source != this) {
if constexpr(allocator_traits::propagate_on_container_copy_assignment::value) {
this->_allocator = source._allocator;
}
}
return *this;
}
auto& operator=(base_handler&& source) noexcept(NO_EXCEPT) {
if(&source != this) {
if constexpr(allocator_traits::propagate_on_container_move_assignment::value) {
this->_allocator = source._allocator;
}
}
return *this;
}
};
} // namespace internal
template<class Allocator>
struct cloneable {
template<class NodeType>
struct handler : internal::base_handler<Allocator, NodeType> {
using internal::base_handler<Allocator, NodeType>::base_handler;
using node_type = NodeType;
using node_pointer = std::shared_ptr<node_type>;
inline static node_pointer nil = std::make_shared<node_type>();
template<class... Args>
inline auto create(Args&&... args) noexcept(NO_EXCEPT) {
return std::allocate_shared<node_type>(this->_allocator, std::forward<Args>(args)...);
}
inline auto clone(const node_pointer& ptr) noexcept(NO_EXCEPT) {
return this->create(*ptr);
}
inline constexpr bool disposable(const node_pointer&) const noexcept { return false; }
inline constexpr void dispose(const node_pointer&) const noexcept {}
};
};
template<class Allocator>
struct reusing {
template<class NodeType>
struct handler : internal::base_handler<Allocator, NodeType> {
using node_type = NodeType;
using node_pointer = std::add_pointer_t<node_type>;
private:
using base = internal::base_handler<Allocator, NodeType>;
using node_allocator_traits = typename base::node_allocator_traits;
inline static int _instance_count = 0;
public:
using base::base;
using allocator_type = typename base::allocator_type;
inline static node_pointer nil;
handler(const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT) : base(allocator) {
if(handler::_instance_count++ == 0) {
handler::nil = new node_type{};
}
}
~handler() noexcept {
if(--handler::_instance_count == 0) {
delete handler::nil;
}
}
template<class... Args>
inline auto create(Args&&... args) noexcept(NO_EXCEPT) {
node_pointer node = node_allocator_traits::allocate(this->_allocator, 1);
node_allocator_traits::construct(this->_allocator, node, std::forward<Args>(args)...);
return node;
}
inline auto clone(const node_pointer ptr) const noexcept { return ptr; }
inline bool disposable(const node_pointer node) const noexcept(NO_EXCEPT) {
return node != handler::nil;
}
inline void dispose(const node_pointer node) noexcept(NO_EXCEPT) {
node_allocator_traits::destroy(this->_allocator, node);
node_allocator_traits::deallocate(this->_allocator, node, 1);
}
};
};
} // namespace node_handlers
} // namespace uni
#line 25 "data_structure/dynamic_segment_tree.hpp"
#line 28 "data_structure/dynamic_segment_tree.hpp"
#line 30 "data_structure/dynamic_segment_tree.hpp"
namespace uni {
namespace internal {
namespace dynamic_segment_tree_impl {
// Thanks to: atcoder::segtree
template<algebraic::internal::monoid Monoid, class NodeHandler>
struct core {
using size_type = internal::size_t;
using operand = Monoid;
struct node_type;
using node_handler = NodeHandler::template handler<node_type>;
using allocator_type = typename node_handler::allocator_type;
using node_pointer = typename node_handler::node_pointer;
protected:
[[no_unique_address]] node_handler _node_handler;
public:
explicit core(const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT) : _node_handler(allocator) {}
core(const core&, const allocator_type& allocator) noexcept(NO_EXCEPT) : _node_handler(allocator) {}
core(core&&, const allocator_type& allocator) noexcept(NO_EXCEPT) : _node_handler(allocator) {}
struct node_type {
size_type index;
operand val, acc;
node_pointer left = node_handler::nil, right = node_handler::nil;
node_type() noexcept = default;
node_type(const size_type _index, const operand& _val) noexcept(NO_EXCEPT)
: index(_index), val(_val), acc(_val)
{}
};
protected:
inline void pull(const node_pointer& tree) const noexcept(NO_EXCEPT) {
tree->acc = tree->left->acc + tree->val + tree->right->acc;
}
inline void dispose(const node_pointer& tree) noexcept(NO_EXCEPT) {
if(this->_node_handler.disposable(tree)) {
this->dispose(tree->left);
this->dispose(tree->right);
this->_node_handler.dispose(tree);
}
}
public:
template<std::random_access_iterator I>
node_pointer build(const size_type lower, const size_type upper, const size_type l, const size_type r, I first) noexcept(NO_EXCEPT) {
const size_type middle = (lower + upper) >> 1;
const auto itr = std::ranges::next(first, middle);
if(middle < l || r <= middle) return node_handler::nil;
node_pointer node = this->_node_handler.create(middle, *itr);
node->left = this->build(lower, middle, l, middle, first);
node->right = this->build(middle, upper, middle + 1, r, first);
this->pull(node);
return node;
}
template<std::random_access_iterator I, std::sentinel_for<I> S>
node_pointer build(I first, S last) noexcept(NO_EXCEPT) {
const size_type size = std::ranges::distance(first, last);
return this->build(0, size, 0, size, first);
}
void set(node_pointer& tree, const size_type lower, const size_type upper, size_type pos, operand val) noexcept(NO_EXCEPT) {
if(tree == node_handler::nil) {
tree = this->_node_handler.create(pos, val);
return;
}
tree = this->_node_handler.clone(tree);
if(tree->index == pos) {
tree->val = val;
this->pull(tree);
return;
}
const size_type middle = (lower + upper) >> 1;
if(pos < middle) {
if(tree->index < pos) std::swap(tree->index, pos), std::swap(tree->val, val);
this->set(tree->left, lower, middle, pos, val);
}
else {
if(pos < tree->index) std::swap(tree->index, pos), std::swap(tree->val, val);
this->set(tree->right, middle, upper, pos, val);
}
this->pull(tree);
}
operand get(const node_pointer& tree, const size_type lower, const size_type upper, const size_type pos) const noexcept(NO_EXCEPT) {
if(tree == node_handler::nil) return {};
if(tree->index == pos) return tree->val;
const size_type middle = (lower + upper) >> 1;
if(pos < middle) return this->get(tree->left, lower, middle, pos);
else return this->get(tree->right, middle, upper, pos);
}
operand fold(const node_pointer& tree, const size_type lower, const size_type upper, const size_type l, const size_type r) const noexcept(NO_EXCEPT) {
if(tree == node_handler::nil || upper <= l || r <= lower) return {};
if(l <= lower && upper <= r) return tree->acc;
const size_type middle = (lower + upper) >> 1;
operand val = this->fold(tree->left, lower, middle, l, r);
if(l <= tree->index && tree->index < r) val = val + tree->val;
return val + this->fold(tree->right, middle, upper, l, r);
}
void clear(const node_pointer& tree, const size_type lower, const size_type upper, const size_type l, const size_type r) const noexcept(NO_EXCEPT) {
if(tree == node_handler::nil || upper <= l || r <= lower) return;
if(l <= lower && upper <= r) {
this->dispose(tree);
tree = node_handler::nil;
return;
}
const size_type middle = (lower + upper) >> 1;
this->clear(tree->left, lower, middle, l, r);
this->clear(tree->right, middle, upper, l, r);
this->pull(tree);
}
template<class F>
size_type max_right(const node_pointer& tree, const size_type lower, const size_type upper, const size_type l, F&& f, operand& acc) const {
if(tree == node_handler::nil || upper <= l) return -1;
if(f(acc + tree->acc)) {
acc = acc + tree->acc;
return -1;
}
const size_type middle = (lower + upper) >> 1;
const size_type res = this->max_right(tree->left, lower, middle, l, f, acc);
if(res != -1) return res;
if(l <= tree->index && !f(acc = acc + tree->val)) return tree->index;
return this->max_right(tree->right, middle, upper, l, std::forward<F>(f), acc);
}
template<class F>
size_type min_left(const node_pointer& tree, const size_type lower, const size_type upper, const size_type r, F&& f, operand& acc) const {
if(tree == node_handler::nil || r <= lower) return 0;
if(f(tree->acc + acc)) {
acc = tree->acc + acc;
return 0;
}
const size_type middle = (lower + upper) >> 1;
const size_type res = this->min_left(tree->right, middle, upper, r, f, acc);
if(res != 0) return res;
if(tree->index < r && !f(acc = tree->val + acc)) {
return tree->index + 1;
}
return this->min_left(tree->left, lower, middle, r, std::forward<F>(f), acc);
}
public:
debugger::debug_t dump_rich(const node_pointer& tree, const std::string prefix = " ", const int dir = 0) const {
if(!tree || tree == node_handler::nil) return prefix + "\n";
const auto left = this->dump_rich(tree->left, prefix + (dir == 1 ? "| " : " "), -1);
const auto here = prefix + "--+ " + debugger::dump(tree->index) + " : " + debugger::dump(tree->val) + "\n";
const auto right = this->dump_rich(tree->right, prefix + (dir == -1 ? "| " : " "), 1);
return left + here + right;
}
debugger::debug_t _debug(const node_pointer tree) const {
if(!tree || tree == node_handler::nil) return "";
return
"(" +
this->_debug(tree->left) + " " +
debugger::dump(tree->index) + " : " + debugger::dump(tree->val) +
this->_debug(tree->right) +
")";
}
};
} // namespace dynamic_segment_tree_impl
} // namespace internal
template<class T, class = node_handlers::reusing<std::allocator<T>>>
struct dynamic_segment_tree : internal::unconstructible {};
template<actions::internal::operatable_action Action, class NodeHandler>
struct dynamic_segment_tree<Action, NodeHandler>
: private internal::dynamic_segment_tree_impl::core<typename Action::operand, NodeHandler>
{
private:
using core = typename internal::dynamic_segment_tree_impl::core<typename Action::operand, NodeHandler>;
public:
using value_type = typename core::operand;
using size_type = typename core::size_type;
using node_handler = typename core::node_handler;
using allocator_type = typename core::allocator_type;
using node_type = typename core::node_type;
using node_pointer = typename core::node_pointer;
private:
inline auto _positivize_index(const size_type p) const noexcept(NO_EXCEPT) {
return p < 0 ? this->_n + p : p;
}
size_type _n = 0;
node_pointer _root = node_handler::nil;
public:
~dynamic_segment_tree() { this->dispose(this->_root); }
dynamic_segment_tree(const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT) : core(allocator) {};
dynamic_segment_tree(const dynamic_segment_tree& source, const allocator_type& allocator) noexcept(NO_EXCEPT)
: core(allocator), _n(source._n), _root(source._root)
{}
dynamic_segment_tree(dynamic_segment_tree&& source, const allocator_type& allocator) noexcept(NO_EXCEPT)
: core(allocator), _n(source._n), _root(source._root)
{}
explicit dynamic_segment_tree(const size_type n, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: core(allocator), _n(n)
{}
template<std::convertible_to<value_type> T>
dynamic_segment_tree(const std::initializer_list<T>& init_list, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: dynamic_segment_tree(init_list, allocator)
{}
template<std::input_iterator I, std::sized_sentinel_for<I> S>
dynamic_segment_tree(I first, S last, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT) : dynamic_segment_tree(allocator) {
this->assign(first, last);
}
template<std::ranges::input_range R>
requires (!std::same_as<std::remove_cvref_t<R>, dynamic_segment_tree>)
dynamic_segment_tree(R&& range, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: dynamic_segment_tree(ALL(range), allocator)
{}
inline auto clone() const noexcept(NO_EXCEPT) { return *this; }
inline auto size() const noexcept(NO_EXCEPT) { return this->_n; }
inline auto& clear() noexcept(NO_EXCEPT) {
this->dispose(this->_root);
this->_n = 0;
this->_root = node_handler::nil;
return *this;
}
template<std::convertible_to<value_type> T>
inline auto& assign(const std::initializer_list<T>& init_list) noexcept(NO_EXCEPT) { return this->assign(init_list); }
template<std::input_iterator I, std::sized_sentinel_for<I> S>
inline auto& assign(I first, S last) noexcept(NO_EXCEPT) {
this->_n = std::ranges::distance(first, last);
this->_root = this->build(first, last);
return *this;
}
template<std::ranges::input_range R>
inline auto& assign(R&& range) noexcept(NO_EXCEPT) { return this->assign(ALL(range)); }
inline auto& set(const size_type pos, value_type val) noexcept(NO_EXCEPT) {
assert(pos < this->_n);
this->core::set(this->_root, 0, this->_n, pos, val);
return *this;
}
inline auto get(const size_type pos) const noexcept(NO_EXCEPT) {
assert(pos < this->_n);
return this->core::get(this->_root, 0, this->_n, pos);
}
inline auto& add(const size_type pos, const value_type& val) noexcept(NO_EXCEPT) {
assert(0 <= pos && pos < this->_n);
this->set(pos, this->get(pos) + val);
return *this;
}
inline auto fold(const size_type l, const size_type r) const noexcept(NO_EXCEPT) {
assert(0 <= l && l <= r && r <= this->_n);
return this->core::fold(this->_root, 0, this->_n, l, r);
}
inline auto fold() const noexcept(NO_EXCEPT) { return this->_root->acc; }
inline auto& clear(const size_type l, const size_type r) noexcept(NO_EXCEPT) {
assert(0 <= l && l <= r && r <= this->_n);
this->core::clear(this->_root, 0, this->_n, l, r);
return *this;
}
template<bool (*f)(value_type)>
inline auto max_right(const size_type l) const noexcept(NO_EXCEPT) {
return this->max_right(l, [](const value_type& val) { return f(val); });
}
template<class F>
inline auto max_right(const size_type l, const F &f) const noexcept(NO_EXCEPT) {
assert(0 <= l && l <= this->_n);
value_type acc;
assert(f(acc));
const auto res = this->core::max_right(this->_root, 0, this->_n, l, f, acc);
return res == -1 ? this->_n : res;
}
template<bool (*f)(value_type)>
inline auto min_left(const size_type r) const noexcept(NO_EXCEPT) {
return this->min_left(r, [](const value_type& val) noexcept(NO_EXCEPT) { return f(val); });
}
template<class F>
inline auto min_left(const size_type r, const F &f) const noexcept(NO_EXCEPT) {
assert(0 <= r && r <= this->_n);
value_type acc;
assert(f(acc));
return this->core::min_left(this->_root, 0, this->_n, r, f, acc);
}
struct point_reference : internal::point_reference<dynamic_segment_tree> {
point_reference(dynamic_segment_tree *const super, const size_type p) noexcept(NO_EXCEPT)
: internal::point_reference<dynamic_segment_tree>(super, super->_positivize_index(p))
{
assert(0 <= this->_pos && this->_pos < this->_super->_n);
}
inline operator value_type() const noexcept(NO_EXCEPT) { return this->_super->get(this->_pos); }
inline auto val() const noexcept(NO_EXCEPT) { return this->_super->get(this->_pos); }
inline auto& operator=(const value_type& v) noexcept(NO_EXCEPT) {
this->_super->set(this->_pos, v);
return *this;
}
inline auto& operator+=(const value_type& v) noexcept(NO_EXCEPT) {
this->_super->add(this->_pos, v);
return *this;
}
};
struct range_reference : internal::range_reference<dynamic_segment_tree> {
range_reference(dynamic_segment_tree *const super, const size_type l, const size_type r) noexcept(NO_EXCEPT)
: internal::range_reference<dynamic_segment_tree>(super, super->_positivize_index(l), super->_positivize_index(r))
{
assert(0 <= this->_begin && this->_begin <= this->_end && this->_end <= this->_super->_n);
}
inline auto fold() noexcept(NO_EXCEPT) {
return this->_super->fold(this->_begin, this->_end);
}
};
inline auto operator[](const size_type p) noexcept(NO_EXCEPT) { return point_reference(this, p); }
inline auto operator()(const size_type l, const size_type r) noexcept(NO_EXCEPT) { return range_reference(this, l, r); }
public:
struct iterator;
protected:
using iterator_interface = internal::container_iterator_interface<value_type, const dynamic_segment_tree, iterator>;
public:
struct iterator : iterator_interface {
using iterator_interface::iterator_interface;
};
inline auto begin() const noexcept(NO_EXCEPT) { return iterator(this, 0); }
inline auto end() const noexcept(NO_EXCEPT) { return iterator(this, this->_n); }
inline auto rbegin() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
using core::dump_rich;
using core::_debug;
debugger::debug_t dump_rich(const std::string prefix = " ") const {
return "\n" + this->dump_rich(this->_root, prefix);
}
debugger::debug_t _debug() const {
return "[ " + this->_debug(this->_root) + " ]";
}
};
template<class Action, class Allocator = std::allocator<Action>>
using persistent_dynamic_segment_tree = dynamic_segment_tree<Action, node_handlers::cloneable<Allocator>>;
namespace pmr {
template<class Action>
using dynamic_segment_tree = uni::dynamic_segment_tree<Action, std::pmr::polymorphic_allocator<Action>>;
template<class Action>
using persistent_dynamic_segment_tree = uni::persistent_dynamic_segment_tree<Action, std::pmr::polymorphic_allocator<Action>>;
}; // namespace pmr
} // namespace uni
#line 2 "data_structure/dynamic_sequence.hpp"
#line 12 "data_structure/dynamic_sequence.hpp"
#line 15 "data_structure/dynamic_sequence.hpp"
#line 2 "internal/uncopyable.hpp"
namespace uni {
namespace internal {
struct uncopyable {
uncopyable() noexcept {}
uncopyable(const uncopyable&) = delete;
uncopyable& operator=(const uncopyable&) = delete;
};
} // namespace internal
} // namespace uni
#line 22 "data_structure/dynamic_sequence.hpp"
#line 25 "data_structure/dynamic_sequence.hpp"
#line 27 "data_structure/dynamic_sequence.hpp"
#line 2 "data_structure/internal/basic_tree_concept.hpp"
#line 6 "data_structure/internal/basic_tree_concept.hpp"
#line 8 "data_structure/internal/basic_tree_concept.hpp"
namespace uni {
namespace internal {
template<class T>
concept basic_tree =
std::default_initializable<T> &&
std::integral<typename T::size_type> &&
requires (T base, typename T::size_type key, typename T::node_pointer tree, const typename T::node_pointer const_tree) {
base.split(const_tree, key, tree, tree);
base.merge(tree, const_tree, const_tree);
};
} // namespace internal
} // namespace name
#line 2 "data_structure/internal/tree_dumper.hpp"
#line 5 "data_structure/internal/tree_dumper.hpp"
#line 9 "data_structure/internal/tree_dumper.hpp"
namespace uni {
namespace internal {
template<class Derived, class Core, bool LEAF_ONLY>
struct dumpable_tree {
private:
using node_handler = Core::node_handler;
using node_pointer = Core::node_pointer;
using size_type = Core::size_type;
inline auto _push(const node_pointer& tree) {
return static_cast<Derived*>(this)->_impl.push(tree);
// return static_cast<Derived*>(this)->push(tree);
}
public:
debugger::debug_t dump_rich(node_pointer tree, const std::string prefix, const int dir, size_type& index)
requires (!LEAF_ONLY)
{
if(!tree || tree == node_handler::nil) return prefix + "\n";
this->_push(tree);
// debug(tree->priority >= tree->left->priority, tree->priority, tree->left->priority);
// debug(tree->priority >= tree->right->priority, tree->priority, tree->right->priority);
assert(tree->priority >= tree->left->priority);
assert(tree->priority >= tree->right->priority);
const auto left = this->dump_rich(tree->left, prefix + (dir == 1 ? "| " : " "), -1, index);
const auto here =
prefix + "--+ [" +
debugger::dump(index) + ", " + debugger::dump(index + tree->length) + ") : " +
"<" + debugger::dump(tree->priority) + "> " +
debugger::dump(tree->data) + " [" + debugger::dump(tree->length) + "]\n";
index += tree->length;
const auto right = this->dump_rich(tree->right, prefix + (dir == -1 ? "| " : " "), 1, index);
return left + here + right;
}
debugger::debug_t dump_rich(node_pointer tree, const std::string prefix, const int dir, size_type& index)
requires
(
LEAF_ONLY &&
requires {
typename Core::node_colors;
}
)
{
if(!tree || tree == node_handler::nil) return prefix + "\n";
this->_push(tree);
const auto left = this->dump_rich(tree->left, prefix + (dir == 1 ? "| " : " "), -1, index);
const auto right = this->dump_rich(tree->right, prefix + (dir == -1 ? "| " : " "), 1, index);
const auto color = tree->color == Core::node_colors::BLACK ? "<->" : "<+>";
const auto here = [&]() -> std::string {
if(tree->is_leaf()) {
index += tree->size;
return
prefix + "--+ [" +
debugger::dump(index - tree->size) + ", " + debugger::dump(index) + ") : " +
debugger::COLOR_STRING + color + debugger::COLOR_INIT + " " +
debugger::dump(tree->data) + " [" + debugger::dump(tree->size) + "]\n";
}
return "";
}();
return left + here + right;
}
inline debugger::debug_t dump_rich(const node_pointer& tree, const std::string prefix = " ", const int dir = 0) {
size_type index = 0;
return this->dump_rich(tree, prefix, dir, index);
}
debugger::debug_t _debug(node_pointer tree)
requires (!LEAF_ONLY)
{
if(!tree || tree == node_handler::nil) return "";
this->_push(tree);
return
"(" +
this->_debug(tree->left) + " " +
debugger::dump(tree->data) + " [" +
debugger::dump(tree->length) + "] " +
this->_debug(tree->right) +
")";
}
debugger::debug_t _debug(node_pointer tree)
requires LEAF_ONLY
{
if(!tree || tree == node_handler::nil) return "";
this->_push(tree);
return
"(" +
this->_debug(tree->left) + " " +
(
tree->is_leaf()
?
debugger::dump(tree->data) + " [" +
debugger::dump(tree->size) + "] "
:
""
) +
this->_debug(tree->right) +
")";
}
};
} // namespace internal
} // namespace uni
#line 2 "data_structure/internal/dynamic_tree.hpp"
#line 6 "data_structure/internal/dynamic_tree.hpp"
#line 9 "data_structure/internal/dynamic_tree.hpp"
#line 12 "data_structure/internal/dynamic_tree.hpp"
#line 15 "data_structure/internal/dynamic_tree.hpp"
#line 17 "data_structure/internal/dynamic_tree.hpp"
namespace uni {
namespace internal {
namespace dynamic_tree_impl {
namespace internal {
template<class T>
consteval auto to_val() {
if constexpr(actions::internal::operatable_action<T>) return typename T::operand{};
else return T{};
}
template<class T>
consteval auto to_acc() {
if constexpr(actions::internal::operatable_action<T>) return typename T::operand{};
else return dummy{};
}
template<class T>
consteval auto to_lazy() {
if constexpr(actions::internal::effective_action<T>) return typename T::operation{};
else return dummy{};
}
template<class T, bool LEAF_ONLY, bool MAY_BE_LAZY = true>
struct data_type {
using val_t = decltype(to_val<T>());
using acc_t = decltype(to_acc<T>());
using lazy_t = decltype(to_lazy<T>());
val_t val;
[[no_unique_address]] acc_t acc;
[[no_unique_address]] std::conditional_t<MAY_BE_LAZY, lazy_t, dummy> lazy;
bool rev = false;
data_type() noexcept = default;
data_type(const val_t& _val) noexcept(NO_EXCEPT) : val(_val) {}
auto _debug() const { return this->val; }
friend bool operator==(const data_type& lhs, const data_type& rhs) noexcept(NO_EXCEPT) {
return lhs.val == rhs.val;
}
friend auto operator<=>(const data_type& lhs, const data_type& rhs) noexcept(NO_EXCEPT) {
return lhs.val <=> rhs.val;
}
};
template<class ActionOrValue, class Derived, class Context>
struct basic_core
: Context::substance<Derived, internal::data_type<ActionOrValue, Context::LEAF_ONLY>>
{
using data_type = internal::data_type<ActionOrValue, Context::LEAF_ONLY>;
private:
using base = typename Context::substance<Derived, data_type>;
static_assert(basic_tree<base>);
public:
using base::base;
using node_handler = typename base::node_handler;
using node_pointer = typename base::node_pointer;
using size_type = typename base::size_type;
using operand = data_type::val_t;
using operation = data_type::lazy_t;
inline auto val(const node_pointer& node) const noexcept(NO_EXCEPT) {
if constexpr(Context::LEAF_ONLY) {
if(node->is_leaf()) return node->size * node->data.val;
return node->data.val;
}
else {
return node->data.acc;
}
}
using base::split;
using base::merge;
inline void split(const node_pointer tree, const size_type l, const size_type r, node_pointer& t0, node_pointer& t1, node_pointer& t2) noexcept(NO_EXCEPT) {
// See: https://twitter.com/KakurenboUni/status/1784576244321018209
this->split(tree, l, t0, t1);
this->split(t1, r - l, t1, t2);
}
inline void split(
const node_pointer tree,
const size_type l, const size_type m, const size_type r,
node_pointer& t0, node_pointer& t1, node_pointer& t2, node_pointer& t3
) noexcept(NO_EXCEPT) {
// See: https://twitter.com/KakurenboUni/status/1784576244321018209
this->split(tree, l, m, t0, t1, t2);
this->split(t2, r - m, t2, t3);
}
inline void merge(node_pointer& tree, node_pointer t0, const node_pointer t1, const node_pointer t2) noexcept(NO_EXCEPT) {
this->merge(t0, t0, t1);
this->merge(tree, t0, t2);
}
void erase(node_pointer& tree, const size_type l, const size_type r) noexcept(NO_EXCEPT) {
assert(l <= r);
node_pointer t0, t1, t2;
this->split(tree, l, r, t0, t1, t2);
this->dispose(t1);
this->merge(tree, t0, t2);
}
auto pop(node_pointer& tree, const size_type pos, const size_type count = 1) noexcept(NO_EXCEPT) {
assert(0 <= count);
if(count == 0) return operand{};
node_pointer t0, t1, t2;
this->split(tree, pos, pos + count, t0, t1, t2);
const auto res = this->val(t1);
this->dispose(t1);
this->merge(tree, t0, t2);
return res;
}
operand get(node_pointer tree, const size_type pos) noexcept(NO_EXCEPT) {
if(tree == node_handler::nil || pos < 0 || pos >= tree->size) return {};
this->base::push(tree);
const auto lower_bound = tree->left->size;
const auto upper_bound = tree->size - tree->right->size;
if(pos < lower_bound) {
return this->get(tree->left, pos);
}
else if(pos >= upper_bound) {
return this->get(tree->right, pos - upper_bound);
}
else {
return tree->data.val;
}
}
template<std::forward_iterator I>
requires std::output_iterator<I, operand>
void enumerate(node_pointer tree, I& itr) noexcept(NO_EXCEPT) {
if(tree == node_handler::nil) return;
this->base::push(tree);
this->enumerate(tree->left, itr);
if constexpr(Context::LEAF_ONLY) {
if(tree->is_leaf()) {
REP(tree->size) *(itr++) = tree->data.val;
}
}
else {
REP(tree->length) *(itr++) = tree->data.val;
}
this->enumerate(tree->right, itr);
}
auto fold(node_pointer& tree, size_type l, size_type r) noexcept(NO_EXCEPT) {
assert(l <= r);
if(l == r) return operand{};
node_pointer t0, t1, t2;
this->split(tree, l, r, t0, t1, t2);
const operand res = this->val(t1);
this->merge(tree, t0, t1, t2);
return res;
}
};
} // namespace internal
} // namespace dynamic_tree_impl
} // namespace internal
} // namespace uni
#line 31 "data_structure/dynamic_sequence.hpp"
#line 2 "data_structure/treap.hpp"
#line 13 "data_structure/treap.hpp"
#line 17 "data_structure/treap.hpp"
#line 23 "data_structure/treap.hpp"
#line 25 "data_structure/treap.hpp"
#line 27 "data_structure/treap.hpp"
#line 29 "data_structure/treap.hpp"
#line 32 "data_structure/treap.hpp"
namespace uni {
namespace internal {
// Thanks to: https://github.com/xuzijian629/library2/blob/master/treap/implicit_treap.cpp
template<class Allocator, class Derived, std::integral SizeType, class ValueType, i64 Id>
struct treap_impl : private uncopyable {
using size_type = SizeType;
using value_type = ValueType;
struct node_type;
using node_handler = typename uni::node_handlers::reusing<Allocator>::template handler<node_type>;
using allocator_type = typename node_handler::allocator_type;
using node_pointer = typename node_handler::node_pointer;
private:
using derived = Derived;
inline auto* _derived() noexcept(NO_EXCEPT) {
return static_cast<derived*>(this);
}
inline const auto* _derived() const noexcept(NO_EXCEPT) {
return static_cast<const derived*>(this);
}
[[no_unique_address]] node_handler _node_handler;
static inline random_engine_32bit _rand;
using priority_type = random_engine_32bit::result_type;
public:
void pull(const node_pointer tree) noexcept(NO_EXCEPT) {
if(tree == node_handler::nil) return;
tree->size = tree->left->size + tree->length + tree->right->size;
this->_derived()->pull(tree);
}
void push(const node_pointer tree) noexcept(NO_EXCEPT) {
if(tree == node_handler::nil) return;
this->_derived()->push(tree);
}
node_pointer create(const value_type& val, const size_type size) noexcept(NO_EXCEPT) {
if(size == 0) return node_handler::nil;
return this->_node_handler.create(val, size);
}
void dispose(node_pointer tree) noexcept(NO_EXCEPT) {
if(this->_node_handler.disposable(tree)) {
this->dispose(tree->left);
this->dispose(tree->right);
this->_node_handler.dispose(tree);
}
}
template<class... Args>
inline void constexpr clone(Args&&...) const noexcept {}
private:
void _rotate_right(node_pointer& tree) noexcept(NO_EXCEPT) { // push ommitted
auto t = tree->left;
tree->left = t->right;
this->pull(tree);
t->right = tree;
this->pull(t);
tree = std::move(t);
}
void _rectify(const node_pointer tree) const noexcept(NO_EXCEPT) {
if(tree->size == 0) return;
std::vector<priority_type> priorities(tree->size);
std::ranges::generate(priorities, treap_impl::_rand);
std::ranges::make_heap(priorities);
std::queue<node_pointer> queue;
queue.push(tree);
auto itr = std::ranges::begin(priorities);
while(!queue.empty()) {
node_pointer node = queue.front();
queue.pop();
node->priority = *(itr++);
if(node->left != node_handler::nil) queue.push(node->left);
if(node->right != node_handler::nil) queue.push(node->right);
}
}
template<std::random_access_iterator I, std::sized_sentinel_for<I> S>
requires std::constructible_from<value_type, std::iter_value_t<I>>
node_pointer _build(I first, S last) noexcept(NO_EXCEPT) {
if(first == last) return node_handler::nil;
const auto length = std::ranges::distance(first, last);
const auto middle = std::ranges::next(first, length >> 1);
node_pointer tree = this->create(value_type{ *middle }, 1);
tree->left = this->_build(first, middle);
tree->right = this->_build(std::ranges::next(middle), last);
this->pull(tree);
return tree;
}
template<std::random_access_iterator I, std::sized_sentinel_for<I> S>
requires
std::constructible_from<value_type, typename std::iter_value_t<I>::first_type> &&
std::integral<typename std::iter_value_t<I>::second_type>
node_pointer _build(I first, S last) noexcept(NO_EXCEPT) {
if(first == last) return node_handler::nil;
const auto length = std::ranges::distance(first, last);
const auto middle = std::ranges::next(first, length >> 1);
node_pointer tree = this->create(value_type{ middle->first }, middle->second );
tree->left = this->_build(first, middle);
tree->right = this->_build(std::ranges::next(middle), last);
this->pull(tree);
return tree;
}
void _split(node_pointer tree, const size_type pos, node_pointer& left, node_pointer& right) noexcept(NO_EXCEPT) {
if(tree == node_handler::nil) {
left = right = node_handler::nil;
return;
}
this->push(tree);
const auto lower_bound = tree->left->size;
const auto upper_bound = tree->size - tree->right->size;
if(pos <= lower_bound) {
node_pointer t;
this->split(tree->left, pos, left, t);
tree->left = t;
if(tree->priority < t->priority) this->_rotate_right(tree);
right = std::move(tree);
this->pull(right);
}
else if(pos >= upper_bound) {
this->split(tree->right, pos - upper_bound, tree->right, right);
left = std::move(tree);
this->pull(left);
}
else {
tree->length = pos - lower_bound;
this->merge(tree->right, this->create(tree->data, upper_bound - pos), tree->right);
this->split(tree->right, 0, tree->right, right), left = std::move(tree);
this->pull(left);
}
}
public:
explicit treap_impl(const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT) : _node_handler(allocator) {}
template<std::random_access_iterator I, std::sized_sentinel_for<I> S>
node_pointer build(I first, S last) {
const auto tree = this->_build(first, last);
this->_rectify(tree);
return tree;
}
struct node_type {
priority_type priority = std::numeric_limits<priority_type>::lowest();
node_pointer left = node_handler::nil, right = node_handler::nil;
size_type length, size;
[[no_unique_address]] value_type data;
node_type() noexcept = default;
node_type(const value_type& _data, const size_type _size) noexcept(NO_EXCEPT)
: priority(treap_impl::_rand()), length(_size), size(_size), data(_data)
{}
};
template<bool STRICT = false, bool RETURN_EXISTENCE = false>
void split(const node_pointer tree, const value_type& val, node_pointer& left, node_pointer& right, bool* exist = nullptr) noexcept(NO_EXCEPT) {
if(tree == node_handler::nil) {
left = right = node_handler::nil;
return;
}
this->push(tree);
if constexpr(RETURN_EXISTENCE) *exist |= val == tree->data;
if(val < tree->data || (!STRICT && val == tree->data)) {
this->template split<STRICT, RETURN_EXISTENCE>(tree->left, val, left, tree->left, exist);
right = std::move(tree);
this->pull(right);
}
else {
this->template split<STRICT, RETURN_EXISTENCE>(tree->right, val, tree->right, right, exist);
left = std::move(tree);
this->pull(left);
}
}
void split(const node_pointer tree, const size_type pos, node_pointer& left, node_pointer& right) noexcept(NO_EXCEPT) {
if(pos <= 0) {
left = node_handler::nil;
this->merge(right, this->create(value_type{}, -pos), std::move(tree));
}
else if(tree->size <= pos) {
right = node_handler::nil;
this->merge(left, std::move(tree), this->create(value_type{}, pos - tree->size));
}
else {
this->_split(std::move(tree), pos, left, right);
}
}
void merge(node_pointer& tree, const node_pointer left, const node_pointer right) noexcept(NO_EXCEPT) {
this->push(left);
this->push(right);
if(left == node_handler::nil || right == node_handler::nil) {
tree = left == node_handler::nil ? right : left;
}
else if(left->priority < right->priority) {
this->merge(right->left, left, right->left), tree = std::move(right);
}
else {
this->merge(left->right, left->right, right), tree = std::move(left);
}
this->pull(tree);
}
};
} // namespace internal
template<std::integral SizeType = i64, class Allocator = std::allocator<SizeType>, i64 Id = -1>
struct treap_context {
static constexpr bool LEAF_ONLY = false;
template<class Derived, class ValueType = internal::dummy>
using substance = internal::treap_impl<Allocator, Derived, SizeType, ValueType, Id>;
};
namespace pmr {
template<std::integral SizeType = i64, i64 Id = -1>
using treap_context = uni::treap_context<SizeType, std::pmr::polymorphic_allocator<SizeType>, Id>;
} // namespace pmr
} // namespace uni
#line 33 "data_structure/dynamic_sequence.hpp"
#line 35 "data_structure/dynamic_sequence.hpp"
#line 38 "data_structure/dynamic_sequence.hpp"
#line 40 "data_structure/dynamic_sequence.hpp"
namespace uni {
namespace internal {
namespace dynamic_tree_impl {
template<class ActionOrValue, class Context>
struct sequence_core
: internal::basic_core<ActionOrValue, sequence_core<ActionOrValue, Context>, Context>
// ,
// dumpable_tree<
// sequence_core<ActionOrValue, Context>,
// internal::basic_core<ActionOrValue, sequence_core<ActionOrValue, Context>, Context>,
// Context::LEAF_ONLY
// >
{
private:
using base = typename internal::basic_core<ActionOrValue, sequence_core, Context>;
public:
static constexpr bool ACC = actions::internal::operatable_action<ActionOrValue>;
static constexpr bool LAZY = actions::internal::effective_action<ActionOrValue>;
using base::base;
using data_type = base::data_type;
using operand = base::operand;
using operation = base::operation;
using node_handler = typename base::node_handler;
using node_type = typename base::node_type;
using node_pointer = typename base::node_pointer;
using size_type = typename base::size_type;
inline void pull(const node_pointer& tree) const noexcept(NO_EXCEPT) {
if constexpr(ACC) {
if constexpr(Context::LEAF_ONLY) {
tree->data.val = this->val(tree->left) + this->val(tree->right);
}
else {
tree->data.acc = tree->left->data.acc + tree->length * tree->data.val + tree->right->data.acc;
}
}
}
inline void push(const node_pointer& tree) noexcept(NO_EXCEPT) {
if(tree->data.rev) {
tree->data.rev = false;
std::swap(tree->left, tree->right);
if(tree->left != node_handler::nil) {
this->clone(tree->left);
tree->left->data.rev ^= 1;
}
if(tree->right != node_handler::nil) {
this->clone(tree->right);
tree->right->data.rev ^= 1;
}
}
if constexpr(LAZY) {
if(tree->data.lazy != operation{}) {
if constexpr(Context::LEAF_ONLY) {
if(tree->left != node_handler::nil) {
this->clone(tree->left);
if(tree->left->is_leaf()) {
tree->left->data.val = ActionOrValue::mapping(tree->data.lazy, tree->left->data.val);
}
else {
tree->left->data.lazy = tree->data.lazy + tree->left->data.lazy;
tree->left->data.val = ActionOrValue::mapping(ActionOrValue::power(tree->data.lazy, tree->left->size), tree->left->data.val);
}
}
if(tree->right != node_handler::nil) {
this->clone(tree->right);
if(tree->right->is_leaf()) {
tree->right->data.val = ActionOrValue::mapping(tree->data.lazy, tree->right->data.val);
}
else {
tree->right->data.lazy = tree->data.lazy + tree->right->data.lazy;
tree->right->data.val = ActionOrValue::mapping(ActionOrValue::power(tree->data.lazy, tree->right->size), tree->right->data.val);
}
}
}
else {
if(tree->left != node_handler::nil) {
tree->left->data.lazy = tree->data.lazy + tree->left->data.lazy;
tree->left->data.acc = ActionOrValue::mapping(ActionOrValue::power(tree->data.lazy, tree->left->size), tree->left->data.acc);
}
if(tree->right != node_handler::nil) {
tree->right->data.lazy = tree->data.lazy + tree->right->data.lazy;
tree->right->data.acc = ActionOrValue::mapping(ActionOrValue::power(tree->data.lazy, tree->right->size), tree->right->data.acc);
}
}
tree->data.val = ActionOrValue::mapping(tree->data.lazy, tree->data.val);
tree->data.lazy = operation{};
}
}
}
inline void update(node_pointer& tree) noexcept(NO_EXCEPT) {
if(tree == node_handler::nil) return;
this->base::push(tree);
this->base::pull(tree);
}
void insert(node_pointer& tree, const size_type pos, const operand& val, const size_type count = 1) noexcept(NO_EXCEPT) {
assert(count >= 0);
if(count == 0) return;
node_pointer t0, t1;
this->split(tree, pos, t0, t1);
this->merge(tree, t0, this->create(val, count), t1);
}
template<std::input_iterator I, std::sized_sentinel_for<I> S>
void insert(node_pointer& tree, const size_type pos, I first, S last) noexcept(NO_EXCEPT) {
node_pointer t0, t1;
this->split(tree, pos, t0, t1);
this->merge(tree, t0, this->build(first, last), t1);
}
void add(node_pointer& tree, const size_type pos, const operand& val) noexcept(NO_EXCEPT) {
node_pointer t0, t1, t2;
this->split(tree, pos, t0, t1);
this->split(t1, 1, t1, t2);
const auto prev = this->val(t1);
this->dispose(t1);
t1 = this->create(data_type{ prev + val }, 1);
this->merge(tree, t0, t1, t2);
}
void fill(node_pointer& tree, const size_type l, const size_type r, const operand& val) noexcept(NO_EXCEPT) {
assert(l <= r);
if(l == r) return;
node_pointer t0, t1, t2;
this->split(tree, l, r, t0, t1, t2);
// this->split(tree, l, r, t0, t1, t2);
// this->split(tree, l, t0, t1);
// debug(this->dump_rich(t0), this->dump_rich(t1));
// this->split(t1, r - l, t1, t2);
// debug(this->dump_rich(t1), this->dump_rich(t2));
this->dispose(t1);
t1 = this->create(val, r - l);
this->merge(tree, t0, t1, t2);
// this->merge(t0, t0, t1);
// debug(this->dump_rich(t0));
// this->merge(tree, t0, t2);
// debug(this->dump_rich(tree));
}
template<std::input_iterator I, std::sized_sentinel_for<I> S>
void fill(node_pointer& tree, const size_type pos, I first, S last) noexcept(NO_EXCEPT) {
node_pointer t0, t1, t2;
this->split(tree, pos, pos + std::ranges::distance(first, last), t0, t1, t2);
this->dispose(t1);
this->merge(tree, t0, this->build(first, last), t2);
}
void apply(node_pointer& tree, const size_type l, const size_type r, const operation& val) noexcept(NO_EXCEPT)
requires LAZY
{
assert(l <= r);
if(l == r) return;
node_pointer t0, t1, t2;
this->split(tree, l, r, t0, t1, t2);
if(t1 == node_handler::nil) t1 = this->create(data_type{}, r - l);
t1->data.lazy = val + t1->data.lazy;
this->merge(tree, t0, t1, t2);
}
void reverse(node_pointer& tree, const size_type l, const size_type r) noexcept(NO_EXCEPT) {
assert(l <= r);
if(l == r) return;
node_pointer t0, t1, t2;
this->split(tree, l, r, t0, t1, t2);
if(t1 != node_handler::nil) t1->data.rev ^= 1;
this->merge(tree, t0, t1, t2);
}
void shift_left(node_pointer& tree, const size_type l, const size_type r, const size_type count = 1) noexcept(NO_EXCEPT) {
assert(l <= r);
if(count < 0) return this->shift_right(tree, l, r, -count);
if(count == 0) return;
if(count >= r - l) return this->fill(tree, l, r, {});
node_pointer t0, t1, t2, t3;
this->split(tree, l, l + count, r, t0, t1, t2, t3);
this->dispose(t1);
this->merge(t2, t2, this->create({}, count));
this->merge(tree, t0, t2, t3);
}
void shift_right(node_pointer& tree, const size_type l, const size_type r, const size_type count = 1) noexcept(NO_EXCEPT) {
assert(l <= r);
if(count < 0) return this->shift_left(tree, l, r, -count);
if(count == 0) return;
if(count >= r - l) return this->fill(tree, l, r, {});
node_pointer t0, t1, t2, t3;
this->split(tree, l, r - count, r, t0, t1, t2, t3);
this->dispose(t2);
this->merge(t1, this->create({}, count), t1);
this->merge(tree, t0, t1, t3);
}
void rotate(node_pointer& tree, const size_type l, const size_type m, const size_type r) noexcept(NO_EXCEPT) {
assert(l <= m && m < r);
if(l == m) return;
node_pointer t0, t1, t2, t3;
this->split(tree, l, m, r, t0, t1, t2, t3);
this->merge(t2, t2, t1);
this->merge(tree, t0, t2, t3);
}
template<bool LEFT>
size_type find(const node_pointer& tree, operand& val, const size_type offset) noexcept(NO_EXCEPT) {
if(tree->data.acc + val == val) {
return -1;
}
if constexpr(LEFT) {
if(tree->left != node_handler::nil and tree->left->data.acc + val != val) {
return this->find<true>(tree->left, val, offset);
}
else {
return tree->data.val + val != val ? offset + tree->left->size : this->find<true>(tree->right, val, offset + tree->left->size + 1);
}
}
else {
if(tree->right != node_handler::nil and tree->right->data.acc + val != val) {
return this->find<false>(tree->right, val, offset + tree->left->size + 1);
}
else {
return tree->data.val + val != val ? offset + tree->left->size : this->find<false>(tree->left, val, offset);
}
}
}
template<bool LEFT>
inline size_type find(node_pointer& tree, const size_type l, const size_type r, const operand& val) noexcept(NO_EXCEPT) {
if(l == r) return -1;
node_pointer t0, t1, t2;
this->split(tree, l, r, t0, t1, t2);
const size_type res = this->find<LEFT>(t1, val, l);
this->merge(tree, t0, t1, t2);
return res;
}
};
} // namespace dynamic_tree_impl
} // namespace internal
template<class ActionOrValue, class Context = treap_context<>>
requires internal::available_with<internal::dynamic_tree_impl::sequence_core, ActionOrValue, Context>
struct dynamic_sequence
: private internal::dumpable_tree<
dynamic_sequence<ActionOrValue, Context>,
internal::dynamic_tree_impl::sequence_core<ActionOrValue, Context>,
Context::LEAF_ONLY
>
{
private:
using sequence_core = internal::dynamic_tree_impl::sequence_core<ActionOrValue, Context>;
template<class T>
static consteval auto _to_operator() {
if constexpr(requires { typename T::value_type; }) return typename T::value_type{};
else return T{};
}
public:
using operand = typename sequence_core::operand;
using operation = typename sequence_core::operation;
using value_type = operand;
using operator_type = decltype(_to_operator<operation>());
using node_handler = typename sequence_core::node_handler;
using allocator_type = typename sequence_core::allocator_type;
using node_type = typename sequence_core::node_type;
using node_pointer = typename sequence_core::node_pointer;
using size_type = typename sequence_core::size_type;
private:
using dumper = internal::dumpable_tree<dynamic_sequence, sequence_core, Context::LEAF_ONLY>;
friend dumper;
sequence_core _impl;
node_pointer _root = node_handler::nil;
size_type _offset = 0;
template<std::same_as<size_type>... SizeTypes>
inline void _normalize_index(SizeTypes&... indices) noexcept(NO_EXCEPT) {
const auto min_index = std::min({ indices... });
((indices -= this->_offset), ...);
if(min_index < this->_offset) this->_offset = min_index;
}
public:
~dynamic_sequence() { this->_impl.dispose(this->_root); }
dynamic_sequence(const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT) : _impl(allocator) {};
dynamic_sequence(const node_pointer& root, const size_type offset = 0, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: _impl(allocator), _root(root), _offset(offset)
{};
template<std::input_iterator I, std::sized_sentinel_for<I> S>
dynamic_sequence(I first, S last, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: _impl(allocator)
{
this->assign(first, last);
}
explicit dynamic_sequence(const size_type size, const value_type& val, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: _impl(allocator)
{
this->assign(size, val);
}
explicit dynamic_sequence(const size_type size, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: dynamic_sequence(size, value_type{}, allocator)
{}
template<std::ranges::input_range R>
requires (!std::same_as<std::remove_cvref_t<R>, dynamic_sequence>)
explicit dynamic_sequence(R&& range, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: dynamic_sequence(ALL(range), allocator)
{}
template<std::convertible_to<value_type> T>
dynamic_sequence(const std::initializer_list<T>& values, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: dynamic_sequence(values, allocator)
{}
inline auto offset() const noexcept(NO_EXCEPT) { return this->_offset; }
inline auto& root() noexcept(NO_EXCEPT) { return this->_root; }
inline const auto& root() const noexcept(NO_EXCEPT) { return this->_root; }
inline auto size() const noexcept(NO_EXCEPT) { return this->_root->size; }
inline bool empty() const noexcept(NO_EXCEPT) { return this->size() == 0; }
template<internal::resizable_range Container>
inline auto to() noexcept(NO_EXCEPT) {
Container res;
res.resize(this->size());
auto itr = std::ranges::begin(res);
this->_impl.enumerate(this->_root, itr);
return res;
}
inline void clear() noexcept(NO_EXCEPT) {
this->_impl.dispose(this->_root);
this->_root = node_handler::nil;
this->_offset = 0;
}
inline auto clone() const noexcept { return *this; }
inline auto clone(size_type l, size_type r) noexcept(NO_EXCEPT) {
this->_normalize_index(l, r);
node_pointer t0, t1, t2;
this->_impl.split(this->_root, l, r, t0, t1, t2);
this->_impl.merge(this->_root, t0, t1, t2);
return dynamic_sequence(t1, this->_offset);
}
inline auto split(size_type pos) noexcept(NO_EXCEPT) {
this->_normalize_index(pos);
node_pointer t0, t1;
this->_impl.split(this->_root, pos, t0, t1);
return std::make_pair(dynamic_sequence(t0, this->_offset), dynamic_sequence(t1, this->_offset));
}
inline auto extract(size_type l, size_type r) noexcept(NO_EXCEPT) {
this->_normalize_index(l, r);
node_pointer t0, t1, t2;
this->_impl.split(this->_root, l, r, t0, t1, t2);
this->_impl.merge(this->_root, t0, t2);
return dynamic_sequence(t1, this->_offset);
}
inline auto& insert(size_type pos, const dynamic_sequence& other) noexcept(NO_EXCEPT) {
this->_normalize_index(pos);
node_pointer t0, t1;
this->_impl.split(this->_root, pos, t0, t1);
this->_impl.merge(this->_root, t0, other._root, t1);
return *this;
}
inline auto& replace(size_type l, size_type r, const dynamic_sequence& other) noexcept(NO_EXCEPT) {
this->_normalize_index(l, r);
node_pointer t0, t1, t2;
this->_impl.split(this->_root, l, r, t0, t1, t2);
this->_impl.merge(this->_root, t0, other._root, t2);
return *this;
}
inline auto& merge(const dynamic_sequence& other) noexcept(NO_EXCEPT) {
this->_impl.merge(this->_root, this->_root, other._root);
return *this;
}
template<std::input_iterator I, std::sized_sentinel_for<I> S>
inline auto& assign(I first, S last) noexcept(NO_EXCEPT) {
this->clear();
this->_root = this->_impl.build(first, last);
return *this;
}
inline auto& assign(const size_type size, const value_type& val = value_type{}) noexcept(NO_EXCEPT) {
this->clear();
this->_impl.insert(this->_root, 0, val, size);
return *this;
}
template<std::ranges::input_range R>
inline auto& assign(R&& range) noexcept(NO_EXCEPT) {
return this->assign(ALL(range));
}
template<std::convertible_to<value_type> T>
inline auto& assign(const std::initializer_list<T>& values) noexcept(NO_EXCEPT) {
return this->assign(values);
}
inline auto& resize(const size_type size, const value_type& val = value_type{}) noexcept(NO_EXCEPT) {
if(this->size() > size) this->_impl.erase(this->_root, size, this->size());
if(this->size() < size) this->push_back(val, size - this->size());
return *this;
}
inline auto& expand(size_type l, size_type r) noexcept(NO_EXCEPT) {
this->_normalize_index(l, r);
node_pointer t0, t1, t2;
this->_impl.split(this->_root, l, r, t0, t1, t2);
this->_impl.merge(this->_root, t0, t1, t2);
return *this;
}
inline auto& expand(size_type pos) noexcept(NO_EXCEPT) {
this->_normalize_index(pos);
node_pointer t0, t1;
this->_impl.split(this->_root, pos, t0, t1);
this->_impl.merge(this->_root, t0, t1);
return *this;
}
inline auto& fill(const value_type& val) noexcept(NO_EXCEPT) {
this->_impl.fill(this->_root, 0, this->size(), val);
return *this;
}
inline auto fold() noexcept(NO_EXCEPT) {
return this->_impl.val(this->_root);
}
inline auto& apply(const operator_type& val) noexcept(NO_EXCEPT) {
this->_root->data.lazy = this->_root->data.lazy + val;
this->update(this->_root);
return *this;
}
inline auto front() noexcept(NO_EXCEPT) {
return this->_impl.fold(this->_root, 0, 1);
}
inline auto back() noexcept(NO_EXCEPT) {
return this->_impl.fold(this->_root, this->size() - 1, this->size());
}
inline auto& push_front(const value_type& val, const size_type count = 1) noexcept(NO_EXCEPT) {
this->_impl.insert(this->_root, 0, val, count);
return *this;
}
inline auto& push_back(const value_type& val, const size_type count = 1) noexcept(NO_EXCEPT) {
this->_impl.insert(this->_root, this->size(), val, count);
return *this;
}
inline auto& reverse() noexcept(NO_EXCEPT) {
this->_root->data.rev ^= 1;
this->_impl.update(this->_root);
return *this;
}
inline auto& shift_left(const size_type count = 1) noexcept(NO_EXCEPT) {
this->_impl.shift_left(this->_root, 0, this->size(), count);
return *this;
}
inline auto& shift_right(const size_type count = 1) noexcept(NO_EXCEPT) {
this->_impl.shift_right(this->_root, 0, this->size(), count);
return *this;
}
// Same usage as: std::rotate(:m:)
inline auto& rotate(size_type m) noexcept(NO_EXCEPT) {
this->_normalize_index(m);
this->_impl.rotate(this->_root, 0, m, this->size());
return *this;
}
// Same usage as: std::rotate(:m:)
inline auto& rotate_left(const size_type count = 1) noexcept(NO_EXCEPT) {
assert(!this->empty());
this->_impl.rotate(this->_root, 0, uni::mod(count, this->size()), this->size());
return *this;
}
// Same usage as: std::rotate(:m:)
inline auto& rotate_right(const size_type count = 1) noexcept(NO_EXCEPT) {
assert(!this->empty());
this->_impl.rotate(this->_root, 0, uni::mod(-count, this->size()), this->size());
return *this;
}
template<std::input_iterator I, std::sized_sentinel_for<I> S>
inline auto& insert(size_type pos, I first, S last) noexcept(NO_EXCEPT) {
this->_normalize_index(pos);
this->_impl.insert(this->_root, pos, first, last);
return *this;
}
inline auto& insert(size_type pos, const operand& val, const size_type count = 1) noexcept(NO_EXCEPT) {
this->_normalize_index(pos);
this->_impl.insert(this->_root, pos, val, count);
return *this;
}
inline auto& erase(size_type l, size_type r) noexcept(NO_EXCEPT) {
this->_normalize_index(l, r);
this->_impl.erase(this->_root, l, r);
return *this;
}
inline auto& erase(const size_type pos) noexcept(NO_EXCEPT) {
return this->erase(pos, pos + 1);
}
inline auto pop(size_type pos, const size_type count = 1) noexcept(NO_EXCEPT) {
this->_normalize_index(pos);
return this->_impl.pop(this->_root, pos, count);
}
inline auto get(size_type pos) noexcept(NO_EXCEPT) {
this->_normalize_index(pos);
return this->_impl.get(this->_root, pos);
}
inline auto& add(size_type pos, const value_type& val) noexcept(NO_EXCEPT) {
this->_normalize_index(pos);
this->_impl.add(this->_root, pos, val);
return *this;
}
inline auto& fill(size_type l, size_type r, const value_type& val) noexcept(NO_EXCEPT) {
this->_normalize_index(l, r);
this->_impl.fill(this->_root, l, r, val);
return *this;
}
inline auto fold(size_type l, size_type r) noexcept(NO_EXCEPT) {
this->_normalize_index(l, r);
return this->_impl.fold(this->_root, l, r);
}
inline auto& apply(size_type l, size_type r, const operation& val) noexcept(NO_EXCEPT) {
this->_normalize_index(l, r);
this->_impl.apply(this->_root, l, r, val);
return *this;
}
inline auto& reverse(size_type l, size_type r) noexcept(NO_EXCEPT) {
this->_normalize_index(l, r);
this->_impl.reverse(this->_root, l, r);
return *this;
}
inline auto& rotate(size_type l, size_type m, size_type r) noexcept(NO_EXCEPT) {
this->_normalize_index(l, m, r);
this->_impl.rotate(this->_root, l, m, r);
return *this;
}
inline auto& shift_left(size_type l, size_type r, const size_type count = 1) noexcept(NO_EXCEPT) {
this->_normalize_index(l, r);
this->_impl.shift_left(this->_root, l, r, count);
return *this;
}
inline auto& shift_right(size_type l, size_type r, const size_type count = 1) noexcept(NO_EXCEPT) {
this->_normalize_index(l, r);
this->_impl.shift_right(this->_root, l, r, count);
return *this;
}
inline auto pop_front(const size_type count = 1) noexcept(NO_EXCEPT) {
return this->_impl.pop(this->_root, 0, count);
}
inline auto pop_back(const size_type count = 1) noexcept(NO_EXCEPT) {
return this->_impl.pop(this->_root, this->size() - count, count);
}
template<std::ranges::input_range R>
requires (!std::same_as<std::remove_cvref_t<R>, dynamic_sequence>)
inline auto& insert(const size_type pos, R&& range) noexcept(NO_EXCEPT) {
return this->insert(pos, ALL(range));
}
inline auto& set(const size_type pos, const value_type& val) noexcept(NO_EXCEPT) {
return this->fill(pos, pos + 1, val);
}
inline auto& apply(const size_type pos, const operator_type& val) noexcept(NO_EXCEPT) {
return this->apply(pos, pos + 1, val);
}
inline auto& rotate_left(const size_type l, const size_type r, const size_type count = 1) noexcept(NO_EXCEPT) {
assert(l < r);
return this->rotate(l, l + uni::mod(count, r - l), r);
}
inline auto& rotate_right(const size_type l, const size_type r, const size_type count = 1) noexcept(NO_EXCEPT) {
assert(l < r);
return this->rotate(l, l + uni::mod(-count, r - l), r);
}
// Find the min / max k in [l, r) that satisfies (this[k] + x) != x.
// If no such k is found, return -1.
template<bool LEFT = true>
inline auto find(const size_type l, const size_type r, const value_type& val) noexcept(NO_EXCEPT) {
return this->template find<LEFT>(l, r - 1, r);
}
// Find the min / max k in whole that satisfies (this[k] + x) != x.
// If no such k is found, return -1.
template<bool LEFT = true>
inline auto find(const value_type& val) noexcept(NO_EXCEPT) {
return this->find<LEFT>(0, this->size(), val);
}
struct point_reference : internal::point_reference<dynamic_sequence, size_type> {
point_reference(dynamic_sequence *const super, const size_type pos) noexcept(NO_EXCEPT)
: internal::point_reference<dynamic_sequence, size_type>(super, pos)
{}
operator value_type() noexcept(NO_EXCEPT) { return this->_super->get(this->_pos); }
auto val() noexcept(NO_EXCEPT) { return this->_super->get(this->_pos); }
inline auto& operator=(const value_type& val) noexcept(NO_EXCEPT) {
this->_super->set(this->_pos, val);
return *this;
}
inline auto& operator+=(const value_type& val) noexcept(NO_EXCEPT) {
this->_super->add(this->_pos, val);
return *this;
}
inline auto& operator*=(const operator_type& val) noexcept(NO_EXCEPT) {
this->_super->apply(this->_pos, val);
return *this;
}
};
struct range_reference : internal::range_reference<dynamic_sequence, size_type> {
range_reference(dynamic_sequence *const super, const size_type l, const size_type r) noexcept(NO_EXCEPT)
: internal::range_reference<dynamic_sequence, size_type>(super, l, r)
{}
inline auto clone() noexcept(NO_EXCEPT) {
return this->_super->clone(this->_begin, this->_end);
}
inline auto fold() noexcept(NO_EXCEPT) {
return this->_super->fold(this->_begin, this->_end);
}
inline auto& operator=(const value_type& val) noexcept(NO_EXCEPT) {
this->_super->fill(this->_begin, this->_end, val);
return *this;
}
inline auto& operator*=(const operator_type& val) noexcept(NO_EXCEPT) {
this->_super->apply(this->_begin, this->_end, val);
return *this;
}
// Find the min / max k in [l, r) that satisfies (this[k] + x) != x.
// If no such k is found, return -1.
template<bool LEFT = true>
inline auto find(const value_type& val) noexcept(NO_EXCEPT) {
return this->_super->template find<LEFT>(this->_begin, this->_end, val);
}
};
inline auto operator[](const size_type pos) noexcept(NO_EXCEPT) { return point_reference(this, pos); }
inline auto operator()(const size_type l, const size_type r) noexcept(NO_EXCEPT) { return range_reference(this, l, r); }
struct iterator;
protected:
using iterator_interface = internal::container_iterator_interface<value_type, dynamic_sequence, iterator>;
public:
struct iterator : iterator_interface {
using iterator_interface::iterator_interface;
};
inline auto begin() noexcept(NO_EXCEPT) { return iterator(this, 0); }
inline auto end() noexcept(NO_EXCEPT) { return iterator(this, this->size()); }
inline auto rbegin() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
inline auto traverse() const noexcept(NO_EXCEPT) { return typename sequence_core::traverser(this->_root); }
using dumper::dump_rich;
using dumper::_debug;
debugger::debug_t dump_rich(const std::string prefix = " ") {
return "\n" + this->dump_rich(this->_root, prefix);
}
debugger::debug_t _debug() {
return "[ " + this->_debug(this->_root) + " ]";
}
};
} // namespace uni
#line 2 "data_structure/dynamic_set.hpp"
#line 12 "data_structure/dynamic_set.hpp"
#line 15 "data_structure/dynamic_set.hpp"
#line 22 "data_structure/dynamic_set.hpp"
#line 25 "data_structure/dynamic_set.hpp"
#line 27 "data_structure/dynamic_set.hpp"
#line 31 "data_structure/dynamic_set.hpp"
#line 33 "data_structure/dynamic_set.hpp"
#line 35 "data_structure/dynamic_set.hpp"
#line 38 "data_structure/dynamic_set.hpp"
#line 40 "data_structure/dynamic_set.hpp"
namespace uni {
namespace internal {
namespace dynamic_tree_impl {
template<class ActionOrValue, class Context>
requires (!Context::LEAF_ONLY)
struct set_core : internal::basic_core<ActionOrValue, set_core<ActionOrValue, Context>, Context> {
private:
using base = internal::basic_core<ActionOrValue, set_core, Context>;
public:
using base::base;
using data_type = base::data_type;
using operand = base::operand;
using node_handler = typename base::node_handler;
using node_type = typename base::node_type;
using node_pointer = typename base::node_pointer;
using size_type = typename base::size_type;
inline void pull(const node_pointer tree) const noexcept(NO_EXCEPT) {
tree->data.acc = tree->left->data.acc + tree->length * tree->data.val + tree->right->data.acc;
}
inline constexpr void push(const node_pointer) const noexcept(NO_EXCEPT) { /* do nothing */ }
template<std::random_access_iterator I, std::sized_sentinel_for<I> S>
node_pointer build(I first, S last) {
std::vector<i64> val;
val.assign(first, last);
std::ranges::sort(val);
return this->base::build(ALL(val));
}
void insert(node_pointer& tree, const operand& val, const size_type count = 1) noexcept(NO_EXCEPT) {
if(count == 0) return;
if(count < 0) return this->erase(tree, val, -count);
node_pointer t0, t1;
this->split(tree, { val }, t0, t1);
this->merge(tree, t0, this->create(val, count), t1);
}
void insert_unique(node_pointer& tree, const operand& val, const size_type count = 1) noexcept(NO_EXCEPT) {
if(count == 0) return;
if(count < 0) return this->erase(tree, val, -count);
node_pointer t0, t1;
bool exist = false;
this->template split<false, true>(tree, { val }, t0, t1, &exist);
if(exist) this->merge(tree, t0, t1);
else this->merge(tree, t0, this->create(val, count), t1);
}
void erase(node_pointer& tree, const operand& val, const size_type count = 1) noexcept(NO_EXCEPT) {
if(count == 0) return;
if(count < 0) return this->insert(tree, val, -count);
node_pointer t0, t1, t2;
this->split(tree, { val }, t0, t1);
this->split(t1, count, t1, t2);
this->dispose(t1);
this->merge(tree, t0, t2);
}
void erase_limit(node_pointer& tree, const operand& val, size_type count = 1) noexcept(NO_EXCEPT) {
if(count == 0) return;
if(count < 0) return this->insert(tree, val, -count);
node_pointer t0, t1, t2, t3;
this->split(tree, { val }, t0, t1);
this->template split<true>(t1, { val }, t1, t3);
if(count >= t1->size) count = t1->size;
this->split(t1, count, t1, t2);
this->dispose(t1);
this->merge(t2, t0, t2);
this->merge(tree, t2, t3);
}
auto fold(node_pointer tree, const size_type l, const size_type r) noexcept(NO_EXCEPT) {
assert(0 <= l && l <= r && r <= tree->size);
return this->base::fold(tree, l, r);
}
void erase(node_pointer& tree, const size_type l, const size_type r) noexcept(NO_EXCEPT) {
assert(0 <= l && l <= r && r <= tree->size);
this->base::erase(tree, l, r);
}
auto pop(node_pointer& tree, const size_type pos, const size_type count = 1) noexcept(NO_EXCEPT) {
assert(0 <= pos && 0 <= count && pos + count <= tree->size);
return this->base::pop(tree, pos, count);
}
auto get(node_pointer tree, const size_type pos) noexcept(NO_EXCEPT) {
assert(0 <= pos && pos < tree->size);
return this->base::get(tree, pos);
}
template<bool STRICT = false>
auto find(node_pointer& tree, const operand& val) noexcept(NO_EXCEPT) {
node_pointer t0, t1;
this->template split<STRICT>(tree, { val }, t0, t1);
const auto res = t0->size;
this->merge(tree, t0, t1);
return res;
}
auto equal_range(node_pointer& tree, const operand& val) noexcept(NO_EXCEPT) {
node_pointer t0, t1, t2;
this->template split<true>(tree, { val }, t1, t2);
this->split(t1, { val }, t0, t1);
const auto lower = t0->size;
this->merge(t1, t0, t1);
const auto upper = t1->size;
this->merge(tree, t1, t2);
return std::make_pair(std::move(lower), std::move(upper));
}
};
} // namespace dynamic_tree_impl
} // namespace internal
template<class Value, class Context = treap_context<>>
struct dynamic_set : dynamic_set<actions::make_full_t<Value>, Context> {
using dynamic_set<actions::make_full_t<Value>, Context>::dynamic_set;
};
template<actions::internal::full_action ActionOrValue, class Context>
requires internal::available_with<internal::dynamic_tree_impl::set_core, ActionOrValue, Context>
struct dynamic_set<ActionOrValue, Context>
: private internal::dumpable_tree<
dynamic_set<ActionOrValue, Context>,
internal::dynamic_tree_impl::set_core<ActionOrValue, Context>,
Context::LEAF_ONLY
>
{
public:
using action = ActionOrValue;
using operand = typename action::operand;
using value_type = operand;
using set_core = internal::dynamic_tree_impl::set_core<ActionOrValue, Context>;
using node_handler = typename set_core::node_handler;
using allocator_type = typename set_core::allocator_type;
using node_type = typename set_core::node_type;
using node_pointer = typename set_core::node_pointer;
using size_type = typename set_core::size_type;
private:
using dumper = internal::dumpable_tree<dynamic_set, set_core, Context::LEAF_ONLY>;
friend dumper;
set_core _impl;
node_pointer _root = node_handler::nil;
size_type _offset = 0;
public:
~dynamic_set() { this->_impl.dispose(this->_root); }
dynamic_set(const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT) : _impl(allocator) {};
template<std::input_iterator I, std::sized_sentinel_for<I> S>
dynamic_set(I first, S last, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: _impl(allocator)
{
this->assign(first, last);
}
explicit dynamic_set(const size_type size, const value_type& val, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: _impl(allocator)
{
this->assign(size, val);
}
explicit dynamic_set(const size_type size, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: dynamic_set(size, value_type{}, allocator)
{}
template<std::ranges::input_range R>
explicit dynamic_set(R&& range, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: dynamic_set(ALL(range), allocator)
{}
template<std::convertible_to<value_type> T>
dynamic_set(const std::initializer_list<T>& values, const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT)
: dynamic_set(values, allocator)
{}
inline node_pointer& root() noexcept(NO_EXCEPT) { return this->_root; }
inline const node_pointer& root() const noexcept(NO_EXCEPT) { return this->_root; }
size_type size() const noexcept(NO_EXCEPT) { return this->_root->size; }
bool empty() const noexcept(NO_EXCEPT) { return this->size() == 0; }
template<internal::resizable_range Container>
inline auto to() noexcept(NO_EXCEPT) {
Container res;
res.resize(this->size());
auto itr = std::ranges::begin(res);
this->_impl.enumerate(this->_root, itr);
return res;
}
inline void clear() noexcept(NO_EXCEPT) {
this->_impl.dispose(this->_root);
this->_root = node_handler::nil;
}
template<bool UNIQUE = false, std::input_iterator I, std::sized_sentinel_for<I> S>
inline auto& assign(I first, S last) noexcept(NO_EXCEPT) {
this->clear();
this->insert<UNIQUE>(first, last);
return *this;
}
template<bool UNIQUE = false>
inline auto& assign(const size_type size, const value_type& val = value_type{}) noexcept(NO_EXCEPT) {
this->clear();
this->insert<UNIQUE>(val, size);
return *this;
}
template<bool UNIQUE = false, std::ranges::input_range R>
inline auto& assign(R&& range) noexcept(NO_EXCEPT) {
return this->assign<UNIQUE>(ALL(range));
}
template<bool UNIQUE = false, std::convertible_to<value_type> T>
inline auto& assign(const std::initializer_list<T>& values) noexcept(NO_EXCEPT) {
return this->assign<UNIQUE>(values);
}
template<bool UNIQUE = false>
inline auto& insert(const operand& val, const size_type count = 1) noexcept(NO_EXCEPT) {
if constexpr(UNIQUE) this->_impl.insert_unique(this->_root, val, count);
else this->_impl.insert(this->_root, val, count);
return *this;
}
template<bool UNIQUE = false, std::input_iterator I, std::sized_sentinel_for<I> S>
inline auto& insert(I first, S last) noexcept(NO_EXCEPT) {
for(; first != last; ++first) this->template insert<UNIQUE>(*first);
return *this;
}
template<bool UNIQUE = false, std::ranges::input_range R>
inline auto& insert(R&& range) noexcept(NO_EXCEPT) {
return this->template insert<UNIQUE>(ALL(range));
}
inline auto& fill(const value_type& val) noexcept(NO_EXCEPT) {
const size_type size = this->size();
this->clear();
this->insert(val, size);
return *this;
}
template<bool LIMIT = true>
inline auto& erase(const value_type& val, const size_type count = 1) noexcept(NO_EXCEPT) {
if constexpr(LIMIT) this->_impl.erase_limit(this->_root, val, count);
else this->_impl.erase(this->_root, val, count);
return *this;
}
inline auto& erase(const size_type l, const size_type r) noexcept(NO_EXCEPT) {
this->_impl.erase(this->_root, l, r);
return *this;
}
inline value_type pop(const size_type pos, const size_type count = 1) noexcept(NO_EXCEPT) {
return this->_impl.pop(this->_root, pos, count);
}
inline value_type pop_min(const size_type count = 1) noexcept(NO_EXCEPT) {
return this->pop(0, count);
}
inline value_type pop_max(const size_type count = 1) noexcept(NO_EXCEPT) {
return this->pop(this->size() - count, count);
}
inline operand fold(const size_type l, const size_type r) noexcept(NO_EXCEPT) {
return this->_impl.fold(this->_root, l, r);
}
inline value_type get(const size_type k) noexcept(NO_EXCEPT) {
return this->_impl.get(this->_root, k);
}
inline operand median(const size_type l, const size_type r) noexcept(NO_EXCEPT) {
return this->get((r - l) >> 1);
}
inline value_type min() noexcept(NO_EXCEPT) {
return this->get(0);
}
inline value_type median() noexcept(NO_EXCEPT) {
return this->get(this->size() >> 1);
}
inline value_type max() noexcept(NO_EXCEPT) {
return this->get(this->size() - 1);
}
inline auto fold() noexcept(NO_EXCEPT) {
return this->_root->data.acc;
}
inline value_type operator[](const size_type k) noexcept(NO_EXCEPT) {
return this->get(k);
}
inline value_type operator()(const size_type l, const size_type r) noexcept(NO_EXCEPT) {
return this->fold(l, r);
}
struct iterator;
inline auto lower_bound(const value_type& val) noexcept(NO_EXCEPT) {
return iterator{ this, this->_impl.template find<false>(this->_root, val) };
}
inline auto upper_bound(const value_type& val) noexcept(NO_EXCEPT) {
return iterator{ this, this->_impl.template find<true>(this->_root, val) };
}
inline auto equal_range(const value_type& val) noexcept(NO_EXCEPT) {
const auto [ lower, upper ] = this->_impl.equal_range(this->_root, val);
return std::make_pair(iterator{ this, lower }, iterator{ this, upper });
}
inline size_type count(const value_type& val) noexcept(NO_EXCEPT) {
const auto [ lower, upper ] = this->_impl.equal_range(this->_root, val);
return upper - lower;
}
inline bool contains(const value_type& val) noexcept(NO_EXCEPT) {
return this->count(val) == 1;
}
inline auto& erase(const iterator& itr) noexcept(NO_EXCEPT) {
return this->erase(itr.pos(), itr.pos() + 1);
}
inline auto& erase(const iterator& l, const iterator& r) noexcept(NO_EXCEPT) {
return this->erase(l.pos(), r.pos());
}
protected:
using iterator_interface = internal::container_iterator_interface<value_type,dynamic_set,iterator>;
public:
struct iterator : iterator_interface {
using iterator_interface::iterator_interface;
};
inline auto begin() noexcept(NO_EXCEPT) { return iterator{ this, 0 }; }
inline auto end() noexcept(NO_EXCEPT) { return iterator{ this, this->size() }; }
inline auto rbegin() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
using dumper::dump_rich;
using dumper::_debug;
debugger::debug_t dump_rich(const std::string prefix = " ") {
return "\n" + this->dump_rich(this->_root, prefix);
}
debugger::debug_t _debug() {
return "[ " + this->_debug(this->_root) + " ]";
}
};
} // namespace uni
#line 2 "data_structure/fenwick_tree.hpp"
#line 12 "data_structure/fenwick_tree.hpp"
#line 21 "data_structure/fenwick_tree.hpp"
#line 24 "data_structure/fenwick_tree.hpp"
#line 27 "data_structure/fenwick_tree.hpp"
namespace uni {
namespace internal {
namespace fenwick_tree_impl {
// Thanks to: atcoder::fenwick_tree
template<algebraic::internal::monoid Operand>
struct core {
using operand = Operand;
using size_type = internal::size_t;
private:
size_type _n = 0, _bit_ceil = 0;
std::vector<operand> _data;
inline void _init() noexcept(NO_EXCEPT) {
FOR(i, 1, this->_n) {
size_type j = i + (i & -i);
if(j <= this->_n) this->_data[j-1] = this->_data[j-1] + this->_data[i-1];
}
}
public:
core() noexcept(NO_EXCEPT) {}
explicit core(const size_type n) noexcept(NO_EXCEPT)
: _n(n), _bit_ceil(std::bit_ceil<std::make_unsigned_t<size_type>>(n)), _data(n, operand{})
{}
inline size_type size() const noexcept(NO_EXCEPT) { return this->_n; }
template<std::input_iterator I, std::sentinel_for<I> S>
inline void assign(I first, S last) noexcept(NO_EXCEPT) {
if constexpr(std::sized_sentinel_for<S, I>) {
assert(std::ranges::distance(first, last) == this->size());
}
for(size_type i = 0; first < last; ++i, ++first) this->_data[i] = *first;
this->_init();
}
inline void add(size_type p, const operand& x) noexcept(NO_EXCEPT) {
for(p++; p<=this->_n; p += p & -p) this->_data[p-1] = this->_data[p-1] + x;
}
inline void set(const size_type p, const operand& x) noexcept(NO_EXCEPT) {
assert(this->get(p) == this->fold(p, p+1));
this->add(p, x + -this->get(p));
}
inline operand fold(size_type r) const noexcept(NO_EXCEPT) {
operand s = operand{};
for(; r>0; r -= r & -r) s = s + this->_data[r-1];
return s;
}
inline operand fold(size_type l, size_type r) const noexcept(NO_EXCEPT) {
operand s = operand{};
for(; l < r; r -= r & -r) s = s + this->_data[r-1];
for(; r < l; l -= l & -l) s = s + -this->_data[l-1];
return s;
}
inline operand get(size_type p) const noexcept(NO_EXCEPT) {
return this->fold(p, p+1);
}
template<class F>
inline size_type max_right(size_type l, F&& f) const noexcept(NO_EXCEPT)
requires algebraic::internal::invertible<operand>
{
assert(0 <= l && l <= this->_n);
assert(f(operand{}));
if(l == this->_n) return this->_n;
operand inv = -this->fold(l);
size_type p = 0, q = this->_bit_ceil;
for(size_type k=q; k>0; k >>= 1) {
if(p+k <= this->_n and f(this->_data[p+k-1] + inv)) {
inv = inv + this->_data[(p+=k)-1];
}
}
return p;
}
template<class F> inline size_type min_left(size_type r, F&& f) const noexcept(NO_EXCEPT)
requires algebraic::internal::invertible<operand>
{
assert(0 <= r && r <= this->_n);
assert(f(operand{}));
if(r == 0) return 0;
operand acc = this->fold(r);
size_type p = 0, q = std::bit_ceil<std::make_unsigned_t<size_type>>(r);
for(size_type k=q; k>0; k >>= 1) {
if(p+k < r and !f(acc + -this->_data[p+k-1])) {
acc = acc + -this->_data[(p+=k)-1];
}
}
if(p == 0 and f(acc)) return 0;
return p + 1;
}
};
} // namespace fenwick_tree_impl
} // namespace internal
template<class Value>
struct fenwick_tree : internal::unconstructible {};
template<algebraic::internal::monoid Monoid>
struct fenwick_tree<Monoid> : internal::fenwick_tree_impl::core<Monoid> {
static_assert(algebraic::internal::commutative<Monoid>);
private:
using core = typename internal::fenwick_tree_impl::core<Monoid>;
core _impl;
public:
using value_type = typename core::operand;
using size_type = typename core::size_type;
protected:
inline size_type _positivize_index(const size_type p) const noexcept(NO_EXCEPT) {
return p < 0 ? this->_impl.size() + p : p;
}
public:
fenwick_tree() noexcept(NO_EXCEPT) : _impl() {}
explicit fenwick_tree(const size_type n) noexcept(NO_EXCEPT) : _impl(n) {}
explicit fenwick_tree(const size_type n, const value_type& v) noexcept(NO_EXCEPT) : _impl(n) { this->_impl.fill(v); }
template<std::convertible_to<value_type> T>
fenwick_tree(const std::initializer_list<T>& init_list) noexcept(NO_EXCEPT) : fenwick_tree(ALL(init_list)) {}
template<std::input_iterator I, std::sized_sentinel_for<I> S>
explicit fenwick_tree(I first, S last) noexcept(NO_EXCEPT)
: fenwick_tree(static_cast<size_type>(std::ranges::distance(first, last)))
{ this->assign(first, last); }
template<std::ranges::input_range R>
explicit fenwick_tree(R&& range) noexcept(NO_EXCEPT) : fenwick_tree(ALL(range)) {}
template<std::convertible_to<value_type> T>
inline auto& assign(const std::initializer_list<T>& init_list) noexcept(NO_EXCEPT){ return this->assign(ALL(init_list)); }
template<std::input_iterator I, std::sentinel_for<I> S>
inline auto& assign(I first, S last) noexcept(NO_EXCEPT) {
this->_impl.assign(first, last);
return *this;
}
template<std::ranges::input_range R>
inline auto& assign(R&& range) noexcept(NO_EXCEPT) { return this->assign(ALL(range)); }
inline auto& fill(const value_type& v = value_type()) noexcept(NO_EXCEPT) {
std::fill(this->data(), this->data() + this->_impl.size(), v);
this->_init();
return *this;
}
inline auto size() const noexcept(NO_EXCEPT) { return this->_impl.size(); }
inline bool empty() const noexcept(NO_EXCEPT) { return this->_impl.size() == 0; }
struct point_reference : internal::point_reference<fenwick_tree> {
point_reference(fenwick_tree *const super, const size_type p) noexcept(NO_EXCEPT)
: internal::point_reference<fenwick_tree>(super, super->_positivize_index(p))
{
assert(0 <= this->_pos && this->_pos < this->_super->size());
}
operator value_type() const noexcept(NO_EXCEPT) { return this->_super->get(this->_pos); }
auto val() const noexcept(NO_EXCEPT) { return this->_super->get(this->_pos); }
inline auto& operator=(const value_type& v) noexcept(NO_EXCEPT) {
this->_super->set(this->_pos, v);
return *this;
}
inline auto& operator+=(const value_type& v) noexcept(NO_EXCEPT) {
this->_super->add(this->_pos, v);
return *this;
}
};
struct range_reference : internal::range_reference<fenwick_tree> {
range_reference(fenwick_tree *const super, const size_type l, const size_type r) noexcept(NO_EXCEPT)
: internal::range_reference<fenwick_tree>(super, super->_positivize_index(l), super->_positivize_index(r))
{
assert(0 <= this->_begin && this->_begin <= this->_end && this->_end <= this->_super->size());
}
inline auto fold() noexcept(NO_EXCEPT) {
if(this->_begin == 0 and this->_end == this->_super->size()) return this->_super->fold();
if(this->_begin == 0) return this->_super->fold(this->_end);
return this->_super->fold(this->_begin, this->_end);
}
};
inline auto& add(const size_type p, const value_type& x) noexcept(NO_EXCEPT) {
assert(0 <= p && p < this->_impl.size());
this->_impl.add(p, x);
return *this;
}
inline auto& set(const size_type p, const value_type& x) noexcept(NO_EXCEPT)
requires algebraic::internal::invertible<value_type>
{
assert(0 <= p && p < this->_impl.size());
this->_impl.set(p, x);
return *this;
}
inline value_type get(const size_type p) const noexcept(NO_EXCEPT)
requires algebraic::internal::invertible<value_type>
{
assert(0 <= p && p < this->_impl.size());
return this->_impl.get(p);
}
inline auto operator[](const size_type p) noexcept(NO_EXCEPT) { return point_reference(this, p); }
inline const auto operator()(const size_type l, const size_type r) const noexcept(NO_EXCEPT) {
return range_reference(this, l, r);
}
inline auto operator()(const size_type l, const size_type r) noexcept(NO_EXCEPT) {
return range_reference(this, l, r);
}
inline auto fold(const size_type l, const size_type r) const noexcept(NO_EXCEPT)
requires algebraic::internal::invertible<value_type>
{
assert(0 <= l && l <= r && r <= this->_impl.size());
return this->_impl.fold(l, r);
}
inline auto fold(const size_type r) const noexcept(NO_EXCEPT) {
assert(0 <= r && r <= this->_impl.size());
return this->_impl.fold(r);
}
inline auto fold() const noexcept(NO_EXCEPT) {
return this->_impl.fold(this->_impl.size());
}
struct iterator;
protected:
using iterator_interface = internal::container_iterator_interface<value_type, const fenwick_tree, iterator>;
public:
struct iterator : iterator_interface {
using iterator_interface::iterator_interface;
};
inline auto begin() const noexcept(NO_EXCEPT) { return iterator(this, 0); }
inline auto end() const noexcept(NO_EXCEPT) { return iterator(this, this->_impl.size()); }
inline auto rbegin() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
};
template<actions::internal::operatable_action Action>
struct fenwick_tree<Action> : fenwick_tree<typename Action::operand> {
using fenwick_tree<typename Action::operand>::fenwick_tree;
};
} // namespace uni
#line 2 "data_structure/foldable_deque.hpp"
#line 6 "data_structure/foldable_deque.hpp"
#line 9 "data_structure/foldable_deque.hpp"
#line 12 "data_structure/foldable_deque.hpp"
#line 14 "data_structure/foldable_deque.hpp"
#line 2 "data_structure/foldable_stack.hpp"
#line 6 "data_structure/foldable_stack.hpp"
#line 10 "data_structure/foldable_stack.hpp"
#line 14 "data_structure/foldable_stack.hpp"
#line 17 "data_structure/foldable_stack.hpp"
#line 19 "data_structure/foldable_stack.hpp"
namespace uni {
template<class, template<class...> class = stack>
struct foldable_stack : internal::unconstructible {};
template<algebraic::internal::monoid Monoid, template<class...> class Stack>
struct foldable_stack<Monoid, Stack> {
using fold_type = Monoid;
using value_type = Monoid::value_type;
using size_type = Stack<Monoid>::size_type;
Stack<value_type> _val;
Stack<fold_type> _acc;
inline bool empty() const noexcept(NO_EXCEPT) { return this->_val.empty(); }
inline auto size() const noexcept(NO_EXCEPT) { return this->_val.size(); }
inline decltype(auto) top() const noexcept(NO_EXCEPT) {
assert(!this->empty());
return this->_val.top();
}
template<std::convertible_to<value_type> T = value_type>
requires std::is_move_constructible_v<T>
inline decltype(auto) top_or(T&& val) const noexcept(NO_EXCEPT) {
if(this->empty()) return static_cast<value_type>(std::forward<T>(val));
else return this->top();
}
inline auto fold() const noexcept(NO_EXCEPT) {
if(this->empty()) return fold_type();
return this->_acc.top();
}
template<std::convertible_to<fold_type> T = value_type>
auto& push(T&& x) noexcept(NO_EXCEPT) {
const auto acc = this->fold();
this->_val.push(x);
this->_acc.push(acc + std::forward<T>(x));
return *this;
}
template<class... Args>
decltype(auto) emplace(Args&&... args) noexcept(NO_EXCEPT) {
const auto acc = this->fold();
decltype(auto) res = this->_val.emplace(std::forward<Args>(args)...);
this->_acc.push(acc + res);
return res;
}
inline auto& pop() noexcept(NO_EXCEPT) {
this->_val.pop(), this->_acc.pop();
return *this;
}
};
template<actions::internal::operatable_action Action, template<class...> class Stack>
struct foldable_stack<Action, Stack> : foldable_stack<typename Action::operand> {
using foldable_stack<typename Action::operand>::foldable_stack;
};
} // namespace uni
#line 16 "data_structure/foldable_deque.hpp"
namespace uni {
namespace internal {
template<algebraic::internal::monoid Monoid, template<class...> class Stack>
using foldable_deque_base = deque_by_stack<foldable_stack<algebraic::make_opposite_t<Monoid>, Stack>, foldable_stack<Monoid, Stack>>;
} // namespace internal
template<class, template<class...> class = stack>
struct foldable_deque : internal::unconstructible {};
template<algebraic::internal::monoid Monoid, template<class...> class Stack>
struct foldable_deque<Monoid, Stack> : internal::foldable_deque_base<Monoid, Stack> {
using internal::foldable_deque_base<Monoid, Stack>::foldable_deque_base;
inline auto fold() const noexcept(NO_EXCEPT) {
return Monoid(this->_front.fold()) + this->_back.fold();
}
};
template<actions::internal::operatable_action Action, template<class...> class Stack>
struct foldable_deque<Action, Stack> : foldable_deque<typename Action::operand> {
using foldable_deque<typename Action::operand>::foldable_deque;
};
} // namespace uni
#line 2 "data_structure/foldable_queue.hpp"
#line 6 "data_structure/foldable_queue.hpp"
#line 9 "data_structure/foldable_queue.hpp"
#line 12 "data_structure/foldable_queue.hpp"
#line 14 "data_structure/foldable_queue.hpp"
#line 16 "data_structure/foldable_queue.hpp"
namespace uni {
namespace internal {
template<algebraic::internal::monoid Monoid, template<class...> class Stack>
using foldable_queue_base = queue_by_stack<foldable_stack<Monoid, Stack>, foldable_stack<algebraic::make_opposite_t<Monoid>, Stack>>;
} // namespace internal
template<class, template<class...> class = stack>
struct foldable_queue : internal::unconstructible {};
template<algebraic::internal::monoid Monoid, template<class...> class Stack>
struct foldable_queue<Monoid, Stack> : internal::foldable_queue_base<Monoid, Stack> {
using internal::foldable_queue_base<Monoid, Stack>::foldable_queue_base;
inline auto fold() const noexcept(NO_EXCEPT) {
return Monoid(this->_out.fold()) + this->_in.fold();
}
};
template<actions::internal::operatable_action Action, template<class...> class Stack>
struct foldable_queue<Action, Stack> : foldable_queue<typename Action::operand> {
using foldable_queue<typename Action::operand>::foldable_queue;
};
} // namespace uni
#line 2 "data_structure/kth_element.hpp"
#line 11 "data_structure/kth_element.hpp"
#line 15 "data_structure/kth_element.hpp"
namespace uni {
// Thanks to: https://qiita.com/drken/items/1b7e6e459c24a83bb7fd
template<
class T,
std::ranges::output_range<T> Container = std::vector<T>,
std::strict_weak_order<T, T> Comparer = std::less<T>,
std::strict_weak_order<T, T> RevComparer = std::greater<T>,
std::integral Size = internal::size_t
>
struct kth_element {
using value_type = T;
using size_type = Size;
protected:
size_type _k;
std::priority_queue<T, Container, Comparer> _small;
std::priority_queue<T, Container, RevComparer> _large;
public:
kth_element(const size_type k = 0) noexcept(NO_EXCEPT) : _k(k + 1) { assert(k >= 0); }
inline bool has() const noexcept(NO_EXCEPT) { return std::ssize(this->_small) == this->_k; }
inline value_type value() const noexcept(NO_EXCEPT) { return this->_small.top(); }
inline std::optional<value_type> get() const noexcept(NO_EXCEPT) {
if(this->has()) return this->value();
return {};
}
template<std::convertible_to<T> U = T>
inline auto value_or(U&& v) const noexcept(NO_EXCEPT) {
return this->get().value_or(std::forward<U>(v));
}
inline void push(const value_type& v) noexcept(NO_EXCEPT) {
if(std::ssize(this->_small) < this->_k) {
this->_small.push(v);
return;
}
const auto kth = this->_small.top();
if(Comparer{}(v, kth)) {
this->_small.pop();
this->_small.push(v);
this->_large.push(kth);
}
else {
this->_large.push(v);
}
}
inline void pop() noexcept(NO_EXCEPT) {
assert(this->has());
this->_small.pop();
if(this->_large.empty()) return;
const auto v = this->_large.top();
this->_large.pop();
this->_small.push(v);
}
};
} // namespace uni
#line 2 "data_structure/lazy_segment_tree.hpp"
#line 12 "data_structure/lazy_segment_tree.hpp"
#line 15 "data_structure/lazy_segment_tree.hpp"
#line 21 "data_structure/lazy_segment_tree.hpp"
#line 24 "data_structure/lazy_segment_tree.hpp"
#line 26 "data_structure/lazy_segment_tree.hpp"
#line 29 "data_structure/lazy_segment_tree.hpp"
namespace uni {
namespace internal {
namespace lazy_segment_tree_impl {
// Thanks to: atcoder::lazy_segtree
template<actions::internal::full_action Action>
requires
algebraic::internal::monoid<typename Action::operand> &&
algebraic::internal::monoid<typename Action::operation>
struct core {
using size_type = internal::size_t;
using action = Action;
using operand = typename Action::operand;
using operation = typename Action::operation;
private:
size_type _n = 0, _size = 0, _depth = 0;
std::valarray<size_type> _lengths;
std::valarray<operand> _values;
std::valarray<operation> _lazy;
inline void _pull(const size_type p) noexcept(NO_EXCEPT) {
this->_values[p] = this->_values[p << 1] + this->_values[p << 1 | 1];
}
inline void _all_apply(const size_type p, const operation& f) noexcept(NO_EXCEPT) {
this->_values[p] = action::mapping(action::power(f, this->_lengths[p]), this->_values[p]);
if(p < this->_size) this->_lazy[p] = f + this->_lazy[p];
}
inline void _push(const size_type p) noexcept(NO_EXCEPT) {
this->_all_apply(p << 1, this->_lazy[p]);
this->_all_apply(p << 1 | 1, this->_lazy[p]);
this->_lazy[p] = operation{};
}
inline void _init() noexcept(NO_EXCEPT) {
REPD(p, 1, this->_size) {
this->_lengths[p] = this->_lengths[p << 1] + this->_lengths[p << 1 | 1];
this->_pull(p);
}
}
public:
core() noexcept = default;
explicit core(const size_type n) noexcept(NO_EXCEPT)
: _n(n), _size(std::bit_ceil(uni::to_unsigned(n))), _depth(std::countr_zero(uni::to_unsigned(this->_size))),
_lengths(this->_size << 1), _values(this->_size << 1), _lazy(this->_size)
{}
inline size_type size() const noexcept(NO_EXCEPT) { return this->_n; }
inline size_type allocated() const noexcept(NO_EXCEPT) { return this->_values.size(); }
inline size_type depth() const noexcept(NO_EXCEPT) { return this->_depth; }
inline operand fold_all() const noexcept(NO_EXCEPT) { return this->_values[1]; }
inline void fill( const operand& v = operand()) noexcept(NO_EXCEPT) {
REP(p, 0, this->_n) {
this->_lengths[this->_size + p] = 1, this->_values[this->_size + p] = v;
}
this->_init();
}
template<std::input_iterator I, std::sentinel_for<I> S>
inline void assign(I first, S last) noexcept(NO_EXCEPT) {
if constexpr(std::sized_sentinel_for<operand, I>) {
assert(std::ranges::distance(first, last) == this->_n);
}
size_type p = 0;
for(auto itr=first; itr!=last; ++itr, ++p) {
this->_lengths[this->_size + p] = 1, this->_values[this->_size + p] = static_cast<operand>(*itr);
}
this->_init();
}
inline void set(size_type p, const operand& x) noexcept(NO_EXCEPT) {
p += this->_size;
FORD(i, 1, this->_depth) this->_push(p >> i);
this->_values[p] = x;
FOR(i, 1, this->_depth) this->_pull(p >> i);
}
inline void add(size_type p, const operand& x) noexcept(NO_EXCEPT) {
p += this->_size;
FORD(i, 1, this->_depth) this->_push(p >> i);
this->_values[p] = this->_values[p] + x;
FOR(i, 1, this->_depth) this->_pull(p >> i);
}
inline operand get(size_type p) noexcept(NO_EXCEPT) {
p += this->_size;
FORD(i, 1, this->_depth) this->_push(p >> i);
return this->_values[p];
}
inline operand fold(size_type l, size_type r) noexcept(NO_EXCEPT) {
if(l == r) return {};
l += this->_size;
r += this->_size;
FORD(i, 1, this->_depth) {
if(((l >> i) << i) != l) this->_push(l >> i);
if(((r >> i) << i) != r) this->_push((r - 1) >> i);
}
operand sml = operand{}, smr = operand{};
while(l < r) {
if(l & 1) sml = sml + this->_values[l++];
if(r & 1) smr = this->_values[--r] + smr;
l >>= 1;
r >>= 1;
}
return sml + smr;
}
inline void apply(size_type p, const operation& f) noexcept(NO_EXCEPT) {
p += this->_size;
FORD(i, 1, this->_depth) this->_push(p >> i);
this->_values[p] = action::mapping(action::power(f, this->_lengths[p]), this->_values[p]);
FOR(i, 1, this->_depth) this->_pull(p >> i);
}
inline void apply(size_type l, size_type r, const operation& f) noexcept(NO_EXCEPT) {
if(l == r) return;
l += this->_size;
r += this->_size;
FORD(i, 1, this->_depth) {
if(((l >> i) << i) != l) this->_push(l >> i);
if(((r >> i) << i) != r) this->_push((r - 1) >> i);
}
{
size_type l2 = l, r2 = r;
while(l < r) {
if(l & 1) this->_all_apply(l++, f);
if(r & 1) this->_all_apply(--r, f);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
FOR(i, 1, this->_depth) {
if(((l >> i) << i) != l) this->_pull(l >> i);
if(((r >> i) << i) != r) this->_pull((r - 1) >> i);
}
}
template<class F>
inline size_type max_right(size_type l, F&& f) noexcept(NO_EXCEPT) {
assert(0 <= l && l <= _n);
assert(f(operand{}));
if(l == _n) return _n;
l += this->_size;
FORD(i, 1, this->_depth) this->_push(l >> i);
operand sm;
do {
while(l % 2 == 0) l >>= 1;
if(!f(sm + this->_values[l])) {
while(l < this->_size) {
this->_push(l);
l = (2 * l);
if(f(sm + this->_values[l])) {
sm = sm + this->_values[l];
l++;
}
}
return l - this->_size;
}
sm = sm + this->_values[l];
l++;
} while((l & -l) != l);
return _n;
}
template<class F>
inline size_type min_left(size_type r, F&& f) noexcept(NO_EXCEPT) {
assert(0 <= r && r <= _n);
assert(f(operand{}));
if(r == 0) return 0;
r += this->_size;
FORD(i, 1, this->_depth) this->_push((r - 1) >> i);
operand sm;
do {
r--;
while(r > 1 && (r % 2)) r >>= 1;
if(!f(this->_values[r] + sm)) {
while(r < this->_size) {
this->_push(r);
r = (2 * r + 1);
if(f(this->_values[r] + sm)) {
sm = this->_values[r] + sm;
r--;
}
}
return r + 1 - this->_size;
}
sm = this->_values[r] + sm;
} while((r & -r) != r);
return 0;
}
};
} // namespace lazy_segment_tree_impl
} // namespace internal
template<class T>
struct lazy_segment_tree : lazy_segment_tree<actions::make_full_t<T>> {
using lazy_segment_tree<actions::make_full_t<T>>::lazy_segment_tree;
};
template<actions::internal::full_action Action>
requires internal::available<internal::lazy_segment_tree_impl::core<Action>>
struct lazy_segment_tree<Action> {
using action = Action;
using operand = Action::operand;
using operation = Action::operation;
private:
using core = internal::lazy_segment_tree_impl::core<action>;
core _impl;
public:
using value_type = operand;
using action_type = operation::value_type;
using size_type = core::size_type;
inline auto size() const noexcept(NO_EXCEPT) { return this->_impl.size(); }
inline auto allocated() const noexcept(NO_EXCEPT) { return this->_impl.allocated(); }
inline auto depth() const noexcept(NO_EXCEPT) { return this->_impl.depth(); }
protected:
inline size_type _positivize_index(const size_type p) const noexcept(NO_EXCEPT) {
return p < 0 ? this->_impl.size() + p : p;
}
public:
lazy_segment_tree() noexcept(NO_EXCEPT) : _impl() {}
explicit lazy_segment_tree(const size_type n, const value_type& v = value_type()) noexcept(NO_EXCEPT) : _impl(n) { this->_impl.fill(v); }
template<std::convertible_to<value_type> T>
lazy_segment_tree(const std::initializer_list<T>& init_list) noexcept(NO_EXCEPT) : lazy_segment_tree(ALL(init_list)) {}
template<std::input_iterator I, std::sized_sentinel_for<I> S>
lazy_segment_tree(I first, S last) noexcept(NO_EXCEPT)
: _impl(static_cast<size_type>(std::ranges::distance(first, last)))
{ this->assign(first, last); }
template<std::ranges::input_range R>
explicit lazy_segment_tree(R&& range) noexcept(NO_EXCEPT) : lazy_segment_tree(ALL(range)) {}
template<std::convertible_to<value_type> T>
inline auto& assign(const std::initializer_list<T>& init_list) noexcept(NO_EXCEPT)
{
return this->assign(ALL(init_list));
}
template<std::input_iterator I, std::sentinel_for<I> S>
inline auto& assign(I first, S last) noexcept(NO_EXCEPT) {
this->_impl.assign(first, last);
return *this;
}
template<std::ranges::input_range R>
inline auto& assign(R&& range) noexcept(NO_EXCEPT) { return this->assign(ALL(range)); }
inline auto& fill( const value_type& v = value_type()) noexcept(NO_EXCEPT) {
this->impl.fill(v);
return *this;
}
bool empty() const noexcept(NO_EXCEPT) { return this->_impl.size() == 0; }
struct point_reference : internal::point_reference<lazy_segment_tree> {
point_reference(lazy_segment_tree *const super, const size_type p) noexcept(NO_EXCEPT)
: internal::point_reference<lazy_segment_tree>(super, super->_positivize_index(p))
{
assert(0 <= this->_pos && this->_pos < this->_super->size());
}
operator value_type() noexcept(NO_EXCEPT) { return this->_super->get(this->_pos); }
auto val() noexcept(NO_EXCEPT) { return this->_super->get(this->_pos); }
inline auto& operator=(const value_type& v) noexcept(NO_EXCEPT) {
this->_super->set(this->_pos, v);
return *this;
}
inline auto& operator+=(const value_type& v) noexcept(NO_EXCEPT) {
this->_super->add(this->_pos, v);
return *this;
}
inline auto& operator*=(const action_type& v) noexcept(NO_EXCEPT) {
this->_super->apply(this->_pos, v);
return *this;
}
};
struct range_reference : internal::range_reference<lazy_segment_tree> {
range_reference(lazy_segment_tree *const super, const size_type l, const size_type r) noexcept(NO_EXCEPT)
: internal::range_reference<lazy_segment_tree>(super, super->_positivize_index(l), super->_positivize_index(r))
{
assert(0 <= this->_begin && this->_begin <= this->_end && this->_end <= this->_super->size());
}
inline auto& operator*=(const action_type& v) noexcept(NO_EXCEPT) {
this->_super->apply(this->_begin, this->_end, v);
return *this;
}
inline auto fold() noexcept(NO_EXCEPT) {
if(this->_begin == 0 && this->_end == this->_super->size()) return this->_super->fold();
return this->_super->fold(this->_begin, this->_end);
}
};
inline auto& set(size_type p, const value_type& v) noexcept(NO_EXCEPT) {
p = this->_positivize_index(p), assert(0 <= p && p < this->_impl.size());
this->_impl.set(p, v);
return *this;
}
inline auto& add(size_type p, const value_type& v) noexcept(NO_EXCEPT) {
p = this->_positivize_index(p), assert(0 <= p && p < this->_impl.size());
this->_impl.add(p, v);
return *this;
}
inline auto& apply(size_type l, size_type r, const action_type& v) noexcept(NO_EXCEPT) {
l = this->_positivize_index(l), r = this->_positivize_index(r);
assert(0 <= l && l <= r && r <= this->_impl.size());
this->_impl.apply(l, r, v);
return *this;
}
inline auto& apply(const size_type p, const action_type& v) noexcept(NO_EXCEPT) {
this->apply(p, p + 1, v);
return *this;
}
inline auto& apply(const action_type& v) noexcept(NO_EXCEPT) { this->apply(0, this->_impl.size(), v); return *this; }
inline auto get(size_type p) noexcept(NO_EXCEPT) {
p = this->_positivize_index(p), assert(0 <= p && p < this->_impl.size());
return this->_impl.get(p);
}
inline auto operator[](const size_type p) noexcept(NO_EXCEPT) { return point_reference(this, p); }
inline auto operator()(const size_type l, const size_type r) noexcept(NO_EXCEPT) { return range_reference(this, l, r); }
inline auto fold(size_type l, size_type r) noexcept(NO_EXCEPT) {
l = this->_positivize_index(l), r = this->_positivize_index(r);
assert(0 <= l && l <= r && r <= this->_impl.size());
return this->_impl.fold(l, r);
}
inline auto fold() noexcept(NO_EXCEPT) { return this->_impl.fold_all(); }
template<bool (*f)(value_type)>
inline auto max_right(const size_type l) noexcept(NO_EXCEPT) {
return this->max_right(l, [](operand x) { return f(x); });
}
template<class F>
inline auto max_right(const size_type l, F&& f) noexcept(NO_EXCEPT) {
return this->_impl.max_right(l, std::forward<F>(f));
}
template<bool (*f)(value_type)>
inline auto min_left(const size_type r) noexcept(NO_EXCEPT) {
return min_left(r, [](operand x) { return f(x); });
}
template<class F>
inline auto min_left(const size_type r, F&& f) noexcept(NO_EXCEPT) {
return this->_impl.min_left(r, std::forward<F>(f));
}
struct iterator;
protected:
using iterator_interface = internal::container_iterator_interface<value_type, lazy_segment_tree, iterator>;
public:
struct iterator : iterator_interface {
using iterator_interface::iterator_interface;
};
inline auto begin() noexcept(NO_EXCEPT) { return iterator(this, 0); }
inline auto end() noexcept(NO_EXCEPT) { return iterator(this, this->_impl.size()); }
inline auto rbegin() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
};
} // namespace uni
#line 2 "data_structure/persistent_queue.hpp"
#line 9 "data_structure/persistent_queue.hpp"
#line 12 "data_structure/persistent_queue.hpp"
#line 16 "data_structure/persistent_queue.hpp"
namespace uni {
// Thanks to: https://tk0-math.hatenablog.com/entry/2020/03/27/194150
template<class ValueType, u32 BUFFER_DEPTH = 20, class Allocator = std::allocator<ValueType>>
struct persistent_queue {
using value_type = ValueType;
using size_type = internal::size_t;
struct node_type;
using node_handler = node_handlers::cloneable<Allocator>::template handler<node_type>;
using node_pointer = typename node_handler::node_pointer;
using allocator_type = typename node_handler::allocator_type;
struct node_type {
value_type value;
node_pointer prev[BUFFER_DEPTH];
};
private:
size_type _size = 0;
node_pointer _head, _tail;
[[no_unique_address]] node_handler _node_handler;
public:
explicit persistent_queue(const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT) : _node_handler(allocator) {}
persistent_queue(const persistent_queue& source, const allocator_type& allocator) noexcept(NO_EXCEPT)
: _size(source._size), _head(source._head), _tail(source._tail), _node_handler(allocator)
{}
persistent_queue(persistent_queue&& source, const allocator_type& allocator) noexcept(NO_EXCEPT)
: _size(source._size), _head(source._head), _tail(source._tail), _node_handler(allocator)
{}
inline auto clone() const noexcept(NO_EXCEPT) { return *this; }
inline bool empty() const noexcept(NO_EXCEPT) { return this->_size == 0; }
inline size_type size() const noexcept(NO_EXCEPT) { return this->_size; }
inline value_type front() const noexcept(NO_EXCEPT) {
assert(!this->empty());
return this->_head->value;
}
template<std::convertible_to<value_type> T = value_type>
requires std::is_move_constructible_v<T>
inline value_type front_or(T&& v) const noexcept(NO_EXCEPT) {
if(this->empty()) return static_cast<value_type>(std::forward<T>(v));
else return this->front();
}
inline value_type back() const noexcept(NO_EXCEPT) {
assert(!this->empty());
return this->_tail->value;
}
template<std::convertible_to<value_type> T = value_type>
requires std::is_move_constructible_v<T>
inline value_type back_or(T&& v) const noexcept(NO_EXCEPT) {
if(this->empty()) return static_cast<value_type>(std::forward<T>(v));
else return this->back();
}
inline auto& clear() noexcept(NO_EXCEPT) {
this->_head.reset(), this->_tail.reset();
this->_size = 0;
return *this;
}
template<std::convertible_to<value_type> T = value_type>
auto& push(T&& x) noexcept(NO_EXCEPT) {
node_pointer node = this->_node_handler.create(x);
node->prev[0] = this->_tail;
REP(i, 1, BUFFER_DEPTH) {
node_pointer prev = node->prev[i - 1];
if(prev) node->prev[i] = prev->prev[i - 1];
else break;
}
if(!this->_head) this->_head = node;
this->_tail = node;
++this->_size;
return *this;
}
auto& pop() noexcept(NO_EXCEPT) {
assert(!this->empty());
if(!this->_head || !this->_tail || this->_size == 1) {
this->clear();
return *this;
}
auto index = to_unsigned(this->_size - 2);
node_pointer node = this->_tail;
while(index != 0) {
const size_type msb = uni::highest_bit_pos(index);
index -= 1 << msb;
node = node->prev[msb];
}
this->_head = node;
--this->_size;
return *this;
}
};
namespace pmr {
template<class T, u32 BUFFER_DEPTH = 20>
using persistent_queue = uni::persistent_queue<T, BUFFER_DEPTH, std::pmr::polymorphic_allocator<T>>;
} // namesapce pmr
} // namespace uni
#line 2 "data_structure/persistent_stack.hpp"
#line 7 "data_structure/persistent_stack.hpp"
#line 10 "data_structure/persistent_stack.hpp"
#line 13 "data_structure/persistent_stack.hpp"
namespace uni {
template<class ValueType, class Allocator = std::allocator<ValueType>>
struct persistent_stack {
using value_type = ValueType;
using size_type = internal::size_t;
struct node_type;
using node_handler = node_handlers::cloneable<Allocator>::template handler<node_type>;
using allocator_type = typename node_handler::allocator_type;
using node_pointer = typename node_handler::node_pointer;
struct node_type {
value_type value;
node_pointer next;
node_type(node_pointer _next, value_type _value) noexcept(NO_EXCEPT)
: value(_value), next(_next)
{}
template<class... Args>
node_type(node_pointer _next, Args&&... args) noexcept(NO_EXCEPT)
: value(std::forward<Args>(args)...), next(_next)
{}
};
private:
size_type _size = 0;
node_pointer _head;
[[no_unique_address]] node_handler _node_handler;
public:
explicit persistent_stack(const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT) : _node_handler(allocator) {};
persistent_stack(const persistent_stack& source, const allocator_type& allocator) noexcept(NO_EXCEPT)
: _size(source._size), _head(source._head), _node_handler(allocator)
{};
persistent_stack(persistent_stack&& source, const allocator_type& allocator) noexcept(NO_EXCEPT)
: _size(source._size), _head(source._head), _node_handler(allocator)
{};
inline auto clone() const noexcept(NO_EXCEPT) { return *this; }
inline bool empty() const noexcept(NO_EXCEPT) { return !this->_head; }
inline size_type size() const noexcept(NO_EXCEPT) { return this->_size; }
inline value_type top() const noexcept(NO_EXCEPT) {
assert(!this->empty());
return this->_head->value;
}
template<std::convertible_to<value_type> T = value_type>
requires std::is_move_constructible_v<T>
inline value_type top_or(T&& v) const noexcept(NO_EXCEPT) {
if(this->empty()) return static_cast<value_type>(std::forward<T>(v));
else return this->top();
}
inline auto& clear() noexcept(NO_EXCEPT) {
this->_head.reset();
this->_size = 0;
return *this;
}
template<std::convertible_to<value_type> T = value_type>
inline auto& push(T&& x) noexcept(NO_EXCEPT) {
this->_head = this->_node_handler.create(this->_head, std::forward<T>(x));
++this->_size;
return *this;
}
template<class... Args>
inline auto& emplace(Args&&... args) noexcept(NO_EXCEPT) {
this->_head = this->_node_handler.create(this->_head, std::forward<Args>(args)...);
++this->_size;
return this->_head->value;
}
inline auto& pop() noexcept(NO_EXCEPT) {
assert(!this->empty());
this->_head = this->_head->next;
--this->_size;
return *this;
}
};
namespace pmr {
template<class T>
using persistent_stack = uni::persistent_stack<T, std::pmr::polymorphic_allocator<T>>;
} // namesapce pmr
} // namespace uni
#line 2 "data_structure/red_black_tree.hpp"
#line 13 "data_structure/red_black_tree.hpp"
#line 17 "data_structure/red_black_tree.hpp"
#line 23 "data_structure/red_black_tree.hpp"
#line 25 "data_structure/red_black_tree.hpp"
#line 27 "data_structure/red_black_tree.hpp"
#line 29 "data_structure/red_black_tree.hpp"
#line 32 "data_structure/red_black_tree.hpp"
namespace uni {
namespace internal {
// Thanks to: http://blog.mitaki28.info/1447078746296/
template<class NodeHandler, class Derived, std::integral SizeType, class ValueType>
struct red_black_tree_impl {
using size_type = SizeType;
using rank_type = int;
using value_type = ValueType;
enum class node_colors : std::int8_t { RED, BLACK };
struct node_type;
using node_handler = typename NodeHandler::handler<node_type>;
using allocator_type = typename node_handler::allocator_type;
using node_pointer = typename node_handler::node_pointer;
struct node_type {
node_pointer left = node_handler::nil, right = node_handler::nil;
node_colors color = node_colors::BLACK;
size_type size = 0;
rank_type rank = 0;
inline constexpr bool is_leaf() const noexcept(NO_EXCEPT) {
return this->left == node_handler::nil && this->right == node_handler::nil;
}
[[no_unique_address]] value_type data;
node_type() noexcept = default;
node_type(const value_type& _data, const size_type _size) noexcept(NO_EXCEPT)
: size(_size), data(_data)
{}
node_type(const node_colors _color, const node_pointer& _left, const node_pointer& _right) noexcept(NO_EXCEPT)
: left(_left), right(_right), color(_color)
{}
};
private:
using derived = Derived;
inline auto* _derived() noexcept(NO_EXCEPT) {
return static_cast<derived*>(this);
}
inline const auto* _derived() const noexcept(NO_EXCEPT) {
return static_cast<const derived*>(this);
}
[[no_unique_address]] node_handler _node_handler;
public:
void pull(const node_pointer& tree) const noexcept(NO_EXCEPT) {
if(tree == node_handler::nil) return;
if(tree->is_leaf()) return;
tree->size = tree->left->size + tree->right->size;
tree->rank = tree->left->rank + (tree->left->color == node_colors::BLACK);
this->_derived()->pull(tree);
}
void push(node_pointer& tree) noexcept(NO_EXCEPT) {
if(tree == node_handler::nil) return;
this->clone(tree);
this->_derived()->push(tree);
this->pull(tree);
}
inline void clone(node_pointer& tree) noexcept(NO_EXCEPT) {
tree = this->_node_handler.clone(tree);
}
node_pointer create(const value_type& val, const size_type size) noexcept(NO_EXCEPT) {
if(size == 0) return node_handler::nil;
return this->_node_handler.create(val, size);
}
node_pointer create(const node_colors color, node_pointer left, node_pointer right) noexcept(NO_EXCEPT) {
this->push(left);
this->push(right);
return this->_node_handler.create(color, std::move(left), std::move(right));
}
void dispose(const node_pointer& tree) noexcept(NO_EXCEPT) {
if(this->_node_handler.disposable(tree)) {
this->dispose(tree->left);
this->dispose(tree->right);
this->_node_handler.dispose(tree);
}
}
private:
void _as_root(node_pointer& node) {
this->clone(node);
if(node->color == node_colors::RED) node->color = node_colors::BLACK;
this->push(node);
}
void _merge(node_pointer& tree, node_pointer left, node_pointer right) noexcept(NO_EXCEPT) {
if(left->rank < right->rank) {
this->push(right);
this->_merge(tree, left, right->left);
if(right->color == node_colors::BLACK && tree->color == node_colors::RED && tree->left->color == node_colors::RED) {
tree->color = node_colors::BLACK;
if(right->right->color == node_colors::BLACK) {
this->clone(right);
right->color = node_colors::RED;
right->left = tree->right;
this->pull(right);
this->clone(tree);
tree->right = std::move(right);
}
else {
this->clone(right->right);
right->right->color = node_colors::BLACK;
this->clone(right);
right->left = tree;
right->color = node_colors::RED;
tree = std::move(right);
}
}
else {
this->clone(right);
right->left = tree;
tree = std::move(right);
}
}
else if(left->rank > right->rank) {
this->push(left);
this->_merge(tree, left->right, right);
if(left->color == node_colors::BLACK && tree->color == node_colors::RED && tree->right->color == node_colors::RED) {
tree->color = node_colors::BLACK;
if(left->left->color == node_colors::BLACK) {
this->clone(left);
left->color = node_colors::RED;
left->right = tree->left;
this->pull(left);
this->clone(tree);
tree->left = std::move(left);
}
else {
this->clone(left->left);
left->left->color = node_colors::BLACK;
this->clone(left);
left->right = tree;
left->color = node_colors::RED;
tree = std::move(left);
}
}
else {
this->clone(left);
left->right = tree;
tree = std::move(left);
}
}
else {
tree = this->create(node_colors::RED, left, right);
}
this->pull(tree);
}
void _split(node_pointer tree, const size_type pos, node_pointer& left, node_pointer& right) {
if(tree == node_handler::nil) {
left = right = node_handler::nil;
return;
}
this->push(tree);
if(tree->is_leaf()) {
left = this->create(tree->data, pos);
right = this->create(tree->data, tree->size - pos);
return;
}
auto l = std::move(tree->left), r = std::move(tree->right);
this->_node_handler.dispose(tree);
if(pos < l->size) {
this->_split(std::move(l), pos, left, right);
this->_as_root(r);
this->merge(right, right, std::move(r));
this->_as_root(left);
return;
}
if(pos > l->size) {
this->_split(std::move(r), pos - l->size, left, right);
this->_as_root(l);
this->merge(left, std::move(l), left);
this->_as_root(right);
return;
}
left = std::move(l), right = std::move(r);
this->_as_root(left), this->_as_root(right);
}
public:
explicit red_black_tree_impl(const allocator_type& allocator = allocator_type()) noexcept(NO_EXCEPT) : _node_handler(allocator) {}
template<std::random_access_iterator I, std::sized_sentinel_for<I> S>
requires std::constructible_from<value_type, std::iter_value_t<I>>
node_pointer build(I first, S last) noexcept(NO_EXCEPT) {
if(first == last) return node_handler::nil;
if(std::ranges::next(first) == last) return this->create(value_type{ *first }, 1);
const auto length = std::ranges::distance(first, last);
const auto middle = std::ranges::next(first, std::bit_floor(to_unsigned(length - 1)));
node_pointer tree;
this->merge(tree, this->build(std::move(first), middle), this->build(middle, std::move(last)));
return tree;
}
template<std::random_access_iterator I, std::sized_sentinel_for<I> S>
requires
std::constructible_from<value_type, typename std::iter_value_t<I>::first_type> &&
std::integral<typename std::iter_value_t<I>::second_type>
node_pointer build(I first, S last) noexcept(NO_EXCEPT) {
if(first == last) return node_handler::nil;
if(std::ranges::next(first) == last) return this->create(value_type{ first->first }, first->second);
const auto length = std::ranges::distance(first, last);
const auto middle = std::ranges::next(first, std::bit_floor(to_unsigned(length - 1)));
node_pointer tree;
this->merge(tree, this->build(std::move(first), middle), this->build(middle, std::move(last)));
return tree;
}
void split(const node_pointer& tree, const size_type pos, node_pointer& left, node_pointer& right) noexcept(NO_EXCEPT) {
if(pos <= 0) {
left = node_handler::nil;
this->merge(right, this->create(value_type{}, -pos), tree);
}
else if(tree->size <= pos) {
right = node_handler::nil;
this->merge(left, tree, this->create(value_type{}, pos - tree->size));
}
else {
this->_split(tree, pos, left, right);
}
}
void merge(node_pointer& tree, const node_pointer& left, const node_pointer& right) noexcept(NO_EXCEPT) {
if(left == node_handler::nil) {
tree = right;
this->push(tree);
}
else if(right == node_handler::nil) {
tree = left;
this->push(tree);
}
else {
this->_merge(tree, left, right);
tree->color = node_colors::BLACK;
}
this->pull(tree);
}
};
} // namespace internal
template<std::integral SizeType = i64, class NodeHandler = uni::node_handlers::reusing<std::allocator<SizeType>>>
struct red_black_tree_context {
static constexpr bool LEAF_ONLY = true;
template<class Derived, class ValueType = internal::dummy>
using substance = internal::red_black_tree_impl<NodeHandler, Derived, SizeType, ValueType>;
};
template<std::integral SizeType = i64, class Allocator = std::allocator<SizeType>>
struct persistent_red_black_tree_context {
static constexpr bool LEAF_ONLY = true;
template<class Derived, class ValueType = internal::dummy>
using substance = internal::red_black_tree_impl<uni::node_handlers::cloneable<Allocator>, Derived, SizeType, ValueType>;
};
namespace pmr {
template<std::integral SizeType = i64>
using red_black_tree_context = uni::red_black_tree_context<SizeType, std::pmr::polymorphic_allocator<SizeType>>;
template<std::integral SizeType = i64>
using persistent_red_black_tree_context = uni::persistent_red_black_tree_context<SizeType, std::pmr::polymorphic_allocator<SizeType>>;
} // namespace pmr
} // namespace uni
#line 2 "data_structure/removable_priority_queue.hpp"
#line 8 "data_structure/removable_priority_queue.hpp"
#line 12 "data_structure/removable_priority_queue.hpp"
namespace uni {
namespace internal {
template<class T, class... Ts>
concept can_removable_priority_queue =
sizeof...(Ts) == 0 &&
requires (T pq, typename T::value_type v) {
{ pq.size() } -> std::same_as<typename T::size_type>;
{ pq.empty() } -> std::same_as<bool>;
pq.top();
pq.pop();
pq.push(v);
pq.emplace(v);
};
} // namespace internal
template<class... Ts>
struct removable_priority_queue {};
template<class ValueType, class... Args>
requires
(!internal::can_removable_priority_queue<ValueType, Args...>) &&
requires () {
typename std::priority_queue<ValueType, Args...>;
}
struct removable_priority_queue<ValueType, Args...> : removable_priority_queue<std::priority_queue<ValueType, Args...>> {
using removable_priority_queue<std::priority_queue<ValueType, Args...>>::removable_priority_queue;
};
template<internal::can_removable_priority_queue PriorityQueue>
struct removable_priority_queue<PriorityQueue>
: removable_priority_queue<PriorityQueue, internal::dummy>
{
using removable_priority_queue<PriorityQueue, internal::dummy>::removable_priority_queue;
};
template<
internal::can_removable_priority_queue PriorityQueue,
class Multiset
>
struct removable_priority_queue<PriorityQueue, Multiset> : PriorityQueue {
using base_type = PriorityQueue;
using multiset_type = Multiset;
using size_type = typename PriorityQueue::size_type;
using value_type = typename PriorityQueue::value_type;
using const_reference = typename PriorityQueue::const_reference;
private:
using self = removable_priority_queue<PriorityQueue, Multiset>;
base_type _deleted;
multiset_type _elements;
static constexpr bool CHECK_EXISTANCE = !std::same_as<multiset_type, internal::dummy>;
void _delete() noexcept(NO_EXCEPT) {
while(!this->_deleted.empty() && this->_deleted.top() == this->base_type::top()) {
this->base_type::pop();
this->_deleted.pop();
}
}
public:
using base_type::base_type;
size_type size() noexcept(NO_EXCEPT) {
if constexpr(!self::CHECK_EXISTANCE) {
assert(this->base_type::size() >= this->_deleted.size());
}
return this->base_type::size() - this->_deleted.size();
}
size_type empty() noexcept(NO_EXCEPT) {
if constexpr(!self::CHECK_EXISTANCE) {
assert(this->base_type::size() >= this->_deleted.size());
}
return this->base_type::size() == this->_deleted.size();
}
void push(const value_type& v) noexcept(NO_EXCEPT) {
if constexpr(self::CHECK_EXISTANCE) this->_elements.insert(v);
return this->base_type::push(v);
}
void push(value_type&& v) noexcept(NO_EXCEPT) {
if constexpr(self::CHECK_EXISTANCE) this->_elements.insert(std::move(v));
return this->base_type::push(std::move(v));
}
template<class... Args>
decltype(auto) emplace(Args&&... args) noexcept(NO_EXCEPT) {
if constexpr(self::CHECK_EXISTANCE) this->_elements.emplace(args...);
return this->base_type::emplace(std::forward<Args>(args)...);
}
std::conditional_t<self::CHECK_EXISTANCE, bool, void> remove(const value_type& v) noexcept(NO_EXCEPT) {
if constexpr(self::CHECK_EXISTANCE) {
if(!this->_elements.contains(v)) return false;
}
this->_deleted.push(v);
if constexpr(self::CHECK_EXISTANCE) return true;
}
std::conditional_t<self::CHECK_EXISTANCE, bool, void> remove(value_type&& v) noexcept(NO_EXCEPT) {
if constexpr(self::CHECK_EXISTANCE) {
if(!this->_elements.contains(v)) return false;
}
this->_deleted.push(std::move(v));
if constexpr(self::CHECK_EXISTANCE) return true;
}
template<class... Args>
std::conditional_t<self::CHECK_EXISTANCE, bool, void> eliminate(Args&&... args) noexcept(NO_EXCEPT) {
if constexpr(self::CHECK_EXISTANCE) {
if(!this->_elements.contains({ args... })) return false;
}
this->_deleted.emplace(std::forward<Args>(args)...);
if constexpr(self::CHECK_EXISTANCE) return true;
}
const_reference top() noexcept(NO_EXCEPT) {
this->_delete();
return this->base_type::top();
}
void pop() noexcept(NO_EXCEPT) {
this->_delete();
this->base_type::pop();
}
};
} // namespace uni
#line 2 "data_structure/restorable_stack.hpp"
#line 6 "data_structure/restorable_stack.hpp"
#line 8 "data_structure/restorable_stack.hpp"
namespace uni {
template<class T, class ID = int, template<class,class> class storage = std::unordered_map>
struct restorable_stack {
using value_type = T;
using key_type = ID;
protected:
struct node;
using node_ptr = std::shared_ptr<node>;
struct node {
std::optional<value_type> val = std::nullopt;
node_ptr parent;
};
node_ptr _current;
storage<key_type, node_ptr> _storage;
public:
restorable_stack() noexcept(NO_EXCEPT) { this->clear(); };
inline bool empty() const noexcept(NO_EXCEPT) {
return !this->_current->val.has_value();
}
inline bool stored(const key_type& x) const noexcept(NO_EXCEPT) {
return this->_storage.count(x);
}
inline const value_type& top() const noexcept(NO_EXCEPT) {
return this->_current->val.value();
}
inline auto get() const noexcept(NO_EXCEPT) {
return this->_current.val;
}
template<std::convertible_to<T> U = T>
inline auto top_or(U &&v) const noexcept(NO_EXCEPT) {
return this->_current->val.value_or(std::forward<U>(v));
}
inline auto& push(const value_type& x) noexcept(NO_EXCEPT) {
this->_current.reset(new node{ x, this->_current });
return *this;
}
inline auto& pop() noexcept(NO_EXCEPT) {
this->_current = this->_current->parent;
return *this;
}
inline auto& save(const key_type& x) noexcept(NO_EXCEPT) {
this->_storage[x] = this->_current;
return *this;
}
inline auto& load(const key_type& x) noexcept(NO_EXCEPT) {
assert(this->stored(x));
this->_current = this->_storage[x];
return *this;
}
inline auto& clear() noexcept(NO_EXCEPT) {
this->_current.reset(new node{});
return *this;
}
inline auto& load_or_clear(const key_type& x) noexcept(NO_EXCEPT) {
if(this->stored(x)) this->load(x);
else this->clear();
return *this;
}
};
} // namespace uni
#line 2 "data_structure/segment_tree_rooter.hpp"
#line 5 "data_structure/segment_tree_rooter.hpp"
#line 9 "data_structure/segment_tree_rooter.hpp"
namespace uni {
template<std::integral SizeType>
struct segment_tree_rooter {
using size_type = SizeType;
private:
size_type _n = 0;
public:
segment_tree_rooter() noexcept = default;
explicit segment_tree_rooter(const size_type n) noexcept(NO_EXCEPT) : _n(n) {};
inline size_type size() const noexcept(NO_EXCEPT) { return this->_n; }
inline size_type allocated() const noexcept(NO_EXCEPT) { return (this->_n << 1) - 1; }
template<std::invocable<size_type> F>
void range_to_nodes(size_type l, size_type r, F&& f) noexcept(NO_EXCEPT) {
l += this->_n;
r += this->_n;
while(l < r) {
if(l & 1) f(l++ - 1);
if(r & 1) f(--r - 1);
l >>= 1;
r >>= 1;
}
}
size_type point_to_node(const size_type p) noexcept(NO_EXCEPT) { return this->_n + p - 1; }
template<std::invocable<size_type> F>
void point_to_path(size_type p, F&& f) noexcept(NO_EXCEPT) {
p += this->_n;
while(p > 0) f(p - 1), p >>= 1;
}
};
}
#line 2 "data_structure/wavelet_matrix.hpp"
#line 19 "data_structure/wavelet_matrix.hpp"
#line 22 "data_structure/wavelet_matrix.hpp"
#line 27 "data_structure/wavelet_matrix.hpp"
#line 29 "data_structure/wavelet_matrix.hpp"
#line 31 "data_structure/wavelet_matrix.hpp"
#line 2 "iterable/compressed.hpp"
#line 10 "iterable/compressed.hpp"
#line 15 "iterable/compressed.hpp"
#line 17 "iterable/compressed.hpp"
namespace uni {
template<class T, class Container = vector<internal::size_t>>
struct compressed : Container {
using size_type = internal::size_t;
using value_type = T;
std::vector<value_type> values;
public:
compressed() noexcept(NO_EXCEPT) = default;
template<std::input_iterator I, std::sized_sentinel_for<I> S>
compressed(I first, S last) noexcept(NO_EXCEPT) {
this->values.assign(first, last);
std::ranges::sort(ALL(this->values));
this->values.erase(std::unique(ALL(this->values)), std::ranges::end(this->values));
this->resize(std::ranges::distance(first, last));
{
auto itr = std::ranges::begin(*this);
auto e = first;
for(; e!=last; ++itr, ++e) *itr = this->rank(*e);
}
}
template<std::ranges::input_range R>
explicit compressed(R&& range) noexcept(NO_EXCEPT) : compressed(ALL(range)) {}
inline size_type rank_sup() const { return static_cast<size_type>(this->values.size()); }
inline size_type rank(const value_type& val) const noexcept(NO_EXCEPT) {
return static_cast<size_type>(
std::ranges::distance(std::ranges::begin(this->values), std::ranges::lower_bound(this->values, val))
);
}
inline size_type rank2(const value_type& val) const noexcept(NO_EXCEPT) {
return static_cast<size_type>(
std::ranges::distance(std::ranges::begin(this->values), std::ranges::upper_bound(this->values, val))
) - 1;
}
inline value_type value(const size_type rank) const noexcept(NO_EXCEPT) {
assert(0 <= rank && rank < this->rank_sup());
return this->values[rank];
}
};
template<std::input_iterator I, std::sized_sentinel_for<I> S>
explicit compressed(I, S) -> compressed<typename std::iterator_traits<I>::value_type>;
template<std::ranges::input_range R>
explicit compressed(R&&) -> compressed<typename std::ranges::range_value_t<R>>;
} // namespace uni
#line 33 "data_structure/wavelet_matrix.hpp"
#line 35 "data_structure/wavelet_matrix.hpp"
#line 38 "data_structure/wavelet_matrix.hpp"
namespace uni {
namespace internal {
namespace wavelet_matrix_impl {
// Thanks to: https://github.com/NyaanNyaan/library/blob/master/data-structure-2d/wavelet-matrix.hpp
template<std::unsigned_integral T, class MapType>
requires std::same_as<T, typename MapType::key_type>
struct base {
using size_type = internal::size_t;
using impl_type = T;
private:
size_type _n;
int _bits;
std::vector<bit_vector> _index;
std::vector<std::vector<impl_type>> _sum;
MapType _first_pos;
impl_type _max = 0;
public:
base() = default;
template<std::ranges::input_range R>
explicit base(R&& range) noexcept(NO_EXCEPT) : base(ALL(range)) {}
template<std::input_iterator I, std::sentinel_for<I> S>
base(I first, S last) noexcept(NO_EXCEPT) { this->build(first, last); }
template<std::convertible_to<impl_type> U>
base(const std::initializer_list<U>& init_list) noexcept(NO_EXCEPT) : base(ALL(init_list)) {}
inline size_type size() const noexcept(NO_EXCEPT) { return this->_n; }
inline size_type bits() const noexcept(NO_EXCEPT) { return this->_bits; }
template<std::ranges::input_range R>
inline void build(R&& range) noexcept(NO_EXCEPT) { this->build(ALL(range)); }
template<std::input_iterator I, std::sized_sentinel_for<I> S>
__attribute__((optimize("O3")))
void build(I first, S last) noexcept(NO_EXCEPT) {
this->_n = static_cast<size_type>(std::ranges::distance(first, last));
this->_max = first == last ? -1 : *std::ranges::max_element(first, last);
this->_bits = std::bit_width(this->_max + 1);
this->_index.assign(this->_bits, this->_n);
std::vector<impl_type> bit(first, last), nxt(this->_n);
this->_sum.assign(this->_bits + 1, std::vector<impl_type>(this->_n + 1));
{
size_type i = 0;
for(auto itr=first; itr!=last; ++i, ++itr) {
assert(*itr >= 0);
this->_sum[this->_bits][i + 1] = this->_sum[this->_bits][i] + *itr;
}
}
REPD(h, this->_bits) {
std::vector<size_type> vals;
for(size_type i = 0; i < this->_n; ++i) {
if((bit[i] >> h) & 1) this->_index[h].set(i);
}
this->_index[h].build();
std::array<typename std::vector<impl_type>::iterator, 2> itrs{
std::ranges::begin(nxt), std::ranges::next(std::ranges::begin(nxt), this->_index[h].zeros())
};
REP(i, this->_n) *itrs[this->_index[h].get(i)]++ = bit[i];
REP(i, this->_n) this->_sum[h][i + 1] = this->_sum[h][i] + nxt[i];
std::swap(bit, nxt);
}
REPD(i, this->_n) this->_first_pos[bit[i]] = static_cast<MapType::mapped_type>(i);
}
protected:
inline auto get(const size_type k) const noexcept(NO_EXCEPT) {
return this->_sum[this->_bits][k + 1] - this->_sum[this->_bits][k];
}
auto select(const impl_type& v, const size_type rank) const noexcept(NO_EXCEPT) {
if(v > this->_max) return this->_n;
if(not this->_first_pos.contains(v)) return this->_n;
size_type pos = this->_first_pos.at(v) + rank;
REP(h, this->_bits) {
if(uni::bit(v, h)) pos = this->_index[h].select1(pos - this->_index[h].zeros());
else pos = this->_index[h].select0(pos);
}
return pos;
}
auto kth_smallest(size_type *const l, size_type *const r, size_type *const k) const noexcept(NO_EXCEPT) {
impl_type val = 0;
for(size_type h = this->_bits - 1; h >= 0; --h) {
size_type l0 = this->_index[h].rank0(*l), r0 = this->_index[h].rank0(*r);
if(*k < r0 - l0) {
*l = l0, *r = r0;
}
else {
*k -= r0 - l0;
val |= impl_type{1} << h;
*l += this->_index[h].zeros() - l0;
*r += this->_index[h].zeros() - r0;
}
}
return val;
}
inline auto kth_smallest(size_type l, size_type r, size_type k) const noexcept(NO_EXCEPT) {
return this->kth_smallest(&l, &r, &k);
}
auto kth_smallest_index(size_type l, size_type r, size_type k) const noexcept(NO_EXCEPT) {
const impl_type val = this->kth_smallest(&l, &r, &k);
size_type left = 0;
REPD(h, this->_bits) {
if(uni::bit(val, h)) left = this->_index[h].rank1(left) + this->_index[h].zeros();
else left = this->_index[h].rank0(left);
}
return this->select(val, l + k - left);
}
inline auto kth_largest(const size_type l, const size_type r, const size_type k) const noexcept(NO_EXCEPT) {
return this->kth_smallest(l, r, r - l - k - 1);
}
inline auto kth_largest_index(const size_type l, const size_type r, const size_type k) const noexcept(NO_EXCEPT) {
return this->kth_smallest_index(l, r, r - l - k - 1);
}
inline auto succ0(const size_type l, const size_type r, const size_type h) const noexcept(NO_EXCEPT) {
return std::make_pair(this->_index[h].rank0(l), this->_index[h].rank0(r));
}
inline auto succ1(const size_type l, const size_type r, const size_type h) const noexcept(NO_EXCEPT) {
const size_type l0 = this->_index[h].rank0(l);
const size_type r0 = this->_index[h].rank0(r);
const size_type vals = this->_index[h].zeros();
return std::make_pair(l + vals - l0, r + vals - r0);
}
impl_type sum_in_range(
const size_type l, const size_type r,
const impl_type& x, const impl_type& y,
const impl_type& cur, const size_type bit
) const noexcept(NO_EXCEPT)
{
if(l == r) return 0;
if(bit == -1) {
if(x <= cur && cur <= y) return cur * (r - l);
return 0;
}
const impl_type nxt = (impl_type{1} << bit) | cur;
const impl_type ones = ((impl_type{1} << bit) - 1) | nxt;
if(ones < x || y < cur) return 0;
if(x <= cur && ones <= y) return this->_sum[bit + 1][r] - this->_sum[bit + 1][l];
const size_type l0 = this->_index[bit].rank0(l), r0 = this->_index[bit].rank0(r);
const size_type l1 = l - l0, r1 = r - r0;
return
this->sum_in_range(l0, r0, x, y, cur, bit - 1) +
this->sum_in_range(this->_index[bit].zeros() + l1, this->_index[bit].zeros() + r1, x, y, nxt, bit - 1);
}
inline auto sum_in_range(const size_type l, const size_type r, const impl_type& x, const impl_type& y) const noexcept(NO_EXCEPT) {
return this->sum_in_range(l, r, x, y, 0, this->_bits - 1);
}
inline auto sum_under(const size_type l, const size_type r, const impl_type& v) const noexcept(NO_EXCEPT) {
return this->sum_in_range(l, r, 0, v - 1);
}
inline auto sum_over(const size_type l, const size_type r, const impl_type& v) const noexcept(NO_EXCEPT) {
return this->sum_in_range(l, r, v + 1, std::numeric_limits<impl_type>::max());
}
inline auto sum_or_under(const size_type l, const size_type r, const impl_type& v) const noexcept(NO_EXCEPT) {
return this->sum_in_range(l, r, 0, v);
}
inline auto sum_or_over(const size_type l, const size_type r, const impl_type& v) const noexcept(NO_EXCEPT) {
return this->sum_in_range(l, r, v, std::numeric_limits<impl_type>::max());
}
inline auto sum(const size_type l, const size_type r) const noexcept(NO_EXCEPT) {
return this->_sum[this->_bits][r] - this->_sum[this->_bits][l];
}
auto count_under(size_type l, size_type r, const impl_type& y) const noexcept(NO_EXCEPT) {
if(y >= (impl_type{1} << this->_bits)) return r - l;
size_type res = 0;
REPD(h, this->_bits) {
bool f = (y >> h) & 1;
size_type l0 = this->_index[h].rank0(l), r0 = this->_index[h].rank0(r);
if(f) {
res += r0 - l0;
l += this->_index[h].zeros() - l0;
r += this->_index[h].zeros() - r0;
} else {
l = l0;
r = r0;
}
}
return res;
}
inline auto count_or_under(const size_type l, const size_type r, const impl_type& v) const noexcept(NO_EXCEPT) {
return this->count_under(l, r, v + 1);
}
inline auto count_or_over(const size_type l, const size_type r, const impl_type& v) const noexcept(NO_EXCEPT) {
return r - l - this->count_under(l, r, v);
}
inline auto count_over(const size_type l, const size_type r, const impl_type& v) const noexcept(NO_EXCEPT) {
return this->count_or_over(l, r, v + 1);
}
inline auto count_in_range(const size_type l, const size_type r, const impl_type& x, const impl_type& y) const noexcept(NO_EXCEPT) {
return this->count_or_under(l, r, y) - this->count_under(l, r, x);
}
inline auto count_equal_to(const size_type l, const size_type r, const impl_type& v) const noexcept(NO_EXCEPT) {
return this->count_in_range(l, r, v, v);
}
inline std::optional<impl_type> next(const size_type l, const size_type r, const impl_type& v, const size_type k) const noexcept(NO_EXCEPT) {
const size_type rank = this->count_under(l, r, v) + k;
if(rank < 0 || rank >= r - l) return {};
return { this->kth_smallest(l, r, rank) };
}
inline std::optional<impl_type> prev(const size_type l, const size_type r, const impl_type& v, const size_type k) const noexcept(NO_EXCEPT) {
const size_type rank = this->count_over(l, r, v) + k;
if(rank < 0 || rank >= r - l) return {};
return this->kth_largest(l, r, rank);
}
};
} // namespace wavelet_matrix_impl
} // namespace internal
template<std::integral T, template<class...> class MapTemplate = gnu::gp_hash_table>
struct compressed_wavelet_matrix;
template<std::integral T, template<class...> class MapTemplate = gnu::gp_hash_table>
struct wavelet_matrix : internal::wavelet_matrix_impl::base<std::make_unsigned_t<T>, MapTemplate<std::make_unsigned_t<T>, u32>> {
using value_type = T;
using impl_type = std::make_unsigned_t<T>;
using map_type = MapTemplate<impl_type, u32>;
using size_type = internal::size_t;
using compressed = compressed_wavelet_matrix<value_type, MapTemplate>;
private:
using base = internal::wavelet_matrix_impl::base<impl_type, map_type>;
public:
protected:
inline size_type _positivize_index(const size_type p) const noexcept(NO_EXCEPT) {
return p < 0 ? this->size() + p : p;
}
public:
using base::base;
inline bool empty() const noexcept(NO_EXCEPT) { return this->size() == 0; }
inline value_type get(size_type p) const noexcept(NO_EXCEPT) {
p = this->_positivize_index(p), assert(0 <= p && p < this->size());
return this->base::get(p);
}
inline auto operator[](const size_type p) const noexcept(NO_EXCEPT) { return this->get(p); }
inline auto select(const value_type& v, const size_type p) const noexcept(NO_EXCEPT) {
return this->base::select(v, p);
}
struct iterator;
struct range_reference;
template<uni::interval_notation rng = uni::interval_notation::right_open>
inline auto range(const size_type l, const size_type r) const noexcept(NO_EXCEPT) {
if constexpr(rng == uni::interval_notation::right_open) return range_reference(this, l, r);
if constexpr(rng == uni::interval_notation::left_open) return range_reference(this, l + 1, r + 1);
if constexpr(rng == uni::interval_notation::open) return range_reference(this, l + 1, r);
if constexpr(rng == uni::interval_notation::closed) return range_reference(this, l, r + 1);
}
inline auto range() const noexcept(NO_EXCEPT) { return range_reference(this, 0, this->size()); }
inline auto operator()(const size_type l, const size_type r) const noexcept(NO_EXCEPT) { return range_reference(this, l, r); }
inline auto subseq(const size_type p, const size_type c) const noexcept(NO_EXCEPT) { return range_reference(this, p, p+c); }
inline auto subseq(const size_type p) const noexcept(NO_EXCEPT) { return range_reference(this, p, this->size()); }
struct range_reference : internal::range_reference<const wavelet_matrix> {
range_reference(const wavelet_matrix *const super, const size_type l, const size_type r) noexcept(NO_EXCEPT)
: internal::range_reference<const wavelet_matrix>(super, super->_positivize_index(l), super->_positivize_index(r))
{
assert(0 <= this->_begin && this->_begin <= this->_end && this->_end <= this->_super->size());
}
inline auto get(const size_type k) const noexcept(NO_EXCEPT) {
k = this->_super->_positivize_index(k);
assert(0 <= k && k < this->size());
return this->_super->get(this->_begin + k);
}
inline auto operator[](const size_type k) const noexcept(NO_EXCEPT) { return this->get(k); }
inline value_type kth_smallest(const size_type k) const noexcept(NO_EXCEPT) {
assert(0 <= k && k < this->size());
return this->_super->base::kth_smallest(this->_begin, this->_end, k);
}
inline auto kth_smallest_element(const size_type k) const noexcept(NO_EXCEPT) {
if(k == this->size()) return this->end();
assert(0 <= k && k < this->size());
return std::ranges::next(this->_super->begin(), this->_super->base::kth_smallest_index(this->_begin, this->_end, k));
}
inline value_type kth_largest(const size_type k) const noexcept(NO_EXCEPT) {
assert(0 <= k && k < this->size());
return this->_super->base::kth_largest(this->_begin, this->_end, k);
}
inline auto kth_largest_element(const size_type k) const noexcept(NO_EXCEPT) {
if(k == this->size()) return this->end();
assert(0 <= k && k < this->size());
return std::ranges::next(this->_super->begin(), this->_super->base::kth_largest_index(this->_begin, this->_end, k));
}
inline auto min() const noexcept(NO_EXCEPT) { return this->kth_smallest(0); }
inline auto max() const noexcept(NO_EXCEPT) { return this->kth_largest(0); }
// (r-l)/2 th smallest (0-origin)
inline auto median() const noexcept(NO_EXCEPT) { return this->kth_smallest(this->size() / 2); }
inline value_type sum_in_range(const value_type& x, const value_type& y) const noexcept(NO_EXCEPT) { return this->_super->base::sum_in_range(this->_begin, this->_end, x, y); }
inline value_type sum_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->_super->base::sum_under(this->_begin, this->_end, v); }
inline value_type sum_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->_super->base::sum_over(this->_begin, this->_end, v); }
inline value_type sum_or_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->_super->base::sum_or_under(this->_begin, this->_end, v); }
inline value_type sum_or_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->_super->base::sum_or_over(this->_begin, this->_end, v); }
inline value_type sum(const value_type& x, const value_type& y) const noexcept(NO_EXCEPT) { return this->_super->base::sum_in_range(this->_begin, this->_end, x, y); }
inline value_type sum() const noexcept(NO_EXCEPT) { return this->_super->base::sum(this->_begin, this->_end); }
template<comparison com>
inline auto sum(const value_type& v) const noexcept(NO_EXCEPT) {
if constexpr(com == comparison::under) return this->sum_under(v);
if constexpr(com == comparison::over) return this->sum_over(v);
if constexpr(com == comparison::or_under) return this->sum_or_under(v);
if constexpr(com == comparison::or_over) return this->sum_or_over(v);
assert(false);
}
inline auto count_in_range(const value_type& x, const value_type& y) const noexcept(NO_EXCEPT) {
return this->_super->base::count_in_range(this->_begin, this->_end, x, y);
}
inline auto count_equal_to(const value_type& v) const noexcept(NO_EXCEPT) { return this->_super->base::count_equal_to(this->_begin, this->_end, v); }
inline auto count_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->_super->base::count_under(this->_begin, this->_end, v); }
inline auto count_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->_super->base::count_over(this->_begin, this->_end, v); }
inline auto count_or_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->_super->base::count_or_under(this->_begin, this->_end, v); }
inline auto count_or_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->_super->base::count_or_over(this->_begin, this->_end, v); }
template<comparison com = comparison::equal_to>
inline auto count(const value_type& v) const noexcept(NO_EXCEPT) {
if constexpr(com == comparison::equal_to) return this->count_equal_to(v);
if constexpr(com == comparison::under) return this->count_under(v);
if constexpr(com == comparison::over) return this->count_over(v);
if constexpr(com == comparison::or_under) return this->count_or_under(v);
if constexpr(com == comparison::or_over) return this->count_or_over(v);
assert(false);
}
inline auto next_element(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) {
return this->kth_smallest_element(std::clamp(this->count_under(v) + k, size_type{ 0 }, this->size()));
}
inline auto prev_element(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) {
return this->kth_largest_element(std::clamp(this->count_over(v) - k, size_type{ 0 }, this->size()));
}
inline std::optional<value_type> next(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) {
return this->_super->base::next(this->_begin, this->_end, v, k);
}
inline std::optional<value_type> prev(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) {
return this->_super->base::prev(this->_begin, this->_end, v, k);
}
};
inline auto kth_smallest(const size_type k) const noexcept(NO_EXCEPT) { return this->range().kth_smallest(k); }
inline auto kth_smallest_element(const size_type k) const noexcept(NO_EXCEPT) { return this->range().kth_smallest_element(k); }
inline auto kth_largest(const size_type k) const noexcept(NO_EXCEPT) { return this->range().kth_largest(k); }
inline auto kth_largest_element(const size_type k) const noexcept(NO_EXCEPT) { return this->range().kth_largest_element(k); }
inline auto min() const noexcept(NO_EXCEPT) { return this->range().kth_smallest(0); }
inline auto max() const noexcept(NO_EXCEPT) { return this->range().kth_largest(0); }
// (size)/2 th smallest (0-origin)
inline auto median() const noexcept(NO_EXCEPT) { return this->range().median(); }
inline auto sum_in_range(const value_type& x, const value_type& y) const noexcept(NO_EXCEPT) { return this->range().sum_in_range(x, y); }
inline auto sum_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().sum_under(v); }
inline auto sum_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().sum_over(v); }
inline auto sum_or_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().sum_or_under(v); }
inline auto sum_or_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().sum_or_over(v); }
inline auto sum(const value_type& x, const value_type& y) const noexcept(NO_EXCEPT) { return this->range().sum_in_range(x, y); }
inline auto sum() const noexcept(NO_EXCEPT) { return this->range().sum(); }
template<comparison com>
inline auto sum(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().template sum<com>(v); }
inline auto count_in_range(const value_type& x, const value_type& y) const noexcept(NO_EXCEPT) { return this->range().count_in_range(x, y); }
inline auto count_equal_to(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().count_equal_to(v); }
inline auto count_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().count_under(v); }
inline auto count_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().count_over(v); }
inline auto count_or_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().count_or_under(v); }
inline auto count_or_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().count_or_over(v); }
template<comparison com = comparison::equal_to>
inline auto count(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().template count<com>(v); }
inline auto next_element(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().next_element(v); }
inline auto prev_element(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().prev_element(v); }
inline auto next(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) { return this->range().next(v, k); }
inline auto prev(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) { return this->range().prev(v, k); }
struct iterator;
protected:
using iterator_interface = internal::container_iterator_interface<value_type, const wavelet_matrix, const iterator>;
public:
struct iterator : iterator_interface {
using iterator_interface::iterator_interface;
};
inline auto begin() const noexcept(NO_EXCEPT) { return iterator(this, 0); }
inline auto end() const noexcept(NO_EXCEPT) { return iterator(this, this->size()); }
inline auto rbegin() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
};
template<std::integral T, template<class...> class MapTemplate>
struct compressed_wavelet_matrix : protected wavelet_matrix<u32, MapTemplate> {
using value_type = T;
using size_type = internal::size_t;
protected:
using core = wavelet_matrix<u32, MapTemplate>;
using compresser = compressed<value_type, valarray<u32>>;
compresser _comp;
public:
compressed_wavelet_matrix() = default;
template<std::ranges::input_range R>
explicit compressed_wavelet_matrix(R&& range) noexcept(NO_EXCEPT) : compressed_wavelet_matrix(ALL(range)) {}
template<std::input_iterator I, std::sentinel_for<I> S>
compressed_wavelet_matrix(I first, S last) noexcept(NO_EXCEPT) { this->build(first, last); }
template<std::input_iterator I, std::sentinel_for<I> S>
inline void build(I first, S last) noexcept(NO_EXCEPT) {
this->_comp = compresser(first, last);
this->core::build(ALL(this->_comp));
}
inline auto get(const size_type k) const noexcept(NO_EXCEPT) { return this->_comp.value(this->core::get(k)); }
inline auto operator[](const size_type k) const noexcept(NO_EXCEPT) { return this->_comp.value(this->core::get(k)); }
struct iterator;
struct range_reference;
template<uni::interval_notation rng = uni::interval_notation::right_open>
inline auto range(const size_type l, const size_type r) const noexcept(NO_EXCEPT) {
if constexpr(rng == uni::interval_notation::right_open) return range_reference(this, l, r);
if constexpr(rng == uni::interval_notation::left_open) return range_reference(this, l + 1, r + 1);
if constexpr(rng == uni::interval_notation::open) return range_reference(this, l + 1, r);
if constexpr(rng == uni::interval_notation::closed) return range_reference(this, l, r + 1);
}
inline auto range() const noexcept(NO_EXCEPT) { return range_reference(this, 0, this->size()); }
inline auto operator()(const size_type l, const size_type r) const noexcept(NO_EXCEPT) { return range_reference(this, l, r); }
inline auto subseq(const size_type p, const size_type c) const noexcept(NO_EXCEPT) { return range_reference(this, p, p+c); }
inline auto subseq(const size_type p) const noexcept(NO_EXCEPT) { return range_reference(this, p, this->size()); }
struct range_reference : internal::range_reference<const compressed_wavelet_matrix> {
range_reference(const compressed_wavelet_matrix *const super, const size_type l, const size_type r) noexcept(NO_EXCEPT)
: internal::range_reference<const compressed_wavelet_matrix>(super, super->_positivize_index(l), super->_positivize_index(r))
{
assert(0 <= this->_begin && this->_begin <= this->_end && this->_end <= this->_super->size());
}
private:
inline auto _range() const noexcept(NO_EXCEPT) { return this->_super->core::range(this->_begin, this->_end); }
public:
inline auto get(const size_type k) const noexcept(NO_EXCEPT) { return this->_super->_comp.value(this->_range().get(k)); }
inline auto operator[](const size_type k) const noexcept(NO_EXCEPT) { return this->get(k); }
inline auto kth_smallest(const size_type k) const noexcept(NO_EXCEPT) { return this->_super->_comp.value(this->_range().kth_smallest(k)); }
inline auto kth_smallest_element(const size_type k) const noexcept(NO_EXCEPT) {
return std::ranges::next(this->_super->begin(), std::ranges::distance(this->_super->core::begin(), this->_range().kth_smallest_element(k)));
}
inline auto kth_largest(const size_type k) const noexcept(NO_EXCEPT) { return this->_super->_comp.value(this->_range().kth_largest(k));}
inline auto kth_largest_element(const size_type k) const noexcept(NO_EXCEPT) {
return std::ranges::next(this->_super->begin(), std::ranges::distance(this->_super->core::begin(), this->_range().kth_largest_element(k)));
}
inline auto min() const noexcept(NO_EXCEPT) { return this->kth_smallest(0); }
inline auto max() const noexcept(NO_EXCEPT) { return this->kth_largest(0); }
// (r-l)/2 th smallest (0-origin)
inline auto median() const noexcept(NO_EXCEPT) { return this->kth_smallest(this->size() / 2); }
inline auto count_in_range(const value_type& x, const value_type& y) const noexcept(NO_EXCEPT) {
return this->_range().count_in_range(this->_super->_comp.rank(x), this->_super->_comp.rank2(y));
}
inline size_type count_equal_to(const value_type& v) const noexcept(NO_EXCEPT) {
const auto p = this->_super->_comp.rank(v);
const auto q = this->_super->_comp.rank2(v);
if(p != q) return 0;
return this->_range().count_equal_to(p);
}
inline auto count_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->_range().count_under(this->_super->_comp.rank(v)); }
inline auto count_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->_range().count_over(this->_super->_comp.rank2(v)); }
inline auto count_or_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->_range().count_or_under(this->_super->_comp.rank2(v)); }
inline auto count_or_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->_range().count_or_over(this->_super->_comp.rank(v)); }
template<comparison com = comparison::equal_to>
inline auto count(const value_type& v) const noexcept(NO_EXCEPT) {
if constexpr(com == comparison::equal_to) return this->count_equal_to(v);
if constexpr(com == comparison::under) return this->count_under(v);
if constexpr(com == comparison::over) return this->count_over(v);
if constexpr(com == comparison::or_under) return this->count_or_under(v);
if constexpr(com == comparison::or_over) return this->count_or_over(v);
assert(false);
}
inline auto next_element(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) {
return this->kth_smallest_element(std::clamp(this->_range().count_under(this->_super->_comp.rank(v) + k), size_type{ 0 }, this->size()));
}
inline auto prev_element(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) {
return this->kth_largest_element(std::clamp(this->_range().count_over(this->_super->_comp.rank2(v) + k), size_type{ 0 }, this->size()));
}
inline std::optional<value_type> next(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) {
const auto res = this->_range().next(this->_super->_comp.rank(v), k);
if(res.has_value()) return this->_super->_comp.value(res.value());
return {};
}
inline std::optional<value_type> prev(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) {
const auto res = this->_range().prev(this->_super->_comp.rank2(v), k);
if(res.has_value()) return this->_super->_comp.value(res.value());
return {};
}
};
inline auto kth_smallest(const size_type k) const noexcept(NO_EXCEPT) { return this->range().kth_smallest(k); }
inline auto kth_smallest_element(const size_type k) const noexcept(NO_EXCEPT) { return this->range().kth_smallest_element(k); }
inline auto kth_largest(const size_type k) const noexcept(NO_EXCEPT) { return this->range().kth_largest(k); }
inline auto kth_largest_element(const size_type k) const noexcept(NO_EXCEPT) { return this->range().kth_largest_element(k); }
inline auto min() const noexcept(NO_EXCEPT) { return this->range().kth_smallest(0); }
inline auto max() const noexcept(NO_EXCEPT) { return this->range().kth_largest(0); }
inline auto median() const noexcept(NO_EXCEPT) { return this->range().median(); }
inline auto count_in_range(const value_type& x, const value_type& y) const noexcept(NO_EXCEPT) { return this->range().count_in_range(x, y); }
inline auto count_equal_to(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().count_equal_to(v); }
inline auto count_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().count_under(v); }
inline auto count_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().count_over(v); }
inline auto count_or_under(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().count_or_under(v); }
inline auto count_or_over(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().count_or_over(v); }
template<comparison com = comparison::equal_to>
inline auto count(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().template count<com>(v); }
inline auto next_element(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().next_element(v); }
inline auto prev_element(const value_type& v) const noexcept(NO_EXCEPT) { return this->range().prev_element(v); }
inline auto next(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) { return this->range().next(v, k); }
inline auto prev(const value_type& v, const size_type k = 0) const noexcept(NO_EXCEPT) { return this->range().prev(v, k); }
struct iterator;
protected:
using iterator_interface = internal::container_iterator_interface<value_type, const compressed_wavelet_matrix, const iterator>;
public:
struct iterator : iterator_interface {
using iterator_interface::iterator_interface;
};
inline auto begin() const noexcept(NO_EXCEPT) { return iterator(this, 0); }
inline auto end() const noexcept(NO_EXCEPT) { return iterator(this, this->size()); }
inline auto rbegin() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
};
template<std::ranges::input_range R>
explicit wavelet_matrix(R&&) -> wavelet_matrix<std::ranges::range_value_t<R>>;
template<std::input_iterator I, std::sentinel_for<I> S>
explicit wavelet_matrix(I, S) -> wavelet_matrix<std::iter_value_t<I>>;
template<std::ranges::input_range R>
explicit compressed_wavelet_matrix(R&&) -> compressed_wavelet_matrix<std::ranges::range_value_t<R>>;
template<std::input_iterator I, std::sentinel_for<I> S>
explicit compressed_wavelet_matrix(I, S) -> compressed_wavelet_matrix<std::iter_value_t<I>>;
} // namespace uni
#line 2 "include/geometries.hpp"
#line 2 "geometry/arrow.hpp"
#line 5 "geometry/arrow.hpp"
#line 7 "geometry/arrow.hpp"
#line 2 "geometry/point.hpp"
#include <complex>
#line 9 "geometry/point.hpp"
#line 12 "geometry/point.hpp"
#line 14 "geometry/point.hpp"
#line 18 "geometry/point.hpp"
#line 2 "numeric/float.hpp"
#line 6 "numeric/float.hpp"
#line 10 "numeric/float.hpp"
namespace uni {
template<class T>
inline std::int32_t compare(const T x, const T y, const T tolerance) {
if(x > y + tolerance) return 1;
if(y > x + tolerance) return -1;
return 0;
}
template<class T>
inline std::int32_t compare(const T x, const T y = 0) {
if constexpr(std::is_floating_point_v<T>) {
return compare(x, y, max(1, x, y) * numeric_limits<T>::arithmetic_epsilon());
}
else {
if(x > y) return 1;
if(x < y) return -1;
return 0;
}
}
} // namespace uni
#line 2 "view/cyclic.hpp"
#line 8 "view/cyclic.hpp"
#line 12 "view/cyclic.hpp"
#line 15 "view/cyclic.hpp"
namespace uni {
template<std::ranges::input_range View>
requires std::ranges::view<View>
struct cyclic_view : std::ranges::view_interface<cyclic_view<View>> {
private:
View _base;
template<bool Const> using Base = internal::maybe_const_t<Const, View>;
template<bool Const> struct iterator_tag {};
template<bool Const>
requires std::ranges::forward_range<Base<Const>>
struct iterator_tag<Const> {
private:
static constexpr auto _iterator_category() noexcept {
using category = typename std::iterator_traits<std::ranges::iterator_t<Base<Const>>>::iterator_category;
if constexpr(std::derived_from<category, std::random_access_iterator_tag>)
return std::random_access_iterator_tag{};
else
return category{};
}
public:
using iterator_category = decltype(_iterator_category());
};
public:
template<bool> class iterator;
constexpr explicit cyclic_view(View base) noexcept(NO_EXCEPT) : _base(std::move(base)) {}
inline constexpr View base() const & noexcept(NO_EXCEPT) requires std::copy_constructible<View>
{
return this->_base;
}
inline constexpr View base() && noexcept(NO_EXCEPT) { return std::move(this->_base); }
inline constexpr auto begin() noexcept(NO_EXCEPT)
requires(!internal::simple_view<View>)
{
return iterator<false>(this, std::ranges::begin(this->_base));
}
inline constexpr auto begin() const noexcept(NO_EXCEPT)
requires std::ranges::range<const View>
{
return iterator<true>(this, std::ranges::begin(this->_base));
}
inline constexpr auto end() noexcept(NO_EXCEPT)
requires(!internal::simple_view<View>)
{
return std::unreachable_sentinel;
}
inline constexpr auto end() const noexcept(NO_EXCEPT)
requires std::ranges::range<const View>
{
return std::unreachable_sentinel;
}
};
template<class Range>
cyclic_view(Range &&) -> cyclic_view<std::views::all_t<Range>>;
template<std::ranges::input_range View>
requires std::ranges::view<View>
template<bool Const>
struct cyclic_view<View>::iterator : iterator_tag<Const> {
private:
using Parent = internal::maybe_const_t<Const, cyclic_view>;
using Base = cyclic_view::Base<Const>;
std::ranges::iterator_t<Base> _current = std::ranges::iterator_t<Base>();
std::ranges::iterator_t<Base> _begin = std::ranges::iterator_t<Base>();
std::ranges::sentinel_t<Base> _end = std::ranges::sentinel_t<Base>();
constexpr iterator(Parent *const parent, const std::ranges::iterator_t<Base> current) noexcept(NO_EXCEPT)
: _current(std::move(current)), _begin(std::ranges::begin(parent->_base)), _end(std::ranges::end(parent->_base))
{}
friend cyclic_view;
public:
using difference_type = std::ranges::range_difference_t<Base>;
using value_type = std::ranges::range_value_t<Base>;
using iterator_concept = typename internal::iterator_concept<Base>;
private:
difference_type _index = 0;
public:
iterator() noexcept(NO_EXCEPT) requires std::default_initializable<std::ranges::iterator_t<Base>> = default;
constexpr iterator(iterator<!Const> itr) noexcept(NO_EXCEPT)
requires
Const && std::convertible_to<std::ranges::iterator_t<View>, std::ranges::iterator_t<Base>> &&
std::convertible_to<std::ranges::sentinel_t<View>, std::ranges::sentinel_t<Base>>
: _current(std::move(itr._current)), _begin(std::move(itr._begin)), _end(std::move(itr._end)), _index(std::move(itr._index))
{}
inline constexpr std::ranges::iterator_t<Base> base() && noexcept(NO_EXCEPT) { return std::move(this->_current); }
inline constexpr const std::ranges::iterator_t<Base> &base() const & noexcept { return this->_current; }
inline constexpr decltype(auto) operator*() const noexcept(NO_EXCEPT) { return *this->_current; }
inline constexpr iterator& operator++() noexcept(NO_EXCEPT)
{
assert(this->_current != _end);
++this->_index;
++this->_current;
if(this->_current == this->_end) this->_current = this->_begin;
return *this;
}
inline constexpr void operator++(int) noexcept(NO_EXCEPT) { ++*this; }
inline constexpr iterator operator++(int) noexcept(NO_EXCEPT)
requires std::ranges::forward_range<Base>
{
const auto res = *this; ++*this; return res;
}
inline constexpr iterator& operator--() noexcept(NO_EXCEPT)
requires std::ranges::bidirectional_range<Base>
{
--this->_index;
if(this->_current == this->_begin) this->_current = std::ranges::prev(this->_end);
else --this->_current;
return *this;
}
inline constexpr iterator operator--(int) noexcept(NO_EXCEPT)
requires std::ranges::bidirectional_range<Base>
{
const auto res = *this; --*this; return res;
}
inline constexpr iterator& operator+=(const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
this->_index += diff;
if(diff > 0) {
auto missing = std::ranges::advance(this->_current, diff, this->_end);
if constexpr(std::ranges::sized_range<Base>) missing %= std::ranges::distance(this->_begin, this->_end);
while(this->_current == this->_end) {
this->_current = this->_begin;
missing = std::ranges::advance(this->_current, missing, this->_end);
}
}
else if(diff < 0) {
auto missing = std::ranges::advance(this->_current, diff, this->_begin);
if constexpr(std::ranges::sized_range<Base>) missing %= std::ranges::distance(this->_begin, this->_end);
while(missing < 0) {
this->_current = this->_end;
missing = std::ranges::advance(this->_current, missing, this->_begin);
}
}
return *this;
}
inline constexpr iterator& operator-=(const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
return *this += -diff;
}
inline constexpr decltype(auto) operator[](const difference_type diff) const noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
return *(*this + diff);
}
friend inline constexpr bool operator==(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires std::equality_comparable<std::ranges::iterator_t<Base>>
{
return lhs._index == rhs._index;
}
friend inline constexpr auto operator<=>(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base> && std::three_way_comparable<std::ranges::iterator_t<Base>>
{
return rhs._index <=> lhs._index;
}
friend inline constexpr iterator operator+(const iterator& itr, const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
auto res = itr; res += diff; return res;
}
friend inline constexpr iterator operator+(const difference_type diff, const iterator& itr) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
return itr + diff;
}
friend inline constexpr iterator operator-(const iterator& itr, const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
auto res = itr; res -= diff; return res;
}
friend inline constexpr const difference_type operator-(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires std::sized_sentinel_for<std::ranges::iterator_t<Base>, std::ranges::iterator_t<Base>>
{
return lhs._index - rhs._index;
}
friend inline constexpr std::ranges::range_rvalue_reference_t<Base> iter_move(const iterator& itr) noexcept(NO_EXCEPT)
{
return std::ranges::iter_move(itr._current);
}
friend inline constexpr void iter_swap(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires std::indirectly_swappable<std::ranges::iterator_t<Base>>
{
std::swap(lhs._index, rhs._index);
std::ranges::iter_swap(lhs._current, rhs._current);
}
};
namespace views {
namespace internal {
template<class Range>
concept can_cyclic_view = requires { cyclic_view(std::declval<Range>()); };
}
struct Cyclic : adaptor::range_adaptor_closure<Cyclic> {
template<std::ranges::viewable_range Range>
requires internal::can_cyclic_view<Range>
inline constexpr auto operator() [[nodiscard]] (Range &&res) const
{
return cyclic_view(std::forward<Range>(res));
}
// using adaptor::range_adaptor_closure<Cyclic>::operator();
// static constexpr int arity = 1;
// static constexpr bool has_simple_call_op = true;
};
inline constexpr Cyclic cyclic;
} // namespace views
} // namespace uni
namespace std::ranges {
template<class View>
inline constexpr bool enable_borrowed_range<uni::cyclic_view<View>> = enable_borrowed_range<View>;
} // namespace std::ranges
#line 22 "geometry/point.hpp"
namespace uni {
template <class T>
struct point {
using value_type = T;
private:
value_type _x, _y;
public:
constexpr point() : point(0, 0) {}
constexpr point(const T& x, const T& y) noexcept(NO_EXCEPT) : _x(x), _y(y) {}
template<class U> constexpr point(const point<U>& p) noexcept(NO_EXCEPT) : _x(p.x()), _y(p.y()) {};
template<class U>
constexpr point& operator=(const point<U>& p) & noexcept(NO_EXCEPT) {
if(&p != this) this->_x = p._x, this->_y = p._y;
return *this;
};
inline constexpr auto& x() noexcept(NO_EXCEPT) { return this->_x; }
inline constexpr auto& y() noexcept(NO_EXCEPT) { return this->_y; }
inline constexpr const auto& x() const noexcept(NO_EXCEPT) { return this->_x; }
inline constexpr const auto& y() const noexcept(NO_EXCEPT) { return this->_y; }
constexpr auto& rotate_quarter() noexcept(NO_EXCEPT) {
const auto x = this->_x - this->_y;
const auto y = this->_x + this->_y;
this->_x = std::move(x), this->_y = std::move(y);
return *this;
}
constexpr auto& operator+=(const point& v) noexcept(NO_EXCEPT) { this->_x += v._x, this->_y += v._y; return *this; }
constexpr auto& operator-=(const point& v) noexcept(NO_EXCEPT) { this->_x -= v._x, this->_y -= v._y; return *this; }
constexpr auto& operator+=(const value_type& v) noexcept(NO_EXCEPT) { this->_x += v, this->_y += v; return *this; }
constexpr auto& operator-=(const value_type& v) noexcept(NO_EXCEPT) { this->_x -= v, this->_y -= v; return *this; }
constexpr auto& operator*=(const value_type& v) noexcept(NO_EXCEPT) { this->_x *= v, this->_y *= v; return *this; }
constexpr auto& operator/=(const value_type& v) noexcept(NO_EXCEPT) { this->_x /= v, this->_y /= v; return *this; }
friend inline constexpr auto operator+(const point& p) noexcept(NO_EXCEPT) { return { +p._x, +p._y }; }
friend inline constexpr auto operator-(const point& p) noexcept(NO_EXCEPT) { return { -p._x, -p._y }; }
friend inline constexpr auto operator+(point a, const point& b) noexcept(NO_EXCEPT) { return a += b; }
friend inline constexpr auto operator-(point a, const point& b) noexcept(NO_EXCEPT) { return a -= b; }
friend constexpr auto operator*(const point& a, const point& b) noexcept(NO_EXCEPT) { return a._x * b._x + a._y * b._y; }
friend inline constexpr auto operator+(point a, const value_type& b) noexcept(NO_EXCEPT) { return a += b; }
friend inline constexpr auto operator-(point a, const value_type& b) noexcept(NO_EXCEPT) { return a -= b; }
friend inline constexpr auto operator*(point a, const value_type& b) noexcept(NO_EXCEPT) { return a *= b; }
friend inline constexpr auto operator/(point a, const value_type& b) noexcept(NO_EXCEPT) { return a /= b; }
friend inline constexpr auto operator+(const value_type& a, point b) noexcept(NO_EXCEPT) { return b += a; }
friend inline constexpr auto operator-(const value_type& a, point b) noexcept(NO_EXCEPT) { return b += a; }
friend inline constexpr auto operator*(const value_type& a, point b) noexcept(NO_EXCEPT) { return b *= a; }
friend inline constexpr auto operator/(const value_type& a, point b) noexcept(NO_EXCEPT) { return b /= a; }
friend inline constexpr bool operator==(const point& a, const point& b) noexcept(NO_EXCEPT) { return compare(a._x, b._x) == 0 and compare(a._y, b._y) == 0; }
friend inline constexpr bool operator!=(const point& a, const point& b) noexcept(NO_EXCEPT) { return !(a == b); }
friend inline constexpr bool operator<(const point& a, const point& b) noexcept(NO_EXCEPT) { return compare(a._x, b._x) != 0 ? compare(a._x, b._x) < 0 : compare(a._y, b._y) < 0; }
friend inline constexpr bool operator>(const point& a, const point& b) noexcept(NO_EXCEPT) { return compare(a._x, b._x) != 0 ? compare(a._x, b._x) > 0 : compare(a._y, b._y) > 0; }
friend inline constexpr bool operator<=(const point& a, const point& b) noexcept(NO_EXCEPT) { return !(a > b); }
friend inline constexpr bool operator>=(const point& a, const point& b) noexcept(NO_EXCEPT) { return !(a < b); }
auto _debug() const { return std::make_pair(this->_x, this->_y); }
};
template<size_t I, class T>
inline const auto& get(const point<T>& p) noexcept(NO_EXCEPT) {
if constexpr(I == 0) { return p.x(); }
else if constexpr(I == 1) { return p.y(); }
else static_assert(uni::internal::EXCEPTION_ON_VALUE<I>);
}
template<size_t I, class T>
inline auto& get(point<T>& p) noexcept(NO_EXCEPT) {
if constexpr(I == 0) return p.x();
else if constexpr(I == 1) return p.y();
else static_assert(internal::EXCEPTION_ON_VALUE<I>);
}
} // namespace uni
namespace std {
template<class T>
struct tuple_size<uni::point<T>> : integral_constant<size_t,2> {};
template<size_t I, class T>
struct tuple_element<I,uni::point<T>> {
using type = typename uni::point<T>::value_type;
};
template<class T>
constexpr auto norm(const uni::point<T>& v) noexcept(NO_EXCEPT) { return v.x() * v.x() + v.y() * v.y(); }
template<class T>
constexpr auto abs(const uni::point<T>& v) noexcept(NO_EXCEPT) {
if constexpr(is_floating_point_v<T>) {
return static_cast<T>(std::abs(std::complex<T>(v.x(), v.y())));
}
else {
return static_cast<T>(sqrt(norm(v)));
}
}
template<class T>
constexpr auto arg(const uni::point<T>& v) noexcept(NO_EXCEPT) {
return static_cast<T>(std::arg(std::complex<T>(v.x(), v.y())));
}
template<class T, class C, class S>
auto& operator>>(basic_istream<C, S>& in, uni::point<T>& v) noexcept(NO_EXCEPT) {
T x, y; in >> x >> y;
v = { x, y };
return in;
}
template<class T, class C, class S>
auto& operator<<(basic_ostream<C, S>& out, const uni::point<T>& v) noexcept(NO_EXCEPT) {
out << v.x() << " " << v.y();
return out;
}
} // namespace std
namespace uni {
template<class T>
constexpr auto distance(const point<T>& a, const point<T>& b) noexcept(NO_EXCEPT) {
return std::abs(a - b);
}
template<class T>
constexpr auto squared_distance(const point<T>& a, const point<T>& b) noexcept(NO_EXCEPT) {
return std::norm(a - b);
}
template<class T>
constexpr auto manhattan_distance(const point<T>& a, const point<T>& b) noexcept(NO_EXCEPT) {
return std::abs(a.x() - b.x()) + std::abs(a.y() - b.y());
}
template<class T>
constexpr auto chebyshev_distance(const point<T>& a, const point<T>& b) noexcept(NO_EXCEPT) {
return std::max(std::abs(a.x() - b.x()), std::abs(a.y() - b.y()));
}
template<class T>
constexpr auto dot(point<T> a, point<T> b, const point<T>& o = point<T>()) noexcept(NO_EXCEPT) {
a -= o, b -= o;
return a * b;
}
template<class T>
constexpr auto cross(point<T> a, point<T> b, const point<T>& o = point<T>()) noexcept(NO_EXCEPT) {
a -= o, b -= o;
return a.x() * b.y() - a.y() * b.x();
}
template<class T, class Angle = T>
constexpr point<T> rotate(const point<T>& p, const Angle angle) noexcept(NO_EXCEPT) {
return {
std::cos(angle) * p.x() - std::sin(angle) * p.y(),
std::sin(angle) * p.x() + std::cos(angle) * p.y()
};
}
template<class T, class Angle = T>
constexpr auto rotate(const point<T>& p, const point<T>& q, const Angle angle) noexcept(NO_EXCEPT) {
return rotate(p - q, angle) + q;
}
template<class T>
inline constexpr auto relation(const point<T>& p, const point<T>& q) noexcept(NO_EXCEPT) { return relation<T>({ 0, 0 }, p, q); }
template<class T>
auto to_degree(const T& radian) { return radian * 180 / PI<T>; }
template<class T>
auto to_radian(const T& degree) { return degree * PI<T> / 180; }
} // namespace uni
#line 2 "geometry/line.hpp"
#line 7 "geometry/line.hpp"
#line 11 "geometry/line.hpp"
namespace uni {
template<class Point>
struct line {
using point_type = Point;
using value_type = typename point_type::value_type;
protected:
point_type _p0, _p1;
public:
constexpr void normalize() noexcept(NO_EXCEPT) { if(this->_p0 > this->_p1) std::swap(this->_p0, this->_p1); }
constexpr line() noexcept = default;
constexpr line(const point_type& p0, const point_type& p1) noexcept(NO_EXCEPT) : _p0(p0), _p1(p1) { this->normalize(); }
constexpr line(const value_type a, const value_type b, const value_type c) noexcept(NO_EXCEPT) {
if(compare(a) == 0) this->_p0 = { 0, c / b }, this->_p1 = { 1, c / b };
else if(compare(b) == 0) this->_p0 = { c / a, 0 }, this->_p1 = { c / a, 1 };
else this->_p0 = { 0, c / b }, this->_p1 = { c / a, 0 };
this->normalize();
}
inline constexpr auto& p0() noexcept(NO_EXCEPT) { return this->_p0; }
inline constexpr auto& p1() noexcept(NO_EXCEPT) { return this->_p1; }
inline constexpr const auto& p0() const noexcept(NO_EXCEPT) { return this->_p0; }
inline constexpr const auto& p1() const noexcept(NO_EXCEPT) { return this->_p1; }
constexpr auto vertices() noexcept(NO_EXCEPT) {
return std::tie(this->_p0, this->_p1);
}
const constexpr auto vertices() const noexcept(NO_EXCEPT) {
return std::make_pair(std::cref(this->_p0), std::cref(this->_p1));
}
constexpr const auto to_vector() const noexcept(NO_EXCEPT) { return this->_p1 - this->_p0; }
constexpr const auto length() const noexcept(NO_EXCEPT) { return uni::distance(this->_p0, this->_p1); }
constexpr const auto squared_length() const noexcept(NO_EXCEPT) { return uni::squared_distance(this->_p0, this->_p1); }
constexpr const auto midpoint() const noexcept(NO_EXCEPT) { return tuple_sum(this->vertices()) / 2; }
constexpr auto projection(const point_type& p) noexcept(NO_EXCEPT) {
const auto q = this->p0() - this->p1();
const auto s1 = (p - this->p0()) * q / std::norm(q);
return this->p0() + q * s1;
}
constexpr auto reflection(const point_type& p) noexcept(NO_EXCEPT) {
return p + (this->projection(p) - p) * 2;
}
// implemented in geometry/basic.hpp
inline constexpr auto relation(const point_type& p) noexcept(NO_EXCEPT);
auto _debug() const { return std::make_pair(this->_p0, this->_p1); }
};
template<size_t I, class Point>
inline const auto& get(const line<Point>& ln) noexcept(NO_EXCEPT) {
if constexpr(I == 0) { return ln.p0(); }
else if constexpr(I == 1) { return ln.p1(); }
else static_assert(uni::internal::EXCEPTION_ON_VALUE<I>);
}
template<size_t I, class Point>
inline auto& get(line<Point>& ln) noexcept(NO_EXCEPT) {
if constexpr(I == 0) return ln.p0();
else if constexpr(I == 1) return ln.p1();
else static_assert(uni::internal::EXCEPTION_ON_VALUE<I>);
}
} // namespace uni
namespace std {
template<class Point>
struct tuple_size<uni::line<Point>> : integral_constant<size_t, 2> {};
template<size_t I, class Point>
struct tuple_element<I, uni::line<Point>> {
using type = typename uni::line<Point>::value_type;
};
template<class Point, class C, class S>
auto& operator>>(basic_istream<C, S>& in, uni::line<Point>& v) noexcept(NO_EXCEPT) {
Point x, y; in >> x >> y;
v = { x, y };
return in;
}
template<class Point, class C, class S>
auto& operator<<(basic_ostream<C, S>& out, const uni::line<Point>& v) noexcept(NO_EXCEPT) {
out << v.p0() << " " << v.p1();
return out;
}
} // namespace std
namespace uni {
template<class Point>
bool parallel(const line<Point>& p, const line<Point>& q) noexcept(NO_EXCEPT) {
return compare(p.to_vector() * q.to_vector()) == 0;
}
template<class Point>
bool orthogonal(const line<Point>& p, const line<Point>& q) noexcept(NO_EXCEPT) {
return compare(cross(p.to_vector(), q.to_vector())) == 0;
}
template<class Point>
constexpr std::optional<Point> intersection(const line<Point>& s, const line<Point>& t) noexcept(NO_EXCEPT) {
using value_type = typename Point::value_type;
const Point p = s.to_vector(), q = t.to_vector();
const value_type d0 = cross(p, q);
const value_type d1 = cross(p, s.p1() - t.p0());
if(compare(d0) == 0 and compare(d1) == 0) return {};
return t.p0() + q * (d1 / d0);
}
namespace internal {
template<class T>
constexpr positional_relation relation(
const line<point<T>>& ln, const point<T>& p,
T *const _al = nullptr, T *const _bl = nullptr
) noexcept(NO_EXCEPT) {
const point<T> a = ln.to_vector();
const point<T> b = p - ln.p0();
T al = std::norm(a), bl = std::norm(b);
if(_al) *_al = al;
if(_bl) *_bl = bl;
const T s1 = al * bl;
const T dot = a * b;
if(compare(s1, dot * dot) != 0) return positional_relation::out;
return positional_relation::in;
}
} // namespace internal
template<class Point>
inline constexpr auto line<Point>::relation(const Point& p) noexcept(NO_EXCEPT) {
return internal::relation(*this, p);
}
template<class Point>
auto distance(const line<Point>& ln, const Point& p) noexcept(NO_EXCEPT) {
return std::abs(cross(ln.p1(), p, ln.p0())) / distance(ln.p1(), ln.p0());
}
template<class Point>
inline auto distance(const Point& p, const line<Point>& ln) noexcept(NO_EXCEPT) { return distance(ln, p); }
template<class Point>
auto squared_distance(const line<Point>& ln, const Point& p) noexcept(NO_EXCEPT) {
const auto r = cross(ln.p1(), p, ln.p0());
return r * r / squared_distance(ln.p1(), ln.p0());
}
template<class Point>
inline auto squared_distance(const Point& p, const line<Point>& ln) noexcept(NO_EXCEPT) { return squared_distance(ln, p); }
} // namespace uni
#line 2 "geometry/segment.hpp"
#line 5 "geometry/segment.hpp"
#line 7 "geometry/segment.hpp"
#line 10 "geometry/segment.hpp"
namespace uni {
template<class Point>
struct segment : line<Point> {
using point_type = Point;
using value_type = typename point_type::value_type;
constexpr segment() noexcept = default;
constexpr segment(const point_type& p0, const point_type& p1) noexcept(NO_EXCEPT) : line<Point>(p1) { this->_normalize(); }
constexpr segment(const line<point_type>& ln) noexcept(NO_EXCEPT) : segment(ln.p0(), ln.p1()) {}
constexpr auto relation(const point_type& p) noexcept(NO_EXCEPT);
};
template<bool ALLOW_END_POINT, class Point>
bool intersecting(const segment<Point>& s0, const segment<Point>& s1) noexcept(NO_EXCEPT) {
const auto cp0 = cross(s0.p1(), s1.p0(), s0.p0());
const auto cp1 = cross(s0.p1(), s1.p1(), s0.p0());
const auto cp2 = cross(s1.p1(), s0.p0(), s1.p0());
const auto cp3 = cross(s1.p1(), s0.p1(), s1.p0());
if(compare(cp0) == 0 and compare(cp1) == 0 and compare(cp2) == 0 and compare(cp3) == 0) {
return std::max(s0.p0(), s1.p0()) <= std::min(s0.p1(), s1.p1());
}
if constexpr(ALLOW_END_POINT) return compare(cp0 * cp1) <= 0 and compare(cp2 * cp3) <= 0;
else return compare(cp0 * cp1) < 0 and compare(cp2 * cp3) < 0;
}
template<class Point>
bool intersecting(const segment<Point>& s0, const segment<Point>& s1) noexcept(NO_EXCEPT) {
return intersecting<true>(s0, s1);
}
template<class Point>
inline constexpr std::optional<Point> intersection(const segment<Point>& s0, const segment<Point>& s1) noexcept(NO_EXCEPT) {
if(!intersecting(s0, s1)) return {};
return intersection(line<Point>(s0), line<Point>(s1));
}
template<class Point>
constexpr auto segment<Point>::relation(const Point& p) noexcept(NO_EXCEPT) {
if(p == this->_p0 or p == this->_p1) return positional_relation::on;
typename Point::value_type al, bl;
if(internal::relation(p, *this, &al, &bl) == positional_relation::out) {
return positional_relation::out;
};
const auto comp = compare(al, bl);
if(comp < 0) return positional_relation::out;
if(comp > 0) return positional_relation::in;
assert(false);
}
template<class Point>
double distance(const segment<Point>& s0, const segment<Point> &s1) {
if(intersecting(s0, s1)) return 0;
return
min(
distance(s0, s1.p0()), distance(s0, s1.p1()),
distance(s1, s0.p0()), distance(s1, s0.p1())
);
}
template<class Point>
double squared_distance(const segment<Point>& s0, const segment<Point> &s1) {
if(intersecting(s0, s1)) return 0;
return
min(
squared_distance(s0, s1.p0()), squared_distance(s0, s1.p1()),
squared_distance(s1, s0.p0()), squared_distance(s1, s0.p1())
);
}
template<class Point>
auto distance(const segment<Point>& seg, const Point& p) noexcept(NO_EXCEPT) {
if(compare(dot(seg.p1(), p, seg.p0())) < 0) return distance(p, seg.p0());
if(compare(dot(seg.p0(), p, seg.p1())) < 0) return distance(p, seg.p1());
return distance(line<Point>(seg), p);
}
template<class Point>
inline auto distance(const Point& p, const segment<Point>& seg) noexcept(NO_EXCEPT) { return distance(seg, p); }
template<class Point>
auto squared_distance(const segment<Point>& seg, const Point& p) noexcept(NO_EXCEPT) {
if(compare(dot(seg.p1(), p, seg.p0())) < 0) return squared_distance(p, seg.p0());
if(compare(dot(seg.p0(), p, seg.p1())) < 0) return squared_distance(p, seg.p1());
return squared_distance(line<Point>(seg), p);
}
template<class Point>
inline auto squared_distance(const Point& p, const segment<Point>& seg) noexcept(NO_EXCEPT) { return squared_distance(seg, p); }
} // namespace uni
#line 11 "geometry/arrow.hpp"
namespace uni {
template<class Point>
struct arrow : segment<Point> {
using point_type = Point;
using value_type = typename point_type::value_type;
constexpr arrow() noexcept = default;
// p0 -> p1
constexpr arrow(const point_type& p0, const point_type& p1) noexcept(NO_EXCEPT) { this->_p0 = p0, this->_p1 = p1; }
constexpr auto relation(const point_type& p) noexcept(NO_EXCEPT);
};
template<class Point>
constexpr auto arrow<Point>::relation(const Point& p) noexcept(NO_EXCEPT) {
if(this->_p0 == p || this->_p1 == p) return positional_relation::on;
const auto q0 = this->_p1 - this->_p0, q1 = p - this->_p0;
const auto comp_qr = compare(cross(q0, q1));
if(comp_qr > 0) return positional_relation::counter_clockwise;
if(comp_qr < 0) return positional_relation::clockwise;
if(compare(q0 * q1) < 0) return positional_relation::backward;
if(compare(std::norm(q0), std::norm(q1)) < 0) return positional_relation::forward;
return positional_relation::in;
}
} // namespace uni
namespace std {
template<class Point, class C, class S>
auto& operator>>(basic_istream<C, S>& in, uni::arrow<Point>& v) noexcept(NO_EXCEPT) {
Point x, y; in >> x >> y;
v = { x, y };
return in;
}
} // namespace std
#line 2 "geometry/circle.hpp"
#line 5 "geometry/circle.hpp"
#line 9 "geometry/circle.hpp"
#line 12 "geometry/circle.hpp"
namespace uni {
template<class Point>
struct circle {
using point_type = Point;
using value_type = typename point_type::value_type;
protected:
point_type _c;
value_type _r2;
public:
circle() noexcept = default;
static constexpr auto raw(const point_type& c, const value_type& r2) noexcept(NO_EXCEPT) {
circle res; res._c = c, res._r2 = r2;
return res;
}
constexpr circle(const point_type& c, const value_type& r) noexcept(NO_EXCEPT) : _c(c), _r2(r * r) {}
explicit constexpr circle(const value_type& r) noexcept(NO_EXCEPT) : _c({ 0, 0 }), _r2(r * r) {}
constexpr circle(const point_type& p0, const point_type& p1, const point_type& p2) noexcept(NO_EXCEPT)
: circle(triangle(p0, p1, p2))
{};
explicit constexpr circle(const segment<point_type>& seg) noexcept(NO_EXCEPT)
: _c(seg.midpoint()), _r2(seg.squared_length() / 4)
{};
inline constexpr auto& center() noexcept(NO_EXCEPT) { return this->_c; }
inline constexpr const auto& center() const noexcept(NO_EXCEPT) { return this->_c; }
inline auto radius() const noexcept(NO_EXCEPT) { return static_cast<value_type>(std::sqrt(this->_r2)); }
inline constexpr auto& squared_radius() noexcept(NO_EXCEPT) { return this->_r2; }
inline constexpr const auto& squared_radius() const noexcept(NO_EXCEPT) { return this->_r2; }
constexpr auto relation(const point_type& p) noexcept(NO_EXCEPT) {
const auto dist = uni::squared_distance(this->_c, p);
const auto comp = compare(dist, this->_r2);
if(comp > 0) return positional_relation::out;
if(comp < 0) return positional_relation::in;
return positional_relation::on;
}
auto _debug() const noexcept(NO_EXCEPT) { return std::make_pair(this->center(), this->radius()); }
};
template<class Point>
int count_common_tangent(const circle<Point>& c0, const circle<Point>& c1) {
const auto dist = distance(c0.center(), c1.center());
const auto l0 = c0.radius() + c1.radius();
const auto l1 = std::abs(c0.radius() - c1.radius());
if(compare(dist, l0) > 0) return 4;
if(compare(dist, l0) == 0) return 3;
if(compare(dist, l1) == 0) return 1;
if(compare(dist, l1) < 0) return 0;
return 2;
}
template<class Point>
auto relation(const circle<Point>& c0, const circle<Point>& c1) {
const auto t = count_common_tangent(c0, c1);
switch(t) {
case 0: return uni::positional_relation::included;
case 1: return uni::positional_relation::inscribed;
case 2: return uni::positional_relation::intersecting;
case 3: return uni::positional_relation::circumscribed;
case 4: return uni::positional_relation::distant;
}
assert(false);
}
} // namespace uni
#line 2 "geometry/convex_hull.hpp"
#line 7 "geometry/convex_hull.hpp"
#line 10 "geometry/convex_hull.hpp"
#line 2 "geometry/polygon.hpp"
#line 6 "geometry/polygon.hpp"
#line 9 "geometry/polygon.hpp"
#line 13 "geometry/polygon.hpp"
#line 16 "geometry/polygon.hpp"
namespace uni {
template<class Point, class Container = vector<Point>>
struct polygon : Container {
using point_type = Point;
using container_type = Container;
using value_type = point_type::value_type;
using size_type = Container::size_type;
static_assert(std::same_as<typename container_type::value_type, point_type>);
using container_type::container_type;
auto doubled_area() noexcept(NO_EXCEPT) {
const auto n = std::ranges::ssize(*this);
const auto view = uni::views::cyclic(*this);
value_type res = 0;
REP(i, n) res += cross(view[i], view[i + 1]);
return res;
}
inline auto area() noexcept(NO_EXCEPT) {
return this->doubled_area() / 2;
}
template<bool = true>
bool is_convex() noexcept(NO_EXCEPT);
// implemented in geometry/convex_hull.hpp
template<bool ALLOW_LINE = true, bool LEAVE_MARGIN = false>
auto convex_hull() noexcept(NO_EXCEPT);
};
template<class Point, class Container>
struct convex_polygon : polygon<Point, Container> {
using polygon<Point, Container>::polygon;
};
namespace internal {
template<bool ALLOW_LINE, std::ranges::sized_range R>
requires std::ranges::forward_range<R>
bool is_convex(R&& range) noexcept(NO_EXCEPT) {
const auto n = std::ranges::size(range);
const auto view = uni::views::cyclic(range);
auto itr0 = std::ranges::begin(view);
auto itr1 = std::ranges::next(itr0);
auto itr2 = std::ranges::next(itr1);
REP(n) {
const auto r = arrow(*(itr0++), *(itr1++)).relation(*(itr2++));
if constexpr(ALLOW_LINE) {
if(r == positional_relation::clockwise) return false;
}
else {
if(r != positional_relation::anti_clockwise) return false;
}
}
return true;
}
} // namespace internal
template<class Point, class Container>
template<bool ALLOW_LINE>
inline bool polygon<Point, Container>::is_convex() noexcept(NO_EXCEPT) {
return
(
internal::is_convex<ALLOW_LINE>(*this) ||
internal::is_convex<ALLOW_LINE>(std::views::reverse(*this))
);
}
} // namespace uni
#line 13 "geometry/convex_hull.hpp"
namespace uni {
template<class Point, class Container>
template<bool ALLOW_LINE, bool LEAVE_MARGIN>
auto polygon<Point, Container>::convex_hull() noexcept(NO_EXCEPT) {
auto remove = [&](const point_type& p, const point_type& q, const point_type& r) -> bool {
if constexpr(ALLOW_LINE) {
return compare(cross(p, q, r)) < 0;
}
else {
return compare(cross(p, q, r)) <= 0;
}
};
std::vector<point_type> points(ALL(*this));
const auto n = std::ranges::ssize(points);
using ssize_type = std::remove_const_t<decltype(n)>;
std::ranges::sort(points);
polygon res(2 * n);
ssize_type k = 0;
for(ssize_type i = 0; i < n; res[k++] = points[i++]) {
while(k >= 2 && remove(points[i], res[k - 2], res[k - 1])) --k;
}
for(auto i = n - 2, t = k + 1; i >= 0; res[k++] = points[i--]) {
while(k >= t && remove(points[i], res[k - 2], res[k - 1])) --k;
}
if constexpr(LEAVE_MARGIN) res.resize(k);
else res.resize(k - 1);
return res;
}
} // namespace uni
#line 2 "geometry/triangle.hpp"
#line 7 "geometry/triangle.hpp"
#line 11 "geometry/triangle.hpp"
#line 14 "geometry/triangle.hpp"
namespace uni {
template<class Point>
struct triangle {
using point_type = Point;
using value_type = typename point_type::value_type;
private:
point_type _p0, _p1, _p2;
protected:
constexpr void _normalize() noexcept(NO_EXCEPT) {
std::array<point_type,3> vs = { this->_p0, this->_p1, this->_p2 };
std::ranges::sort(vs);
std::tie(this->_p0, this->_p1, this->_p2) = std::tie(vs[0], vs[1], vs[2]);
}
public:
constexpr triangle() noexcept(NO_EXCEPT) {}
constexpr triangle(const point_type& p0, const point_type& p1, const point_type& p2 = point_type()) noexcept(NO_EXCEPT) : _p0(p0), _p1(p1), _p2(p2)
{
this->_normalize();
}
inline constexpr auto& p0() noexcept(NO_EXCEPT) { return this->_p0; }
inline constexpr auto& p1() noexcept(NO_EXCEPT) { return this->_p1; }
inline constexpr auto& p2() noexcept(NO_EXCEPT) { return this->_p2; }
inline constexpr const auto& p0() const noexcept(NO_EXCEPT) { return this->_p0; }
inline constexpr const auto& p1() const noexcept(NO_EXCEPT) { return this->_p1; }
inline constexpr const auto& p2() const noexcept(NO_EXCEPT) { return this->_p2; }
inline constexpr auto vertices() noexcept(NO_EXCEPT) { return std::tie(this->_p0, this->_p1, this->_p2); }
inline constexpr auto vertices() const noexcept(NO_EXCEPT) { return std::make_tuple(std::cref(this->_p0), std::cref(this->_p1), std::cref(this->_p2)); }
constexpr const auto signed_area() const noexcept(NO_EXCEPT) { return cross(this->_p0, this->_p1, this->_p2) / 2; }
inline constexpr const auto area() const noexcept(NO_EXCEPT) { return std::abs(this->signed_area()); }
constexpr auto distances() const noexcept(NO_EXCEPT) {
return std::make_tuple(
uni::distance(this->_p1, this->_p2),
uni::distance(this->_p2, this->_p0),
uni::distance(this->_p0, this->_p1)
);
}
constexpr auto squared_distances() const noexcept(NO_EXCEPT) {
return std::make_tuple(
uni::squared_distance(this->_p1, this->_p2),
uni::squared_distance(this->_p2, this->_p0),
uni::squared_distance(this->_p0, this->_p1)
);
}
constexpr auto angles() const noexcept(NO_EXCEPT) {
const auto [ d0, d1, d2 ] = this->distances();
return std::make_tuple(
std::acos((d1 * d1 + d2 * d2 - d0 * d0) / (2 * d1 * d2)),
std::acos((d2 * d2 + d0 * d0 - d1 * d1) / (2 * d2 * d0)),
std::acos((d0 * d0 + d1 * d1 - d2 * d2) / (2 * d0 * d1))
);
}
constexpr point_type barycenter() const noexcept(NO_EXCEPT) { return tuple_sum(this->vertices()) / 3; }
constexpr auto circumcenter() const noexcept(NO_EXCEPT) {
const auto [ d0, d1, d2 ] = this->squared_distances();
const auto t0 = d0 * (d1 + d2 - d0);
const auto t1 = d1 * (d2 + d0 - d1);
const auto t2 = d2 * (d0 + d1 - d2);
return (t0 * this->_p0 + t1 * this->_p1 + t2 * this->_p2) / (t0 + t1 + t2);
}
constexpr auto incenter() const noexcept(NO_EXCEPT) {
const auto [ d0, d1, d2 ] = this->distances();
return (d0 * this->_p0 + d1 * this->_p1 + d2 * this->_p2) / (d0 + d1 + d2);
}
constexpr auto orthocenter() const noexcept(NO_EXCEPT) {
return tuple_sum(this->vertices()) - 2 * this->circumcenter();
}
constexpr triangle excenters() const noexcept(NO_EXCEPT) {
const auto [ d0, d1, d2 ] = this->distances();
return {
(d1 * this->_p1 + d2 * this->_p2 - d0 * this->_p0) / (d1 + d2 - d0),
(d2 * this->_p1 + d0 * this->_p2 - d1 * this->_p0) / (d2 + d0 - d1),
(d0 * this->_p1 + d1 * this->_p2 - d2 * this->_p0) / (d0 + d1 - d2)
};
}
// implemented in geometry/basic.hpp
constexpr auto circumcircle() const noexcept(NO_EXCEPT);
constexpr auto incircle() const noexcept(NO_EXCEPT);
auto _debug() const noexcept(NO_EXCEPT) {
return std::make_tuple(this->_p0, this->_p1, this->_p2);
}
};
template<size_t I, class T>
inline const auto& get(const triangle<T>& t) noexcept(NO_EXCEPT) {
if constexpr(I == 0) { return t.p0(); }
else if constexpr(I == 1) { return t.p1(); }
else if constexpr(I == 2) { return t.p2(); }
else static_assert(internal::EXCEPTION_ON_VALUE<I>);
}
template<size_t I, class T>
inline auto& get(triangle<T>& t) noexcept(NO_EXCEPT) {
if constexpr(I == 0) return t.p0();
else if constexpr(I == 1) return t.p1();
else if constexpr(I == 2) return t.p2();
else static_assert(internal::EXCEPTION_ON_VALUE<I>);
}
} // namespace uni
namespace std {
template<class T>
struct tuple_size<uni::triangle<T>> : integral_constant<size_t,3> {};
template<size_t I, class T>
struct tuple_element<I,uni::triangle<T>> {
using type = typename uni::triangle<T>::value_type;
};
template<class T, class C, class S>
auto& operator>>(basic_istream<C, S>& in, uni::triangle<T>& v) noexcept(NO_EXCEPT) {
typename uni::triangle<T>::point_type p, q, r; in >> p >> q >> r;
v = { p, q, r };
return in;
}
} // namespace std
namespace uni {
template<class> struct circle;
template<class Point>
constexpr auto triangle<Point>::incircle() const noexcept(NO_EXCEPT) {
const auto p = this->incenter();
return circle<Point>::raw(p, squared_distance(p, line(this->_p0, this->_p1)));
}
template<class Point>
constexpr auto triangle<Point>::circumcircle() const noexcept(NO_EXCEPT) {
const auto p = this->circumcenter();
return circle<Point>::raw(p, squared_distance(p, this->_p0));
}
} // namespace uni
#line 2 "include/graph_theory.hpp"
#line 2 "graph/centroid_decomposition.hpp"
#line 6 "graph/centroid_decomposition.hpp"
#line 2 "structure/graph.hpp"
#line 8 "structure/graph.hpp"
#line 12 "structure/graph.hpp"
#line 16 "structure/graph.hpp"
#line 21 "structure/graph.hpp"
#line 2 "structure/grid.hpp"
#line 12 "structure/grid.hpp"
#line 16 "structure/grid.hpp"
#line 19 "structure/grid.hpp"
#line 21 "structure/grid.hpp"
#line 24 "structure/grid.hpp"
namespace uni {
namespace internal {
namespace grid_impl {
template<class T>
struct container_base {
using value_type = T;
using size_type = internal::size_t;
private:
size_type _h, _w;
protected:
inline void _validate_index(__attribute__ ((unused)) const size_type i, __attribute__ ((unused)) const size_type j) const noexcept(NO_EXCEPT) {
assert(0 <= i and i < this->height());
assert(0 <= j and j < this->width());
}
inline size_type _positivize_row_index(const size_type x) const noexcept(NO_EXCEPT) {
return x < 0 ? this->height() + x : x;
}
inline size_type _positivize_col_index(const size_type x) const noexcept(NO_EXCEPT) {
return x < 0 ? this->width() + x : x;
}
public:
container_base() = default;
container_base(const size_type h, const size_type w) noexcept(NO_EXCEPT) : _h(h), _w(w) {}
void resize(const size_type h, const size_type w) noexcept(NO_EXCEPT) {
this->_h = h, this->_w = w;
}
inline size_type height() const noexcept(NO_EXCEPT) { return this->_h; }
inline size_type width() const noexcept(NO_EXCEPT) { return this->_w; }
inline size_type id(const size_type i, const size_type j) const noexcept(NO_EXCEPT) {
const size_type _i = this->_positivize_row_index(i);
const size_type _j = this->_positivize_col_index(j);
this->_validate_index(_i, _j);
return _i * this->width() + _j;
}
inline size_type id(const std::pair<size_type,size_type>& p) const noexcept(NO_EXCEPT) {
return this->id(p.first, p.second);
}
inline std::pair<size_type,size_type> pos(const size_type id) const noexcept(NO_EXCEPT) {
return { id / this->width(), id % this->width() };
}
};
template<class Base>
struct regular_container : Base, container_base<typename Base::value_type::value_type> {
using row_type = typename Base::value_type;
using value_type = typename row_type::value_type;
using size_type = internal::size_t;
explicit regular_container(const size_type n = 0) noexcept(NO_EXCEPT) : regular_container(n, n) {}
regular_container(const size_type h, const size_type w, const value_type &val = value_type()) noexcept(NO_EXCEPT)
: Base(h, row_type(w, val)), container_base<value_type>(h, w)
{}
regular_container(const std::initializer_list<row_type> init_list) noexcept(NO_EXCEPT) : Base(init_list) {
const auto rows = std::ranges::ssize(init_list);
const size_type first_cols = init_list.begin()->size();
if constexpr (DEV_ENV) { ITR(init_row, init_list) assert((size_type)init_row.size() == first_cols); }
this->container_base<value_type>::resize(rows, first_cols);
}
inline void assign(const regular_container &source) noexcept(NO_EXCEPT) {
this->resize(source.height(), source.width());
this->Base::assign(ALL(source));
}
inline void assign(const size_type h, const size_type w, const value_type &val = value_type()) noexcept(NO_EXCEPT) {
this->container_base<value_type>::resize(h, w);
this->Base::resize(h);
ITRR(row, *this) row.assign(w, val);
}
inline void resize(const size_type h, const size_type w) noexcept(NO_EXCEPT) {
this->container_base<value_type>::resize(h, w);
this->Base::resize(h);
ITRR(row, *this) row.resize(w);
}
inline auto& operator()(const size_type i, const size_type j) noexcept(NO_EXCEPT) {
const size_type _i = this->_positivize_row_index(i);
const size_type _j = this->_positivize_col_index(j);
this->_validate_index(_i, _j);
return (*this)[_i][_j];
}
inline const auto& operator()(const size_type i, const size_type j) const noexcept(NO_EXCEPT) {
const size_type _i = this->_positivize_row_index(i);
const size_type _j = this->_positivize_col_index(j);
this->_validate_index(_i, _j);
return (*this)[_i][_j];
}
inline auto& operator()(const std::pair<size_type,size_type>& p) noexcept(NO_EXCEPT) {
return this->operator()(p.first, p.second);
}
inline const auto& operator()(const std::pair<size_type,size_type>& p) const noexcept(NO_EXCEPT) {
return this->operator()(p.first, p.second);
}
};
template<class Base>
struct unfolded_container : Base, container_base<typename Base::value_type> {
using value_type = typename Base::value_type;
using size_type = internal::size_t;
explicit unfolded_container(size_type n = 0) noexcept(NO_EXCEPT) : unfolded_container(n, n) {}
unfolded_container(const size_type h, const size_type w, const value_type &val = value_type()) noexcept(NO_EXCEPT)
: Base(h * w, val), container_base<value_type>(h, w)
{}
unfolded_container(std::initializer_list<std::initializer_list<value_type>> init_list) noexcept(NO_EXCEPT) {
const auto rows = std::ranges::ssize(init_list);
const auto first_cols = std::ranges::ssize(std::ranges::begin(init_list));
this->resize(rows, first_cols);
{
size_type index = 0;
for(
auto itr = std::ranges::begin(init_list), itr_end = std::ranges::end(init_list);
itr!=itr_end;
++itr
)
{
assert((size_type)itr->size() == first_cols);
for(auto v=itr->begin(), v_end=itr->end(); v!=v_end; ++v) (*this)[index++] = *v;
}
}
}
inline void assign(const unfolded_container &source) noexcept(NO_EXCEPT) {
this->resize(source.height(), source.width());
this->Base::assign(ALL(source));
}
inline void assign(const size_type h, const size_type w, const value_type &val = value_type()) noexcept(NO_EXCEPT) {
this->container_base<value_type>::resize(h, w);
this->Base::assign(h * w, val);
}
inline void resize(const size_type h, const size_type w) noexcept(NO_EXCEPT) {
this->container_base<value_type>::resize(h, w);
this->Base::resize(h * w);
}
inline value_type& operator()(const size_type i, const size_type j) noexcept(NO_EXCEPT) {
const size_type _i = this->_positivize_row_index(i);
const size_type _j = this->_positivize_col_index(j);
return this->operator[](this->id(_i, _j));
}
inline value_type& operator()(const std::pair<size_type,size_type>& p) noexcept(NO_EXCEPT) {
return this->operator()(this->id(p.first, p.second));
}
inline const value_type& operator()(const std::pair<size_type,size_type>& p) const noexcept(NO_EXCEPT) {
return this->operator()(this->id(p.first, p.second));
}
};
} // namespace grid_impl
template<class Container>
struct grid_core : Container {
using Container::Container;
using value_type = Container::value_type;
using size_type = internal::size_t;
enum class invert_direction { vertical, horizontal };
enum class rotate_direction { counter_clockwise, clockwise };
inline bool is_valid(const size_type i, const size_type j) const noexcept(NO_EXCEPT) {
return 0 <= i and i < this->height() and 0 <= j and j < this->width();
}
inline bool is_valid(const std::pair<size_type, size_type>& p) const noexcept(NO_EXCEPT) {
return this->is_valid(p.first, p.second);
}
template<std::input_iterator I, std::sentinel_for<I> S>
inline auto vicinities(const size_type i, const size_type j, I dirs_first, S dirs_last) const noexcept(NO_EXCEPT) {
std::vector<std::pair<size_type, size_type>> res;
REP(itr, dirs_first, dirs_last) {
const size_type ii = i + itr->first, jj = j + itr->second;
if(this->is_valid(ii, jj)) res.emplace_back(ii, jj);
}
return res;
}
template<class I, class C>
inline auto vicinities(const std::pair<size_type, size_type>& p, const C dirs) const noexcept(NO_EXCEPT) {
return this->vicinities(p.first, p.second, ALL(dirs));
}
inline auto vicinities4(const size_type i, const size_type j) const noexcept(NO_EXCEPT) { return this->vicinities(i, j, ALL(DIRS4)); }
inline auto vicinities4(const std::pair<size_type, size_type>& p) const noexcept(NO_EXCEPT) { return this->vicinities(p.first, p.second, ALL(DIRS4)); }
inline auto vicinities8(const size_type i, const size_type j) const noexcept(NO_EXCEPT) { return this->vicinities(i, j, ALL(DIRS8)); }
inline auto vicinities8(const std::pair<size_type, size_type>& p) const noexcept(NO_EXCEPT) { return this->vicinities(p.first, p.second, ALL(DIRS8)); }
template<invert_direction DIRECTION = invert_direction::vertical>
inline grid_core& invert() noexcept(NO_EXCEPT) {
grid_core res(this->height(), this->width());
REP(i, this->height()) REP(j, this->width()) {
if constexpr (DIRECTION == invert_direction::vertical) {
res(i,j) = (*this)(this->height()-i-1,j);
}
else {
res(i,j) = (*this)(i, this->width()-j-1);
}
}
this->assign(res);
return *this;
}
template<rotate_direction DIRECTION = rotate_direction::clockwise>
inline grid_core& rotate(const size_type k) noexcept(NO_EXCEPT) {
grid_core res = *this;
REP(i, k) { res = res.rotate<DIRECTION>(); }
this->assign(res);
return *this;
}
template<rotate_direction DIRECTION = rotate_direction::clockwise>
inline grid_core& rotate() noexcept(NO_EXCEPT) {
grid_core res(this->width(), this->height());
REP(i, this->width()) REP(j, this->height()) {
if constexpr (DIRECTION == rotate_direction::clockwise) {
res(i,j) = (*this)(this->height()-j-1,i);
}
else {
res(i,j) = (*this)(j,this->width()-i-1);
}
}
this->assign(res);
return *this;
}
inline grid_core& transpose() noexcept(NO_EXCEPT) {
grid_core res(this->width(), this->height());
REP(i, this->width()) REP(j, this->height()) {
res(i,j) = (*this)(j,i);
}
this->assign(res);
return *this;
}
};
} // namespace internal
template<class T, class row_type = vector<T>, class Base = vector<row_type>>
using grid = internal::grid_core<internal::grid_impl::regular_container<Base>>;
template<class T, class row_type = valarray<T>, class Base = vector<row_type>>
using valgrid = internal::grid_core<internal::grid_impl::regular_container<Base>>;
template<class T, class Base = vector<T>>
using unfolded_grid = internal::grid_core<internal::grid_impl::unfolded_container<Base>>;
template<class T, class Base = valarray<T>>
using unfolded_valgrid = internal::grid_core<internal::grid_impl::unfolded_container<Base>>;
} // namespace uni
#line 24 "structure/graph.hpp"
#line 26 "structure/graph.hpp"
#line 2 "internal/auto_holder.hpp"
#line 5 "internal/auto_holder.hpp"
#line 9 "internal/auto_holder.hpp"
#line 11 "internal/auto_holder.hpp"
namespace uni {
namespace internal {
namespace auto_holder_impl {
template<class T, bool DYNAMIC, class = std::enable_if_t<std::is_integral_v<T> && not DYNAMIC>>
constexpr int _holder_type(resolving_rank<2>) { return 0; }
template<class T, bool>
constexpr auto _holder_type(resolving_rank<1>) -> decltype(std::unordered_set<T>(), 0){ return 1; }
template<class T, bool>
constexpr int _holder_type(resolving_rank<0>) { return 2; }
template<class T, bool DYNAMIC = false>
constexpr int holder_type = _holder_type<T,DYNAMIC>(resolving_rank<10>{});
template<class,class,int> struct holder {};
template<class T, class U>
struct holder<T, U, 0> : vector<U> {
using vector<U>::vector;
};
template<class T, class U>
struct holder<T, U, 1> : gp_hash_table<T, U> {
using gp_hash_table<T, U>::gp_hash_table;
template<class V> inline void assign(const internal::size_t, const V& v) { this->set_default(v); }
};
template<class T, class U>
struct holder<T, U, 2> : map<T, U> {
using map<T, U>::map;
template<class V> inline void assign(const internal::size_t, const V& v) { this->set_default(v); }
};
} // namespace auto_holder_impl
} // namespace internal
template<class T, class U> struct auto_holder : internal::auto_holder_impl::holder<T,U,internal::auto_holder_impl::holder_type<T>> {
using internal::auto_holder_impl::holder<T,U,internal::auto_holder_impl::holder_type<T>>::holder;
};
template<class T, class U> struct dynamic_auto_holder : internal::auto_holder_impl::holder<T,U,internal::auto_holder_impl::holder_type<T,true>> {
using internal::auto_holder_impl::holder<T,U,internal::auto_holder_impl::holder_type<T,true>>::holder;
};
} // namespace uni
#line 28 "structure/graph.hpp"
namespace uni {
namespace internal {
namespace graph_impl {
template<class Node,class Cost> struct edge {
private:
inline static internal::size_t unique() noexcept(NO_EXCEPT) { static internal::size_t id = 0; return id++; }
public:
using cost_type = Cost;
using node_type = Node;
using size_type = internal::size_t;
const size_type id = unique();
const node_type from, to; const Cost cost;
const size_type index = 0;
edge(const node_type u, const node_type v, const Cost w = 1, const size_type i = 0) noexcept(NO_EXCEPT)
: from(u), to(v), cost(w), index(i)
{}
operator node_type() const noexcept(NO_EXCEPT) { return this->to; }
inline node_type opposite(const node_type v) const noexcept(NO_EXCEPT) {
if(this->from == v) return this->to;
if(this->to == v) return this->from;
assert(false);
}
auto _debug() const { return std::make_tuple(index, from, to, cost); };
friend bool operator==(const edge& lhs, const edge& rhs) noexcept(NO_EXCEPT) { return lhs.id == rhs.id; }
friend bool operator!=(const edge& lhs, const edge& rhs) noexcept(NO_EXCEPT) { return lhs.id != rhs.id; }
};
template<class NodeType, class CostType, class EdgeCollector>
struct regular_base : EdgeCollector {
using EdgeCollector::EdgeCollector;
using size_type = internal::size_t;
using node_type = NodeType;
using cost_type = CostType;
inline size_type size() const noexcept(NO_EXCEPT) { return static_cast<size_type>(this->EdgeCollector::size()); }
};
template<class NodeType, class CostType, class Map>
struct virtual_base : Map {
public:
using size_type = internal::size_t;
using node_type = NodeType;
using cost_type = CostType;
protected:
size_type _n = 0;
public:
template<class F>
explicit virtual_base(const size_type n, F&& f) noexcept(NO_EXCEPT)
: Map(std::forward<F>(f)), _n(n)
{}
inline size_type size() const noexcept(NO_EXCEPT) { return this->_n; }
};
template<class NodeType, class CostType, template<class...> class Container>
struct regular_core : regular_base<NodeType,CostType,Container<vector<internal::graph_impl::edge<NodeType,CostType>>>> {
using size_type = internal::size_t;
using node_type = NodeType;
using cost_type = CostType;
using edge_type = typename internal::graph_impl::edge<node_type,cost_type>;
enum class edge_kind { undirected, directed };
private:
using base = regular_base<NodeType,CostType,Container<vector<edge_type>>>;
size_type _directed_edge_count = 0, _undirected_edge_count = 0;
Container<edge_type> _edges;
Container<size_type> _out_degs, _in_degs;
protected:
inline void _add_edge(const size_type u, const size_type v, const cost_type w, const size_type k) noexcept(NO_EXCEPT) {
this->operator[](u).emplace_back(u, v, w, k);
++_out_degs[u], ++_in_degs[v];
++this->_directed_edge_count;
}
public:
explicit regular_core() noexcept(NO_EXCEPT) : base() {}
explicit regular_core(const size_type n = 0) noexcept(NO_EXCEPT)
: base(n), _out_degs(n), _in_degs(n)
{}
auto& clear() noexcept(NO_EXCEPT) {
this->_directed_edge_count = 0, this->_undirected_edge_count = 0;
this->base::clear(), this->_edges.clear();
this->_out_degs.clear(), this->_in_degs.clear();
return *this;
}
auto& resize(const size_type n) noexcept(NO_EXCEPT) {
this->base::resize(n), this->_out_degs.resize(n), this->_in_degs.resize(n);
return *this;
}
inline const auto& edges() const noexcept(NO_EXCEPT) { return this->_edges; }
inline const auto& edge(const size_type k) const noexcept(NO_EXCEPT) { return this->_edges[k]; }
inline const auto& degrees() const noexcept(NO_EXCEPT) { return this->_in_degs; }
inline const auto& degree(const size_type k) const noexcept(NO_EXCEPT) { return this->_in_degs[k]; }
inline const auto& in_degrees() const noexcept(NO_EXCEPT) { return this->_in_degs; }
inline const auto& in_degree(const size_type k) const noexcept(NO_EXCEPT) { return this->_in_degs[k]; }
inline const auto& out_degrees() const noexcept(NO_EXCEPT) { return this->_out_degs; }
inline const auto& out_degree(const size_type k) const noexcept(NO_EXCEPT) { return this->_out_degs[k]; }
inline size_type directed_edges_count() const noexcept(NO_EXCEPT) { return this->_directed_edge_count; }
template<class R = valgrid<bool>>
auto make_has_edges() const noexcept(NO_EXCEPT) {
R res(this->size(), this->size(), false);
REP(i, this->size()) ITR(j, this->operator[](i)) res[i][j] = true;
return res;
}
template<bool SELF_ZERO = true, class T = cost_type, class R = valgrid<T>>
auto make_initial_distance_matrix() const noexcept(NO_EXCEPT) {
R res(this->size(), this->size(), numeric_limits<T>::arithmetic_infinity());
if constexpr(SELF_ZERO) REP(i, this->size()) res[i][i] = 0;
REP(i, this->size()) ITR(j, this->operator[](i)) res[i][j] = j.cost;
return res;
}
template<bool SELF_ZERO = true, class T = cost_type, class R = valgrid<T>>
auto make_distance_matrix() const noexcept(NO_EXCEPT) {
R res = this->make_initial_distance_matrix<SELF_ZERO,T,R>();
REP(k, this->size()) REP(i, this->size()) REP(j, this->size()) {
chmin(res[i][j], res[i][k] + res[k][j]);
}
return res;
}
template<edge_kind EDGE_TYPE = edge_kind::directed>
auto add_edge(const node_type u, const node_type v, const cost_type w = 1) noexcept(NO_EXCEPT) {
assert(0 <= u and u < this->size()), assert(0 <= v and v < this->size());
const size_type k = this->edges().size();
this->_edges.emplace_back(u, v, w, k);
this->_add_edge(u, v, w, k);
if constexpr(EDGE_TYPE == edge_kind::undirected) this->_add_edge(v, u, w, k);
return k;
}
inline auto add_edge_bidirectionally(const node_type u, const node_type v, const cost_type w = 1) noexcept(NO_EXCEPT) {
return this->add_edge<edge_kind::undirected>(u, v, w);
}
template<bool WEIGHTED = false, bool ONE_ORIGIN = true, const edge_kind EDGE_TYPE = edge_kind::directed, class Stream = input_adaptor<>>
void read(const size_type edges, Stream *const ist = &_input) noexcept(NO_EXCEPT) {
REP(edges) {
node_type u, v; cost_type w = 1; *ist >> u >> v; if(ONE_ORIGIN) --u, --v;
if(WEIGHTED) *ist >> w;
this->add_edge<EDGE_TYPE>(u, v, w);
}
}
template<bool WEIGHTED = false, bool ONE_ORIGIN = true, class Stream = input_adaptor<>>
void read_bidirectionally(const size_type edges, Stream *const ist = &_input) noexcept(NO_EXCEPT) {
REP(edges) {
node_type u, v; cost_type w = 1; *ist >> u >> v; if(ONE_ORIGIN) --u, --v;
if(WEIGHTED) *ist >> w;
this->add_edge<edge_kind::undirected>(u, v, w);
}
}
};
template<class Graph>
struct mixin : Graph {
using Graph::Graph;
using size_type = typename Graph::size_type;
using node_type = typename Graph::node_type;
using cost_type = typename Graph::cost_type;
inline size_type vertices() const noexcept(NO_EXCEPT) { return static_cast<size_type>(this->Graph::size()); }
public:
// graph/shortest_path.hpp
template<item_or_convertible_range<node_type> Source, class Dist, class Prev = std::nullptr_t>
void shortest_path_without_cost(Source&&, Dist *const, Prev *const = nullptr, const node_type& = -1, const node_type& = -2) const noexcept(NO_EXCEPT);
template<item_or_convertible_range<node_type> Source>
auto shortest_path_without_cost(Source&&) const noexcept(NO_EXCEPT);
// graph/dijkstra.hpp
template<item_or_convertible_range<node_type> Source, class Dist, class Prev = std::nullptr_t>
void shortest_path_with_01cost(Source&&, Dist *const, Prev *const = nullptr, const node_type& = -1, const node_type& = -2) const noexcept(NO_EXCEPT);
template<item_or_convertible_range<node_type> Source>
auto shortest_path_with_01cost(Source&&) const noexcept(NO_EXCEPT);
// graph/dijkstra.hpp
template<item_or_convertible_range<node_type> Source, class Dist, class Prev = std::nullptr_t>
void shortest_path_with_cost(Source&&, Dist *const, Prev *const = nullptr, const node_type& = -1, const node_type& = -2) const noexcept(NO_EXCEPT);
template<item_or_convertible_range<node_type> Source>
auto shortest_path_with_cost(Source&&) const noexcept(NO_EXCEPT);
// graph/topological_sort.hpp
bool sort_topologically(vector<node_type> *const ) const noexcept(NO_EXCEPT);
bool sort_topologically() const noexcept(NO_EXCEPT);
// graph/topological_sort.hpp
template<class> bool sort_topologically_with_priority(vector<node_type> *const) const noexcept(NO_EXCEPT);
template<class> bool sort_topologically_with_priority() const noexcept(NO_EXCEPT);
// graph/minimum_paph_cover.hpp
size_type minimum_paph_cover_size_as_dag() const noexcept(NO_EXCEPT);
// graph/spanning_tree_cost.hpp
auto minimum_spanning_tree(mixin *const = nullptr) const noexcept(NO_EXCEPT);
// graph/spanning_tree_cost.hpp
auto maximum_spanning_tree(mixin *const = nullptr) const noexcept(NO_EXCEPT);
// graph/reachability.hpp
template<std::ranges::sized_range R>
auto test_reachability(R&&) const noexcept(NO_EXCEPT);
// graph/connected_components.hpp
disjoint_set components() const noexcept(NO_EXCEPT);
// graph/connected_components.hpp
bool is_bipartite() const noexcept(NO_EXCEPT);
// graph/connected_components.hpp
template<class Colors>
bool is_bipartite(Colors *const) const noexcept(NO_EXCEPT);
// graph/parse_grid.hpp
template<bool = false, class G, class U = char>
void parse_grid(const G&, U = '.') noexcept(NO_EXCEPT);
// graph/manhattan_minimum_spanning_tree.hpp
template<
std::input_iterator I0, std::input_iterator I1,
std::sentinel_for<I0> S0, std::sentinel_for<I1> S1
>
cost_type build_manhattan_mst(I0, S0, I1, S1) noexcept(NO_EXCEPT);
};
} // namespace graph_impl
} // namespace internal
template<class Cost = std::int64_t, class Node = internal::size_t, template<class...> class Container = vector>
struct graph : internal::graph_impl::mixin<internal::graph_impl::regular_core<Node, Cost, Container>> {
private:
using base = internal::graph_impl::mixin<internal::graph_impl::regular_core<Node, Cost, Container>>;
public:
using size_type = typename base::size_type;
using node_type = typename base::node_type;
using edge = typename internal::graph_impl::edge<node_type,Cost>;
explicit graph(const size_type n = 0) noexcept(NO_EXCEPT) : base(n) {}
};
template<class Node = internal::size_t, class Cost = std::int64_t, class Edges = virtual_map<Node, vector<typename internal::graph_impl::edge<Node, Cost>>>>
struct virtual_graph : internal::graph_impl::mixin<internal::graph_impl::virtual_base<Node, Cost, Edges>> {
private:
using base = internal::graph_impl::mixin<internal::graph_impl::virtual_base<Node, Cost, Edges>>;
public:
using size_type = typename base::size_type;
using edge = typename internal::graph_impl::edge<Node, Cost>;
private:
size_type _n = 0;
public:
template<class F>
explicit virtual_graph(F&& f, const size_type n = 0) noexcept(NO_EXCEPT)
: base(n, std::forward<F>(f)), _n(n)
{}
};
} // namespace uni
#line 9 "graph/centroid_decomposition.hpp"
namespace uni {
// Thanks to: https://qiita.com/drken/items/4b4c3f1824339b090202
template<class Graph = graph<>>
struct centroid_decomposition {
using size_type = internal::size_t;
std::vector<size_type> centroids;
private:
const Graph& graph;
std::vector<size_type> _size, _parent;
std::vector<bool> _used;
public:
centroid_decomposition(const Graph& _graph) noexcept(NO_EXCEPT)
: graph(_graph),
_size(graph.vertices()), _parent(graph.vertices()), _used(graph.vertices())
{}
inline const auto& sizes() const noexcept(NO_EXCEPT) { return this->_size; }
inline const auto& parents() const noexcept(NO_EXCEPT) { return this->_parent; }
inline const auto& used() const noexcept(NO_EXCEPT) { return this->_used; }
inline size_type size(const size_type v) const noexcept(NO_EXCEPT) {
assert(0 <= v && v < this->graph.vertices());
return this->_size[v];
}
inline size_type parent(const size_type v) const noexcept(NO_EXCEPT) {
assert(0 <= v && v < this->graph.vertices());
return this->_parent[v];
}
inline bool used(const size_type v) const noexcept(NO_EXCEPT) {
assert(0 <= v && v < this->graph.vertices());
return this->_used[v];
}
const std::vector<size_type>& find(const size_type v, const size_type sz, const size_type p = -1) noexcept(NO_EXCEPT) {
assert(not this->_used[v]);
this->_size[v] = 1, this->_parent[v] = p;
bool found = true;
ITR(e, this->graph[v]) {
if(e.to == p) continue;
if(this->_used[e.to]) continue;
this->find(e.to, sz, v);
if(this->_size[e.to] > sz / 2) found = false;
this->_size[v] += this->_size[e.to];
}
if(sz - this->_size[v] > sz / 2) found = false;
if(found) this->centroids.push_back(v);
return this->centroids;
}
auto decompose(const size_type root, const size_type sz) noexcept(NO_EXCEPT) {
assert(not this->_used[root]);
std::vector<std::pair<size_type,size_type>> subtrees;
this->centroids.clear();
this->find(root, sz);
const size_type centroid = this->centroids[0];
this->_used[centroid] = true;
ITR(e, this->graph[centroid]) {
if(this->_used[e.to]) continue;
if(e.to == this->_parent[centroid]) {
subtrees.emplace_back(e.to, sz - this->_size[centroid]);
}
else {
subtrees.emplace_back(e.to, this->_size[e.to]);
}
}
return std::make_pair(centroid, subtrees);
}
auto decompose(const size_type root = 0) noexcept(NO_EXCEPT) {
return this->decompose(root, this->graph.vertices());
}
};
} // namespace uni
#line 2 "graph/centroid_path_decomposition.hpp"
#line 7 "graph/centroid_path_decomposition.hpp"
#line 9 "graph/centroid_path_decomposition.hpp"
#line 12 "graph/centroid_path_decomposition.hpp"
#line 14 "graph/centroid_path_decomposition.hpp"
namespace uni {
// Thanks to: https://kazuma8128.hatenablog.com/entry/2018/07/16/010500#fn-96e76557
class centroid_path_decomposition {
using size_type = internal::size_t;
private:
std::vector<std::vector<size_type>> graph;
public:
std::vector<size_type> in, out, size, head, parent;
private:
size_type _cur = 0;
void _erase_parent(const size_type v, const size_type p) noexcept(NO_EXCEPT) {
this->parent[v] = p;
ITRR(nv, graph[v]) {
if(nv == this->graph[v].back()) break;
if(nv == p) std::swap(nv, this->graph[v].back());
this->_erase_parent(nv, v);
}
this->graph[v].pop_back();
}
void _race_size(const size_type v) noexcept(NO_EXCEPT) {
ITRR(nv, this->graph[v]) {
this->_race_size(nv);
this->size[v] += this->size[nv];
if(this->size[nv] > this->size[this->graph[v].front()]) std::swap(nv, this->graph[v].front());
}
}
void _race_path(const size_type v) noexcept(NO_EXCEPT) {
this->in[v] = this->_cur++;
ITR(nv, this->graph[v]) {
this->head[nv] = (nv == this->graph[v].front() ? this->head[v] : nv);
this->_race_path(nv);
}
this->out[v] = this->_cur;
}
public:
template<class Graph>
centroid_path_decomposition(const Graph& _graph, const size_type root = 0) noexcept(NO_EXCEPT)
: graph(_graph.size()), in(_graph.size(), -1), out(_graph.size(), -1), size(_graph.size(), 1), head(_graph.size()), parent(_graph.size(), -1)
{
REP(v, _graph.size()) ITR(nv, _graph[v]) { this->graph[v].push_back(nv); }
this->build(root);
}
void build(const size_type root = 0) noexcept(NO_EXCEPT) {
ITR(v, this->graph[root]) this->_erase_parent(v, root);
this->_race_size(root);
this->head[root] = root;
this->_race_path(root);
}
size_type id(const size_type v) noexcept(NO_EXCEPT) { return this->in[v]; }
size_type lca(size_type u, size_type v) const noexcept(NO_EXCEPT) {
while(true) {
if(this->in[u] > this->in[v]) std::swap(u, v);
if(this->head[u] == this->head[v]) return u;
v = this->parent[this->head[v]];
}
}
template<class F>
void edges_on_path(size_type u, size_type v, F&& f) noexcept(NO_EXCEPT) {
while(true) {
if(this->in[u] > this->in[v]) std::swap(u, v);
if(this->head[u] != this->head[v]) {
f(this->in[this->head[v]] - 1, this->in[v]);
v = this->parent[this->head[v]];
} else {
if(u != v) f(this->in[u], this->in[v]);
break;
}
}
}
template<class F>
void nodes_on_path(size_type u, size_type v, F&& f) noexcept(NO_EXCEPT) {
while (true) {
if (this->in[u] > this->in[v]) std::swap(u, v);
f(std::max(this->in[this->head[v]], this->in[u]), this->in[v]);
if (this->head[u] != this->head[v])
v = this->parent[this->head[v]];
else {
break;
}
}
}
template<class F>
void subtree(const size_type v, F&& f) noexcept(NO_EXCEPT) { f(this->in[v], this->out[v]); }
};
} // namespace uni
#line 2 "graph/connected_components.hpp"
#line 5 "graph/connected_components.hpp"
#line 7 "graph/connected_components.hpp"
#line 11 "graph/connected_components.hpp"
template<class Graph>
uni::disjoint_set uni::internal::graph_impl::mixin<Graph>::components() const noexcept(NO_EXCEPT) {
uni::disjoint_set disjoint_set(this->vertices());
ITR(edges, *this) ITR(_id, u, v, _w, _idx, edges) {
disjoint_set.merge(u, v);
}
return disjoint_set;
}
#line 2 "graph/is_bipartite.hpp"
#line 6 "graph/is_bipartite.hpp"
#line 8 "graph/is_bipartite.hpp"
#line 11 "graph/is_bipartite.hpp"
template<class Graph>
bool uni::internal::graph_impl::mixin<Graph>::is_bipartite() const noexcept(NO_EXCEPT) {
valarray<std::int8_t> color(0, this->vertices());
this->is_bipartite(&color);
return true;
}
template<class Graph>
template<class Colors>
bool uni::internal::graph_impl::mixin<Graph>::is_bipartite(Colors *const color) const noexcept(NO_EXCEPT) {
color->assign(this->vertices(), 0);
REP(s, this->vertices()) {
if(color->operator[](s) != 0) continue;
std::stack<size_type> stack;
stack.push(s);
color->operator[](s) = 1;
while(not stack.empty()) {
auto v = stack.top(); stack.pop();
auto c = color->operator[](v);
ITR(nv, this->operator[](v)) {
if(color->operator[](nv) == c) return false;
if(color->operator[](nv) == 0) {
color->operator[](nv) = -c;
stack.push(nv);
}
}
}
}
return true;
}
#line 2 "graph/lowest_common_ancestor.hpp"
#line 5 "graph/lowest_common_ancestor.hpp"
#line 8 "graph/lowest_common_ancestor.hpp"
#line 11 "graph/lowest_common_ancestor.hpp"
#line 14 "graph/lowest_common_ancestor.hpp"
#line 16 "graph/lowest_common_ancestor.hpp"
namespace uni {
template<class Graph>
struct lowest_common_ancestor {
using size_type = internal::size_t;
using graph_type = Graph;
using edge_type = typename graph_type::edge_type;
using cost_type = typename graph_type::cost_type;
valarray<valarray<size_type>> parent;
valarray<size_type> depth;
valarray<cost_type> cost;
private:
void dfs(const graph_type &G, const edge_type& e) noexcept(NO_EXCEPT) {
this->parent[0][e.to] = e.from;
if(e.from >= 0) {
this->depth[e.to] = this->depth[e.from] + 1;
this->cost[e.to] = this->cost[e.from] + e.cost;
}
ITR(f, G[e.to]) {
if(f.to != e.from) dfs(G, f);
}
}
public:
lowest_common_ancestor(const graph_type &G, const size_type root = 0) noexcept(NO_EXCEPT) { this->init(G, root); }
void init(const graph_type &G, const size_type root = 0) noexcept(NO_EXCEPT) {
const size_type n = static_cast<size_type>(G.size());
const size_type d = std::bit_width<std::make_unsigned_t<size_type>>(n);
this->parent.assign(d, valarray<size_type>(n, -1));
this->depth.assign(n, 0), this->cost.assign(n, 0);
this->dfs(G, edge_type(-1, root, 0));
REP(k, d-1) REP(v, n) {
if(this->parent[k][v] < 0) this->parent[k+1][v] = -1;
else this->parent[k+1][v] = this->parent[k][this->parent[k][v]];
}
}
size_type operator()(const size_type u, const size_type v) const noexcept(NO_EXCEPT) {
return this->find(u, v);
}
size_type find(size_type u, size_type v) const noexcept(NO_EXCEPT) {
if(this->depth[u] < this->depth[v]) std::swap(u, v);
size_type d = static_cast<size_type>(this->parent.size());
REP(k, d) {
if((this->depth[u] - this->depth[v]) >> k & 1) u = this->parent[k][u];
}
if(u == v) return u;
REPD(k, d) {
if(this->parent[k][u] != this->parent[k][v]) {
u = this->parent[k][u];
v = this->parent[k][v];
}
}
return this->parent[0][u];
}
size_type path_length(const size_type u, const size_type v) const noexcept(NO_EXCEPT) {
return this->depth[u] + this->depth[v] - 2 * this->depth[find(u, v)];
}
size_type distance(const size_type u, const size_type v) const noexcept(NO_EXCEPT) {
return this->cost[u] + this->cost[v] - 2 * this->cost[find(u, v)];
}
};
} // namespace uni
#line 2 "graph/manhattan_minimum_spanning_tree.hpp"
#line 9 "graph/manhattan_minimum_spanning_tree.hpp"
#line 12 "graph/manhattan_minimum_spanning_tree.hpp"
#line 15 "graph/manhattan_minimum_spanning_tree.hpp"
#line 17 "graph/manhattan_minimum_spanning_tree.hpp"
#line 19 "graph/manhattan_minimum_spanning_tree.hpp"
#line 2 "graph/spanning_tree.hpp"
#line 6 "graph/spanning_tree.hpp"
#line 8 "graph/spanning_tree.hpp"
namespace uni {
namespace internal {
namespace graph_impl {
template<class G, template<class...> class Compare, class Cost, class Size>
std::optional<Cost> kruskal(const G& graph, const Compare<std::tuple<Cost, Size, Size>> compare, G *const mst = nullptr) noexcept(NO_EXCEPT) {
disjoint_set ds(graph.size());
std::vector<std::tuple<Cost, Size, Size>> edges;
REP(u, graph.size()) ITR(e, graph[u]) {
edges.emplace_back(e.cost, u, e.to);
}
std::ranges::sort(edges, compare);
if(mst) mst->clear(), mst->resize(graph.size());
Cost res = 0;
typename G::size_type cnt = 0;
ITR(w, u, v, edges) {
if(not ds.same(u, v)) {
ds.merge(u, v);
if(mst) mst->add_edge_bidirectionally(u, v, w);
res += w;
++cnt;
}
}
assert(cnt <= graph.size() - 1);
if(cnt != graph.size() - 1) return {};
return res;
}
} // namespace graph_impl
} // namespace internal
} // namespace uni
template<class Graph>
inline auto uni::internal::graph_impl::mixin<Graph>::minimum_spanning_tree(internal::graph_impl::mixin<Graph> *const mst) const noexcept(NO_EXCEPT) {
return
uni::internal::graph_impl::kruskal<
uni::internal::graph_impl::mixin<Graph>,
std::less, cost_type, size_type
>(*this, {}, mst);
}
template<class Graph>
inline auto uni::internal::graph_impl::mixin<Graph>::maximum_spanning_tree(internal::graph_impl::mixin<Graph> *const mst) const noexcept(NO_EXCEPT) {
return
uni::internal::graph_impl::kruskal<
uni::internal::graph_impl::mixin<Graph>,
std::less, cost_type, size_type
>(*this, {}, mst);
}
#line 22 "graph/manhattan_minimum_spanning_tree.hpp"
namespace uni {
// TODO: Vector View
template <
std::input_iterator I0, std::input_iterator I1,
std::sentinel_for<I0> S0, std::sentinel_for<I1> S1
>
auto manhattan_mst_candidate_edges(
I0 x_first, S0 x_last, I1 y_first, S1 y_last
) noexcept(NO_EXCEPT) {
using size_type = internal::size_t;
using cost_type = std::common_type_t<std::iter_value_t<I0>, std::iter_value_t<I1>>;
std::vector<cost_type> xs(x_first, x_last), ys(y_first, y_last);
assert(xs.size() == ys.size());
std::vector<size_type> indices(xs.size());
std::iota(ALL(indices), 0);
vector<std::tuple<size_type, size_type, cost_type>> res;
REP(_0, 2) {
REP(_1, 2) {
std::ranges::sort(indices, [&](const auto i, const auto j) { return xs[i] + ys[i] < xs[j] + ys[j]; });
std::map<cost_type,size_type> scan;
ITR(i, indices) {
for(auto itr = scan.lower_bound(-ys[i]); itr!=scan.end(); itr=scan.erase(itr)) {
const auto j = itr->second;
if(xs[i] - xs[j] < ys[i] - ys[j]) break;
res.emplace_back(i, j, std::abs(xs[i] - xs[j]) + std::abs(ys[i] - ys[j]));
}
scan[-ys[i]] = i;
}
std::swap(xs, ys);
}
ITRR(x, xs) x *= -1;
}
std::ranges::sort(res, [&](const auto& p, const auto& q) { return std::get<2>(p) < std::get<2>(q); });
return res;
}
template <
std::input_iterator I0, std::input_iterator I1,
std::sentinel_for<I0> S0, std::sentinel_for<I1> S1
>
auto manhattan_mst_edges(
I0 x_first, S0 x_last, I1 y_first, S1 y_last,
std::common_type_t<std::iter_value_t<I0>, std::iter_value_t<I1>> *const cost_sum = nullptr
) noexcept(NO_EXCEPT) {
using cost_type = std::common_type_t<std::iter_value_t<I0>, std::iter_value_t<I1>>;
using size_type = internal::size_t;
assert(std::ranges::distance(x_first, x_last) == std::ranges::distance(y_first, y_last));
if(cost_sum) *cost_sum = 0;
vector<std::tuple<size_type, size_type, cost_type>> res;
disjoint_set uf(std::ranges::distance(x_first, x_last));
ITR(u, v, w, (manhattan_mst_candidate_edges<I0,I1>(x_first, x_last, y_first, y_last))) {
if(not uf.same(u, v)) {
uf.merge(u, v);
res.emplace_back(u, v, w);
if(cost_sum) *cost_sum += w;
}
}
return res;
}
template<class Graph>
template<
std::input_iterator I0, std::input_iterator I1,
std::sentinel_for<I0> S0, std::sentinel_for<I1> S1
>
typename Graph::cost_type internal::graph_impl::mixin<Graph>::build_manhattan_mst(
I0 x_first, S0 x_last, I1 y_first, S1 y_last
) noexcept(NO_EXCEPT)
{
assert(std::ranges::distance(x_first, x_last) == std::ranges::distance(y_first, y_last));
cost_type res = 0;
const auto edges = manhattan_mst_edges<I0, I1, S0, S1>(x_first, x_last, y_first, y_last);
ITR(u, v, w, edges) {
this->add_edge_bidirectionally(u, v, w);
}
return res;
}
} // namespace uni
#line 2 "graph/maximum_bipartite_matching.hpp"
#include <atcoder/maxflow>
#line 9 "graph/maximum_bipartite_matching.hpp"
#line 12 "graph/maximum_bipartite_matching.hpp"
#line 14 "graph/maximum_bipartite_matching.hpp"
namespace uni {
struct maximum_bipartite_matching {
// using size_type = internal::size_t;
using size_type = int;
protected:
using MF = atcoder::mf_graph<size_type>;
size_type _m, _n, _s, _edges = 0;
MF _mf;
public:
explicit maximum_bipartite_matching(const size_type n) noexcept(NO_EXCEPT) : maximum_bipartite_matching(n, n) {}
maximum_bipartite_matching(const size_type m, const size_type n) noexcept(NO_EXCEPT)
: _m(m), _n(n), _s(m + n), _mf(m + n + 2)
{
REP(i, m) {
this->_mf.add_edge(this->_s, i, 1);
}
REP(i, n) {
this->_mf.add_edge(m + i, this->_s + 1, 1);
}
}
inline auto& add(const size_type i, const size_type j) noexcept(NO_EXCEPT) {
assert(0 <= i && i < this->_m);
assert(0 <= j && j < this->_n);
this->_mf.add_edge(i, this->_m + j, 1);
++this->_edges;
return *this;
}
inline size_type max_matched() noexcept(NO_EXCEPT) {
return this->_mf.flow(this->_s, this->_s + 1);
}
inline auto get_matching() noexcept(NO_EXCEPT) {
this->max_matched();
vector<spair<size_type>> res;
REP(i, this->_edges) {
const auto edge = this->_mf.get_edge(this->_s + i);
if(edge.flow == 0) continue;
res.emplace_back(edge.from, edge.to - this->_m);
}
return res;
}
};
} // namespace uni
#line 2 "graph/minimum_paph_cover.hpp"
#line 5 "graph/minimum_paph_cover.hpp"
#line 8 "graph/minimum_paph_cover.hpp"
#line 11 "graph/minimum_paph_cover.hpp"
template<class Graph>
typename uni::internal::graph_impl::mixin<Graph>::size_type uni::internal::graph_impl::mixin<Graph>::minimum_paph_cover_size_as_dag() const noexcept(NO_EXCEPT) {
uni::maximum_bipartite_matching bm(this->size());
REP(i, this->size()) ITR(j, (*this)[i]) {
bm.add(i, j.to);
}
return this->size() - bm.max_matched();
}
#line 2 "graph/parse_grid.hpp"
#line 4 "graph/parse_grid.hpp"
#line 7 "graph/parse_grid.hpp"
template<class Graph>
template<bool REV, class G, class U>
void uni::internal::graph_impl::mixin<Graph>::parse_grid(const G &grid, U available) noexcept(NO_EXCEPT) {
this->clear();
this->resize(grid.height() * grid.width());
REP(i, grid.height()) REP(j, grid.width()) {
if(REV ^ (grid(i, j) != available)) continue;
if(i+1 < grid.height() and (REV ^ (grid(i+1, j) == available))) {
this->template add_edge_bidirectionally(grid.id(i, j), grid.id(i+1, j));
}
if(j+1 < grid.width() and (REV ^ (grid(i, j+1) == available))) {
this->template add_edge_bidirectionally(grid.id(i, j), grid.id(i, j+1));
}
}
}
#line 2 "graph/reachability_test.hpp"
#line 6 "graph/reachability_test.hpp"
#line 10 "graph/reachability_test.hpp"
#line 12 "graph/reachability_test.hpp"
#line 2 "graph/topological_sort.hpp"
#line 6 "graph/topological_sort.hpp"
#line 10 "graph/topological_sort.hpp"
template<class Graph>
template<class comparer>
bool uni::internal::graph_impl::mixin<Graph>::sort_topologically_with_priority(uni::vector<node_type> *const sorted) const noexcept(NO_EXCEPT) {
sorted->clear();
std::vector<size_type> in_degs(this->size());
ITR(v, *this) ITR(e, v) ++in_degs[e.to];
std::priority_queue<node_type,std::vector<node_type>,comparer> que;
REP(i, this->size()) if(in_degs[i] == 0) que.push(i);
while(not que.empty()) {
const node_type v = que.top(); que.pop();
ITR(u, (*this)[v]) if(!(--in_degs[u.to])) que.push(u.to);
sorted->push_back(v);
}
return std::ranges::ssize(*sorted) == std::ranges::ssize(*this);
}
template<class Graph>
template<class comparer>
bool uni::internal::graph_impl::mixin<Graph>::sort_topologically_with_priority() const noexcept(NO_EXCEPT) {
uni::vector<node_type> vs;
return this->sort_topologically_with_priority<comparer>(&vs);
}
template<class Graph>
bool uni::internal::graph_impl::mixin<Graph>::sort_topologically(uni::vector<node_type> *const sorted) const noexcept(NO_EXCEPT) {
sorted->clear();
std::vector<size_type> in_degs(this->size());
ITR(v, *this) ITR(e, v) ++in_degs[e.to];
std::queue<node_type> que;
REP(i, this->size()) if(in_degs[i] == 0) que.push(i);
while(not que.empty()) {
const node_type v = que.front(); que.pop();
ITR(u, (*this)[v]) if(!(--in_degs[u.to])) que.push(u.to);
sorted->push_back(v);
}
return std::ranges::ssize(*sorted) == std::ranges::ssize(*this);
}
template<class Graph>
bool uni::internal::graph_impl::mixin<Graph>::sort_topologically() const noexcept(NO_EXCEPT) {
std::vector<node_type> vs;
return this->sort_topologically(&vs);
}
#line 15 "graph/reachability_test.hpp"
#line 2 "view/chunk.hpp"
#line 6 "view/chunk.hpp"
#line 9 "view/chunk.hpp"
#line 11 "view/chunk.hpp"
namespace uni {
template<std::ranges::view View>
requires std::ranges::input_range<View>
struct chunk_view : std::ranges::view_interface<chunk_view<View>> {
private:
View _base;
std::ranges::range_difference_t<View> _n;
std::ranges::range_difference_t<View> _remainder = 0;
std::optional<std::ranges::iterator_t<View>> _current;
struct outer_iterator;
struct inner_iterator;
public:
constexpr explicit chunk_view(View base, std::ranges::range_difference_t<View> n)
: _base(std::move(base)), _n(n) {
assert(n >= 0);
}
constexpr View base() const &
requires std::copy_constructible<View>
{
return this->_base;
}
constexpr View base() && { return std::move(this->_base); }
constexpr outer_iterator begin() {
this->_current = std::ranges::begin(this->_base);
this->_remainder = this->_n;
return outer_iterator(*this);
}
constexpr std::default_sentinel_t end() const noexcept {
return std::default_sentinel;
}
constexpr auto size()
requires std::ranges::sized_range<View>
{
return to_unsigned(div_ceil(std::ranges::distance(this->_base), this->_n));
}
constexpr auto size() const
requires std::ranges::sized_range<const View>
{
return to_unsigned(div_ceil(std::ranges::distance(this->_base), this->_n));
}
};
template<class Range>
chunk_view(Range&&, std::ranges::range_difference_t<Range>) -> chunk_view<std::views::all_t<Range>>;
template<std::ranges::view View>
requires std::ranges::input_range<View>
struct chunk_view<View>::outer_iterator {
private:
chunk_view *_parent;
constexpr explicit outer_iterator(chunk_view &parent) noexcept
: _parent(std::addressof(parent))
{}
friend chunk_view;
public:
using iterator_concept = std::input_iterator_tag;
using difference_type = std::ranges::range_difference_t<View>;
struct value_type;
outer_iterator(outer_iterator &&) = default;
outer_iterator &operator=(outer_iterator &&) = default;
constexpr value_type operator*() const {
assert(*this != std::default_sentinel);
return value_type(*this->_parent);
}
constexpr outer_iterator &operator++() {
assert(*this != std::default_sentinel);
std::ranges::advance(*this->_parent->_current, this->_parent->_remainder, std::ranges::end(this->_parent->_base));
this->_parent->_remainder = this->_parent->_n;
return *this;
}
constexpr void operator++(int) { ++*this; }
friend constexpr bool operator==(const outer_iterator &lhs, std::default_sentinel_t) {
return *lhs._parent->_current == std::ranges::end(lhs._parent->_base) && lhs._parent->_remainder != 0;
}
friend constexpr difference_type operator-(std::default_sentinel_t, const outer_iterator &rhs)
requires std::sized_sentinel_for<std::ranges::sentinel_t<View>, std::ranges::iterator_t<View>>
{
const auto dist = std::ranges::end(rhs._parent->_base) - *rhs._parent->_current;
if(dist < rhs._parent->_remainder) return dist == 0 ? 0 : 1;
return 1 + div_ceil(dist - rhs._parent->_remainder, rhs._parent->_n);
}
friend constexpr difference_type operator-(const outer_iterator &lhs, std::default_sentinel_t rhs)
requires std::sized_sentinel_for<std::ranges::sentinel_t<View>, std::ranges::iterator_t<View>>
{
return -(rhs - lhs);
}
};
template<std::ranges::view View>
requires std::ranges::input_range<View>
struct chunk_view<View>::outer_iterator::value_type : std::ranges::view_interface<value_type> {
private:
chunk_view *_parent;
constexpr explicit value_type(chunk_view &parent) noexcept
: _parent(std::addressof(parent))
{}
friend outer_iterator;
public:
constexpr inner_iterator begin() const noexcept {
return inner_iterator(*this->_parent);
}
constexpr std::default_sentinel_t end() const noexcept {
return std::default_sentinel;
}
constexpr auto size() const
requires std::sized_sentinel_for<std::ranges::sentinel_t<View>, std::ranges::iterator_t<View>>
{
return to_unsigned(std::ranges::min(this->_parent->_remainder, std::ranges::end(this->_parent->_base) - *this->_parent->_current));
}
};
template<std::ranges::view View>
requires std::ranges::input_range<View>
struct chunk_view<View>::inner_iterator {
private:
chunk_view *_parent;
constexpr explicit inner_iterator(chunk_view &parent) noexcept
: _parent(std::addressof(parent))
{}
friend outer_iterator::value_type;
public:
using iterator_concept = std::input_iterator_tag;
using difference_type = std::ranges::range_difference_t<View>;
using value_type = std::ranges::range_value_t<View>;
inner_iterator(inner_iterator &&) = default;
inner_iterator &operator=(inner_iterator &&) = default;
constexpr const std::ranges::iterator_t<View> &base() const & {
return *this->_parent->_current;
}
constexpr std::ranges::range_reference_t<View> operator*() const {
assert(*this != std::default_sentinel);
return **this->_parent->_current;
}
constexpr inner_iterator &operator++() {
assert(*this != std::default_sentinel);
++*this->_parent->_current;
if(*this->_parent->_current == std::ranges::end(this->_parent->_base)) {
this->_parent->_remainder = 0;
}
else {
--this->_parent->_remainder;
}
return *this;
}
constexpr void operator++(int) { ++*this; }
friend constexpr bool operator==(const inner_iterator &lhs, std::default_sentinel_t) noexcept {
return lhs._parent->_remainder == 0;
}
friend constexpr difference_type operator-(std::default_sentinel_t, const inner_iterator &rhs)
requires std::sized_sentinel_for<std::ranges::sentinel_t<View>, std::ranges::iterator_t<View>>
{
return std::ranges::min(rhs._parent->_remainder, std::ranges::end(rhs._parent->_base) - *rhs._parent->_current);
}
friend constexpr difference_type operator-(const inner_iterator &lhs, std::default_sentinel_t rhs)
requires std::sized_sentinel_for<std::ranges::sentinel_t<View>, std::ranges::iterator_t<View>>
{
return -(rhs - lhs);
}
};
template<std::ranges::view View>
requires std::ranges::forward_range<View>
struct chunk_view<View> : std::ranges::view_interface<chunk_view<View>> {
private:
View _base;
std::ranges::range_difference_t<View> _n;
template<bool> struct iterator;
public:
constexpr explicit chunk_view(View base, const std::ranges::range_difference_t<View> n)
: _base(std::move(base)), _n(n)
{
assert(n > 0);
}
constexpr View base() const &
requires std::copy_constructible<View>
{
return this->_base;
}
constexpr View base() && { return std::move(this->_base); }
constexpr auto begin()
requires(!internal::simple_view<View>)
{
return iterator<false>(this, std::ranges::begin(this->_base));
}
constexpr auto begin() const
requires std::ranges::forward_range<const View>
{
return iterator<true>(this, std::ranges::begin(this->_base));
}
constexpr auto end()
requires(!internal::simple_view<View>)
{
if constexpr(std::ranges::common_range<View> && std::ranges::sized_range<View>) {
const auto missing = (this->_n - std::ranges::distance(this->_base) % this->_n) % this->_n;
return iterator<false>(this, std::ranges::end(this->_base), missing);
}
else if constexpr(std::ranges::common_range<View> && !std::ranges::bidirectional_range<View>) {
return iterator<false>(this, std::ranges::end(this->_base));
}
else {
return std::default_sentinel;
}
}
constexpr auto end() const
requires std::ranges::forward_range<const View>
{
if constexpr(std::ranges::common_range<const View> && std::ranges::sized_range<const View>) {
auto missing = (this->_n - std::ranges::distance(this->_base) % this->_n) % this->_n;
return iterator<true>(this, std::ranges::end(this->_base), missing);
} else if constexpr(std::ranges::common_range<const View> && !std::ranges::bidirectional_range<const View>) {
return iterator<true>(this, std::ranges::end(this->_base));
}
else {
return std::default_sentinel;
}
}
constexpr auto size()
requires std::ranges::sized_range<View>
{
return to_unsigned(div_ceil(std::ranges::distance(this->_base), this->_n));
}
constexpr auto size() const
requires std::ranges::sized_range<const View>
{
return to_unsigned(div_ceil(std::ranges::distance(this->_base), this->_n));
}
};
template<std::ranges::view View>
requires std::ranges::forward_range<View>
template<bool CONST>
struct chunk_view<View>::iterator {
private:
using Parent = internal::maybe_const_t<CONST, chunk_view>;
using Base = internal::maybe_const_t<CONST, View>;
std::ranges::iterator_t<Base> _current = std::ranges::iterator_t<Base>();
std::ranges::sentinel_t<Base> _end = std::ranges::sentinel_t<Base>();
std::ranges::range_difference_t<Base> _n = 0;
std::ranges::range_difference_t<Base> _missing = 0;
constexpr iterator(Parent *parent, std::ranges::iterator_t<Base> current, const std::ranges::range_difference_t<Base> missing = 0)
: _current(current), _end(std::ranges::end(parent->_base)), _n(parent->_n), _missing(missing)
{}
friend chunk_view;
public:
using iterator_category = std::input_iterator_tag;
using iterator_concept = internal::most_primitive_iterator_concept<false, Base>;
using value_type = decltype(std::views::take(std::ranges::subrange(_current, _end), _n));
using difference_type = std::ranges::range_difference_t<Base>;
iterator() = default;
constexpr iterator(iterator<!CONST> itr)
requires
CONST &&
std::convertible_to<std::ranges::iterator_t<View>, std::ranges::iterator_t<Base>> &&
std::convertible_to<std::ranges::sentinel_t<View>, std::ranges::sentinel_t<Base>>
: _current(std::move(itr._current)), _end(std::move(itr._end)), _n(itr._n), _missing(itr._missing)
{}
constexpr std::ranges::iterator_t<Base> base() const { return this->_current; }
constexpr value_type operator*() const {
assert(this->_current != this->_end);
return std::views::take(std::ranges::subrange(this->_current, this->_end), this->_n);
}
constexpr iterator &operator++() {
assert(this->_current != this->_end);
this->_missing = std::ranges::advance(this->_current, this->_n, this->_end);
return *this;
}
constexpr iterator operator++(int) {
auto temp = *this;
return ++*this, temp;
}
constexpr iterator &operator--()
requires std::ranges::bidirectional_range<Base>
{
std::ranges::advance(this->_current, this->_missing - this->_n);
this->_missing = 0;
return *this;
}
constexpr iterator operator--(int)
requires std::ranges::bidirectional_range<Base>
{
auto temp = *this;
return --*this, temp;
}
constexpr iterator &operator+=(difference_type lhs)
requires std::ranges::random_access_range<Base>
{
if(lhs > 0) {
assert(std::ranges::distance(this->_current, this->_end) > this->_n * (lhs - 1));
this->_missing = std::ranges::advance(this->_current, this->_n * lhs, this->_end);
}
else if(lhs < 0) {
std::ranges::advance(this->_current, this->_n * lhs + this->_missing);
this->_missing = 0;
}
return *this;
}
constexpr iterator &operator-=(difference_type lhs)
requires std::ranges::random_access_range<Base>
{
return *this += -lhs;
}
constexpr value_type operator[](difference_type n) const
requires std::ranges::random_access_range<Base>
{
return *(*this + n);
}
friend constexpr bool operator==(const iterator &lhs, const iterator &rhs) {
return lhs._current == rhs._current;
}
friend constexpr bool operator==(const iterator &lhs, std::default_sentinel_t) {
return lhs._current == lhs._end;
}
friend constexpr bool operator<(const iterator &lhs, const iterator &rhs)
requires std::ranges::random_access_range<Base>
{
return lhs._current > rhs._current;
}
friend constexpr bool operator>(const iterator &lhs, const iterator &rhs)
requires std::ranges::random_access_range<Base>
{
return rhs < lhs;
}
friend constexpr bool operator<=(const iterator &lhs, const iterator &rhs)
requires std::ranges::random_access_range<Base>
{
return !(rhs < lhs);
}
friend constexpr bool operator>=(const iterator &lhs, const iterator &rhs)
requires std::ranges::random_access_range<Base>
{
return !(lhs < rhs);
}
friend constexpr auto operator<=>(const iterator &lhs, const iterator &rhs)
requires std::ranges::random_access_range<Base> && std::three_way_comparable<std::ranges::iterator_t<Base>>
{
return lhs._current <=> rhs._current;
}
friend constexpr iterator operator+(const iterator &itr, const difference_type count)
requires std::ranges::random_access_range<Base>
{
auto res = itr;
return res += count, res;
}
friend constexpr iterator operator+(const difference_type count, const iterator &itr)
requires std::ranges::random_access_range<Base>
{
auto res = itr;
return res += count, res;
}
friend constexpr iterator operator-(const iterator &itr, const difference_type count)
requires std::ranges::random_access_range<Base>
{
auto res = itr;
return res -= count, res;
}
friend constexpr difference_type operator-(const iterator &lhs, const iterator &rhs)
requires std::sized_sentinel_for<std::ranges::iterator_t<Base>, std::ranges::iterator_t<Base>>
{
return (lhs._current - rhs._current + lhs._missing - rhs._missing) / lhs._n;
}
friend constexpr difference_type operator-(std::default_sentinel_t rhs, const iterator &lhs)
requires std::sized_sentinel_for<std::ranges::sentinel_t<Base>, std::ranges::iterator_t<Base>>
{
return div_ceil(lhs._end - lhs._current, lhs._n);
}
friend constexpr difference_type operator-(const iterator &lhs, std::default_sentinel_t rhs)
requires std::sized_sentinel_for<std::ranges::sentinel_t<Base>, std::ranges::iterator_t<Base>>
{
return -(rhs - lhs);
}
};
namespace views {
namespace internal {
template<class Range, typename Diff>
concept can_chunk_view = requires { chunk_view(std::declval<Range>(), std::declval<Diff>()); };
} // namespace internal
struct Chunk : adaptor::range_adaptor<Chunk> {
template<std::ranges::viewable_range Range, class Diff = std::ranges::range_difference_t<Range>>
requires internal::can_chunk_view<Range, Diff>
constexpr auto operator() [[nodiscard]] (Range &&res, std::type_identity_t<Diff> n) const {
return chunk_view(std::forward<Range>(res), n);
}
using adaptor::range_adaptor<Chunk>::operator();
static constexpr int arity = 2;
static constexpr bool has_simple_extra_args = true;
};
inline constexpr Chunk chunk;
} // namespace views
} // namespace uni
namespace std::ranges {
template<class View>
inline constexpr bool enable_borrowed_range<uni::chunk_view<View>> = forward_range<View> && enable_borrowed_range<View>;
} // namespace std::ranges
#line 2 "view/enumerate.hpp"
#line 6 "view/enumerate.hpp"
#line 10 "view/enumerate.hpp"
namespace uni {
namespace internal {
template<class Range>
concept range_with_movable_reference =
std::ranges::input_range<Range> && std::move_constructible<std::ranges::range_reference_t<Range>> &&
std::move_constructible<std::ranges::range_rvalue_reference_t<Range>>;
} // namespace internal
template<std::ranges::view View>
requires internal::range_with_movable_reference<View>
struct enumerate_view : public std::ranges::view_interface<enumerate_view<View>> {
private:
View _base = View();
template<bool Const> class iterator;
template<bool Const> class sentinel;
public:
enumerate_view()
requires std::default_initializable<View>
= default;
constexpr explicit enumerate_view(View base) : _base(std::move(base)) {}
constexpr auto begin()
requires(!internal::simple_view<View>)
{
return iterator<false>(std::ranges::begin(this->_base), 0);
}
constexpr auto begin() const
requires internal::range_with_movable_reference<const View>
{
return iterator<true>(std::ranges::begin(this->_base), 0);
}
constexpr auto end()
requires(!internal::simple_view<View>)
{
if constexpr(std::ranges::common_range<View> && std::ranges::sized_range<View>) {
return iterator<false>(std::ranges::end(_base), std::ranges::distance(this->_base));
}
else {
return sentinel<false>(std::ranges::end(_base));
}
}
constexpr auto end() const
requires internal::range_with_movable_reference<const View>
{
if constexpr(std::ranges::common_range<const View> && std::ranges::sized_range<const View>) {
return iterator<true>(std::ranges::end(_base), std::ranges::distance(_base));
}
else {
return sentinel<true>(std::ranges::end(_base));
}
}
constexpr auto size()
requires std::ranges::sized_range<View>
{
return std::ranges::size(_base);
}
constexpr auto size() const
requires std::ranges::sized_range<const View>
{
return std::ranges::size(_base);
}
constexpr View base() const &
requires std::copy_constructible<View>
{
return _base;
}
constexpr View base() && { return std::move(_base); }
};
template<class Range>
enumerate_view(Range&& ) -> enumerate_view<std::views::all_t<Range>>;
template<std::ranges::view View>
requires internal::range_with_movable_reference<View>
template<bool Const>
class enumerate_view<View>::iterator {
using Base = internal::maybe_const_t<Const, View>;
friend enumerate_view;
public:
using iterator_category = std::iterator_traits<std::ranges::iterator_t<Base>>::iterator_category;
using iterator_concept = internal::most_primitive_iterator_concept<Const, View>;
using difference_type = std::ranges::range_difference_t<Base>;
using value_type = std::tuple<difference_type, std::ranges::range_value_t<Base>>;
private:
using rangeeference_type = std::tuple<difference_type, std::ranges::range_reference_t<Base>>;
std::ranges::iterator_t<Base> _current = std::ranges::iterator_t<Base>();
difference_type _pos = 0;
constexpr explicit iterator(std::ranges::iterator_t<Base> current, const difference_type pos)
: _current(std::move(current)), _pos(pos)
{}
public:
iterator()
requires std::default_initializable<std::ranges::iterator_t<Base>>
= default;
constexpr iterator(iterator<!Const> itr)
requires Const && std::convertible_to<std::ranges::iterator_t<View>, std::ranges::iterator_t<Base>>
: _current(std::move(itr._current)), _pos(itr._pos)
{}
constexpr const std::ranges::iterator_t<Base>& base() const & noexcept {
return this->_current;
}
constexpr std::ranges::iterator_t<Base> base() && { return std::move(this->_current); }
constexpr difference_type index() const noexcept { return this->_pos; }
constexpr auto operator*() const {
return rangeeference_type(this->_pos, *this->_current);
}
constexpr iterator& operator++() {
++this->_current;
++this->_pos;
return *this;
}
constexpr void operator++(int) { ++*this; }
constexpr iterator operator++(int)
requires std::ranges::forward_range<Base>
{
auto temp = *this;
++*this;
return temp;
}
constexpr iterator& operator--()
requires std::ranges::bidirectional_range<Base>
{
--this->_current;
--this->_pos;
return *this;
}
constexpr iterator operator--(int)
requires std::ranges::bidirectional_range<Base>
{
auto temp = *this;
--*this;
return temp;
}
constexpr iterator& operator+=(const difference_type diff)
requires std::ranges::random_access_range<Base>
{
this->_current += diff;
this->_pos += diff;
return *this;
}
constexpr iterator& operator-=(const difference_type diff)
requires std::ranges::random_access_range<Base>
{
this->_current -= diff;
this->_pos -= diff;
return *this;
}
constexpr auto operator[](const difference_type diff) const
requires std::ranges::random_access_range<Base>
{
return rangeeference_type(this->_pos + diff, this->_current[diff]);
}
friend constexpr bool operator==(const iterator& lhs, const iterator& rhs) noexcept {
return lhs._pos == rhs._pos;
}
friend constexpr std::strong_ordering
operator<=>(const iterator& lhs, const iterator& rhs) noexcept {
return lhs._pos <=> rhs._pos;
}
friend constexpr iterator operator+(iterator lhs, const difference_type rhs)
requires std::ranges::random_access_range<Base>
{
return (lhs += rhs);
}
friend constexpr iterator operator+(const difference_type lhs, const iterator& rhs)
requires std::ranges::random_access_range<Base>
{
return rhs += lhs;
}
friend constexpr iterator operator-(iterator& lhs, const difference_type rhs)
requires std::ranges::random_access_range<Base>
{
return lhs -= rhs;
}
friend constexpr difference_type operator-(const iterator& lhs, const iterator& rhs) {
return lhs._pos - rhs._pos;
}
friend constexpr auto iter_move(const iterator& itr)
noexcept(
noexcept (std::ranges::iter_move(itr._current)) &&
std::is_nothrow_move_constructible_v<std::ranges::range_rvalue_reference_t<Base>>
)
{
return std::tuple<difference_type, std::ranges::range_rvalue_reference_t<Base>>(
itr._pos, std::ranges::iter_move(itr._current)
);
}
};
template<std::ranges::view View>
requires internal::range_with_movable_reference<View>
template<bool Const>
class enumerate_view<View>::sentinel {
using Base = internal::maybe_const_t<Const, View>;
std::ranges::sentinel_t<Base> _end = std::ranges::sentinel_t<Base>();
constexpr explicit sentinel(std::ranges::sentinel_t<Base> end) : _end(std::move(end)) {}
friend enumerate_view;
public:
sentinel() = default;
constexpr sentinel(sentinel<!Const> other)
requires Const && std::convertible_to<std::ranges::sentinel_t<View>, std::ranges::sentinel_t<Base>>
: _end(std::move(other._end)) {}
constexpr std::ranges::sentinel_t<Base> base() const { return this->_end; }
template<bool Const_>
requires
std::sentinel_for<
std::ranges::sentinel_t<Base>, std::ranges::iterator_t<internal::maybe_const_t<Const_, View>>
>
friend constexpr bool operator==(const iterator<Const_>& lhs, const sentinel& rhs) {
return lhs._current == rhs._end;
}
template<bool Const_>
requires
std::sized_sentinel_for<
std::ranges::sentinel_t<Base>, std::ranges::iterator_t<internal::maybe_const_t<Const_, View>>
>
friend constexpr std::ranges::range_difference_t<internal::maybe_const_t<Const_, View>>
operator-(const iterator<Const_>& lhs, const sentinel& rhs) {
return lhs._current - rhs._end;
}
template<bool Const_>
requires std::sized_sentinel_for<
std::ranges::sentinel_t<Base>, std::ranges::iterator_t<internal::maybe_const_t<Const_, View>>>
friend constexpr std::ranges::range_difference_t<internal::maybe_const_t<Const_, View>>
operator-(const sentinel& lhs, const iterator<Const_>& rhs) {
return lhs._end - rhs._current;
}
};
namespace views {
namespace internal {
template<class T>
concept can_enumerate_view =
requires { enumerate_view<std::views::all_t<T>>(std::declval<T>()); };
} // namespace internal
struct Enumerate : adaptor::range_adaptor_closure<Enumerate> {
template<std::ranges::viewable_range Range>
requires internal::can_enumerate_view<Range>
constexpr auto operator() [[nodiscard]] (Range&& range) const {
return enumerate_view<std::views::all_t<Range>>(std::forward<Range>(range));
}
};
inline constexpr Enumerate enumerate;
} // namespace views
} // namespace uni
namespace std::ranges {
template<class T>
inline constexpr bool enable_borrowed_range<uni::enumerate_view<T>> = enable_borrowed_range<T>;
} // namespace std
#line 18 "graph/reachability_test.hpp"
namespace uni {
template<class Graph>
template<std::ranges::sized_range R>
auto uni::internal::graph_impl::mixin<Graph>::test_reachability(R&& queries) const noexcept(NO_EXCEPT) {
using impl_type = u128;
constexpr auto CHUNK_SIZE = std::numeric_limits<impl_type>::digits;
std::vector<bool> res(std::ranges::size(queries));
uni::vector<node_type> vs;
this->sort_topologically(&vs);
debug(queries);
ITR(i, qs, queries | uni::views::chunk(CHUNK_SIZE) | uni::views::enumerate) {
debug(qs);
std::vector<impl_type> bits(this->size());
ITR(j, p, qs | uni::views::enumerate) {
bits[p.first] = uni::set_bit(bits[p.first], j);
}
ITR(v, vs) ITR(nv, this->operator[](v)) {
bits[nv] |= bits[v];
}
ITR(j, p, qs | uni::views::enumerate) {
res[i * CHUNK_SIZE + j] = uni::bit(bits[p.second], j);
}
}
return res;
}
} // namespace uni
#line 2 "graph/shortest_path.hpp"
#line 5 "graph/shortest_path.hpp"
#line 2 "graph/internal/bfs.hpp"
#line 6 "graph/internal/bfs.hpp"
#line 9 "graph/internal/bfs.hpp"
#line 11 "graph/internal/bfs.hpp"
#line 14 "graph/internal/bfs.hpp"
#line 17 "graph/internal/bfs.hpp"
template<class Graph>
template<uni::internal::item_or_convertible_range<typename Graph::node_type> Source, class Dist, class Prev>
void uni::internal::graph_impl::mixin<Graph>::shortest_path_without_cost(
Source&& s, Dist *const dist, Prev *const prev,
const node_type& unreachable, const node_type& root
) const noexcept(NO_EXCEPT) {
dist->assign(this->size(), uni::numeric_limits<cost_type>::arithmetic_infinity());
if constexpr(!std::is_same_v<Prev, std::nullptr_t>) prev->assign(this->size(), unreachable);
std::queue<node_type> que;
if constexpr(std::ranges::range<Source>) {
ITR(v, s) {
que.push(v), dist->operator[](v) = 0;
if constexpr(!std::is_same_v<Prev, std::nullptr_t>) prev->operator[](v) = root;
}
}
else {
que.push(s), dist->operator[](s) = 0;
if constexpr(!std::is_same_v<Prev, std::nullptr_t>) prev->operator[](s) = root;
}
while(!que.empty()) {
const node_type v = que.front(); que.pop();
ITR(nv, this->operator[](v)) {
if(dist->operator[](nv.to) < uni::numeric_limits<cost_type>::arithmetic_infinity()) { continue; }
dist->operator[](nv.to) = dist->operator[](v) + 1;
if constexpr(!std::is_same_v<Prev, std::nullptr_t>) prev->operator[](nv.to) = v;
que.push(nv.to);
}
}
}
template<class Graph>
template<uni::internal::item_or_convertible_range<typename Graph::node_type> Source>
auto uni::internal::graph_impl::mixin<Graph>::shortest_path_without_cost(Source&& s) const noexcept(NO_EXCEPT) {
uni::auto_holder<node_type, cost_type> dist;
this->shortest_path_without_cost(std::forward<Source>(s), &dist);
return dist;
}
#line 2 "graph/internal/01bfs.hpp"
#line 7 "graph/internal/01bfs.hpp"
#line 9 "graph/internal/01bfs.hpp"
#line 12 "graph/internal/01bfs.hpp"
#line 15 "graph/internal/01bfs.hpp"
#line 18 "graph/internal/01bfs.hpp"
template<class Graph>
template<uni::internal::item_or_convertible_range<typename Graph::node_type> Source, class Dist, class Prev>
void uni::internal::graph_impl::mixin<Graph>::shortest_path_with_01cost(
Source&& s, Dist *const dist, Prev *const prev,
const node_type& unreachable, const node_type& root
) const noexcept(NO_EXCEPT) {
std::deque<node_type> que;
dist->assign(this->size(), uni::numeric_limits<cost_type>::arithmetic_infinity());
if constexpr(!std::is_same_v<Prev, std::nullptr_t>) prev->assign(this->size(), unreachable);
if constexpr(std::ranges::range<Source>) {
ITR(v, s) {
que.push_back(v), dist->operator[](v) = 0;
if constexpr(!std::is_same_v<Prev, std::nullptr_t>) prev->operator[](v) = root;
}
}
else {
que.push_back(s), dist->operator[](s) = 0;
if constexpr(!std::is_same_v<Prev, std::nullptr_t>) prev->operator[](s) = root;
}
while(!que.empty()) {
const auto u = que.front(); que.pop_front();
const cost_type d = dist->operator[](u);
ITR(e, (*this)[u]) {
const node_type v = e.to; const auto cost = e.cost;
if(dist->operator[](v) <= d + cost) continue;
dist->operator[](v) = d + cost;
if constexpr(!std::is_same_v<Prev, std::nullptr_t>) prev->operator[](v) = u;
if(cost) que.push_back(v);
else que.push_front(v);
}
}
}
template<class Graph>
template<uni::internal::item_or_convertible_range<typename Graph::node_type> Source>
auto uni::internal::graph_impl::mixin<Graph>::shortest_path_with_01cost(Source&& s) const noexcept(NO_EXCEPT) {
uni::auto_holder<typename uni::internal::graph_impl::mixin<Graph>::node_type, cost_type> dist;
this->shortest_path_with_01cost(std::forward<Source>(s), &dist);
return dist;
}
#line 2 "graph/internal/dijkstra.hpp"
#line 7 "graph/internal/dijkstra.hpp"
#line 9 "graph/internal/dijkstra.hpp"
#line 11 "graph/internal/dijkstra.hpp"
#line 13 "graph/internal/dijkstra.hpp"
#line 16 "graph/internal/dijkstra.hpp"
template<class Graph>
template<uni::internal::item_or_convertible_range<typename Graph::node_type> Source, class Dist, class Prev>
void uni::internal::graph_impl::mixin<Graph>::shortest_path_with_cost(
Source&& s, Dist *const dist, Prev *const prev,
const node_type& unreachable, const node_type& root
) const noexcept(NO_EXCEPT) {
using state = std::pair<cost_type, node_type>;
std::priority_queue<state, std::vector<state>, std::greater<state>> que;
dist->assign(this->size(), uni::numeric_limits<cost_type>::arithmetic_infinity());
if constexpr(!std::same_as<Prev, std::nullptr_t>) prev->assign(this->size(), unreachable);
if constexpr(std::ranges::range<Source>) {
ITR(v, s) {
que.emplace(0, v), dist->operator[](v) = 0;
if constexpr(!std::is_same_v<Prev, std::nullptr_t>) prev->operator[](v) = root;
}
}
else {
que.emplace(0, s), dist->operator[](s) = 0;
if constexpr(!std::is_same_v<Prev, std::nullptr_t>) prev->operator[](s) = root;
}
while(!que.empty()) {
const auto [d, u] = que.top(); que.pop();
if(dist->operator[](u) < d) continue;
ITR(e, this->operator[](u)) {
const node_type v = e.to; const auto next = d + e.cost;
if(dist->operator[](v) <= next) continue;
dist->operator[](v) = next;
if constexpr(!std::same_as<Prev, std::nullptr_t>) prev->operator[](v) = u;
que.emplace(dist->operator[](v), v);
}
}
}
template<class Graph>
template<uni::internal::item_or_convertible_range<typename Graph::node_type> Source>
auto uni::internal::graph_impl::mixin<Graph>::shortest_path_with_cost(Source&& s) const noexcept(NO_EXCEPT) {
uni::auto_holder<node_type, cost_type> dist;
this->shortest_path_with_cost(std::forward<Source>(s), &dist);
return dist;
}
#line 10 "graph/shortest_path.hpp"
#line 12 "graph/shortest_path.hpp"
namespace uni {
template<class Node, class Prev, class Res>
void restore_path(Node back, const Prev& prev, Res *const res) {
res->clear();
while(back >= 0) {
res->emplace_back(back);
back = prev[back];
}
std::ranges::reverse(*res);
}
template<class Node, class Prev, class Res = uni::vector<Node>>
uni::vector<Node> restore_path(Node back, const Prev& prev) {
uni::vector<Node> res;
restore_path(back, prev, &res);
return res;
}
}
#line 2 "graph/tree_diamiter.hpp"
#line 6 "graph/tree_diamiter.hpp"
#line 8 "graph/tree_diamiter.hpp"
namespace uni {
namespace internal {
template<class Graph>
std::pair<typename Graph::cost_type, typename Graph::node_type> farthest(const Graph& tree, const typename Graph::node_type v, const typename Graph::node_type p, std::vector<typename Graph::node_type> *const prev = nullptr) {
std::pair<typename Graph::cost_type, typename Graph::node_type> res = { 0, v };
for(auto nv : tree[v]) {
if(nv.to == p) continue;
auto next = farthest(tree, nv.to, v, prev);
next.first += nv.cost;
if(res.first < next.first) {
if(prev) prev->operator[](nv.to) = v;
res = next;
}
}
return res;
}
} // namespace internal
template<class Graph>
auto tree_diamiter(const Graph& tree, std::vector<typename Graph::node_type> *const prev = nullptr) {
const auto p = farthest(tree, 0, -1);
return farthest(tree, p.second, -1, prev);
}
} // namespace uni
#line 2 "graph/tree_hash.hpp"
#line 6 "graph/tree_hash.hpp"
#line 9 "graph/tree_hash.hpp"
namespace uni {
template<class Graph>
auto tree_centers(const Graph& tree) {
std::vector<typename Graph::node_type> prev(std::ranges::size(tree), -1);
auto [ diam, v ] = tree_diamiter(tree, &prev);
std::vector<typename Graph::node_type> res;
{
for(typename Graph::size_type i = 0; i < diam / 2; ++i) {
v = prev[v];
}
res.push_back(v);
if(diam % 2 == 1) res.push_back(prev[v]);
}
{
auto rest = std::ranges::unique(res);
res.erase(std::ranges::begin(rest), std::ranges::end(rest));
}
return std::make_pair(diam, res);
}
template<class Graph>
std::size_t tree_hash(const Graph& tree, typename Graph::node_type v, typename Graph::node_type p = -1) {
static std::map<std::vector<typename Graph::node_type>, std::size_t> vals;
std::vector<typename Graph::node_type> children;
for(const auto nv : tree[v]) {
if(nv == p) continue;
children.emplace_back(tree_hash(tree, nv, v));
}
std::ranges::sort(children);
if(!vals.contains(children)) {
vals[children] = 0;
vals[children] = std::ranges::size(vals);
}
return vals[children];
}
} // namespace uni
#line 2 "include/hashes.hpp"
#line 2 "hash/multiset_hasher.hpp"
#line 5 "hash/multiset_hasher.hpp"
#line 8 "hash/multiset_hasher.hpp"
#line 11 "hash/multiset_hasher.hpp"
#line 13 "hash/multiset_hasher.hpp"
#line 15 "hash/multiset_hasher.hpp"
namespace uni {
template<class T, std::uint64_t MOD = 0x1fffffffffffffff, int hasher_id = -1>
requires (MOD < std::numeric_limits<std::make_signed_t<std::uint64_t>>::max())
struct multiset_hasher {
private:
using uint128_t = internal::uint128_t;
public:
using hash_type = std::uint64_t;
using size_type = std::uint64_t;
static constexpr hash_type mod = MOD;
protected:
static inline hash_type _id(const T& v) noexcept(NO_EXCEPT) {
return uni::hash64(v);
}
static constexpr hash_type mask(const size_type a) noexcept(NO_EXCEPT) { return (1ULL << a) - 1; }
static constexpr hash_type mul(hash_type a, hash_type b) noexcept(NO_EXCEPT) {
#ifdef __SIZEOF_INT128__
uint128_t res = static_cast<uint128_t>(a) * b;
#else
hash_type a31 = a >> 31, b31 = b >> 31;
a &= multiset_hasher::mask(31);
b &= multiset_hasher::mask(31);
hash_type x = a * b31 + b * a31;
hash_type res = (a31 * b31 << 1) + (x >> 30) + ((x & multiset_hasher::mask(30)) << 31) + a * b;
#endif
res = (res >> 61) + (res & multiset_hasher::mod);
if(res >= multiset_hasher::mod) res -= multiset_hasher::mod;
return res;
}
hash_type _hash = 0;
inline void _add_hash(const hash_type h, const hash_type count) noexcept(NO_EXCEPT) {
this->_hash += multiset_hasher::mul(h, count);
if(this->_hash >= multiset_hasher::mod) this->_hash -= multiset_hasher::mod;
}
inline void _remove_hash(const hash_type h, const hash_type count) noexcept(NO_EXCEPT) {
auto hash = to_signed(this->_hash);
hash -= multiset_hasher::mul(h, count);
if(hash < 0) hash += multiset_hasher::mod;
this->_hash = hash;
}
public:
multiset_hasher() noexcept(NO_EXCEPT) {}
template<std::input_iterator I, std::sentinel_for<I> S>
multiset_hasher(I first, S last) noexcept(NO_EXCEPT) : multiset_hasher() {
for(auto itr=first; itr != last; ++itr) this->insert(*itr);
}
template<class U>
multiset_hasher(const std::initializer_list<U>& init_list) noexcept(NO_EXCEPT) : multiset_hasher(std::begin(init_list), std::end(init_list)) {}
inline size_type empty() const noexcept(NO_EXCEPT) { return this->get() == 0; }
inline void clear() noexcept(NO_EXCEPT) { this->_hash = 0; }
// return: whether inserted newly
inline void insert(const T& v, size_type count = 1) noexcept(NO_EXCEPT) {
this->_add_hash(multiset_hasher::_id(v), count);
}
// return: iterator of next element erased
inline void erase(const T& v, const size_type count = 1) noexcept(NO_EXCEPT) {
this->_remove_hash(multiset_hasher::_id(v), count);
}
inline hash_type get() const noexcept(NO_EXCEPT) { return this->_hash; }
inline hash_type operator()() const noexcept(NO_EXCEPT) { return this->_hash; }
inline bool operator==(const multiset_hasher& other) const noexcept(NO_EXCEPT) { return this->_hash == other._hash; }
inline bool operator!=(const multiset_hasher& other) const noexcept(NO_EXCEPT) { return this->_hash != other._hash; }
};
} // namespace uni
#line 2 "hash/sequence_hasher.hpp"
#line 6 "hash/sequence_hasher.hpp"
#include <chrono>
#line 11 "hash/sequence_hasher.hpp"
#line 15 "hash/sequence_hasher.hpp"
#line 18 "hash/sequence_hasher.hpp"
#line 20 "hash/sequence_hasher.hpp"
#line 22 "hash/sequence_hasher.hpp"
namespace uni {
// Thanks to: https://github.com/tatyam-prime/kyopro_library/blob/master/RollingHash.cpp
template<std::uint64_t MOD = 0x1fffffffffffffff, std::uint64_t BASE = 0>
struct sequence_hasher {
private:
using uint64_t = std::uint64_t;
using uint128_t = internal::uint128_t;
public:
using size_type = internal::size_t;
using hash_type = uint64_t;
static constexpr hash_type mod = MOD;
inline static hash_type base;
private:
size_type _n = 0, _front = 0;
std::vector<hash_type> _hashed;
inline static std::vector<hash_type> _powers;
protected:
static inline hash_type power(const size_type p) noexcept(NO_EXCEPT) {
if(static_cast<size_type>(sequence_hasher::_powers.size()) <= p) {
size_type n = static_cast<size_type>(sequence_hasher::_powers.size());
sequence_hasher::_powers.resize(p + 1);
if(n == 0) sequence_hasher::_powers[0] = 1;
REP(i, std::max(size_type{ 0 }, n-1), p) sequence_hasher::_powers[i + 1] = sequence_hasher::mul(sequence_hasher::_powers[i], sequence_hasher::base);
}
return sequence_hasher::_powers[p];
}
inline hash_type& hashed(const size_type p) noexcept(NO_EXCEPT) {
if(static_cast<size_type>(this->_hashed.size()) <= p) this->_hashed.resize(p + 1);
return this->_hashed[p];
}
inline const hash_type& hashed(const size_type p) const noexcept(NO_EXCEPT) { return this->_hashed[p]; }
static constexpr hash_type mask(const size_type a) noexcept(NO_EXCEPT) { return (1ULL << a) - 1; }
static constexpr hash_type mul(hash_type a, hash_type b) noexcept(NO_EXCEPT) {
#ifdef __SIZEOF_INT128__
uint128_t res = static_cast<uint128_t>(a) * b;
#else
hash_type a31 = a >> 31, b31 = b >> 31;
a &= sequence_hasher::mask(31);
b &= sequence_hasher::mask(31);
hash_type x = a * b31 + b * a31;
hash_type res = (a31 * b31 << 1) + (x >> 30) + ((x & sequence_hasher::mask(30)) << 31) + a * b;
#endif
if constexpr(sequence_hasher::mod == 0x1fffffffffffffff) {
res = (res >> 61) + (res & sequence_hasher::mod);
if(res >= sequence_hasher::mod) res -= sequence_hasher::mod;
}
else {
res %= sequence_hasher::mod;
}
return static_cast<hash_type>(res);
}
size_type index(size_type k) const noexcept(NO_EXCEPT) { return this->_front + k; }
public:
struct hash {
private:
const hash_type _val;
const size_type _len;
public:
hash(const hash_type val, const size_type len) noexcept(NO_EXCEPT) : _val(val), _len(len) {}
inline hash_type val() const noexcept(NO_EXCEPT) { return this->_val; }
inline operator hash_type() const noexcept(NO_EXCEPT) { return this->_val; }
inline size_type size() const noexcept(NO_EXCEPT) { return this->_len; }
inline bool operator==(const hash& other) const noexcept(NO_EXCEPT) { return this->_val == other._val and this->_len == other._len; }
inline bool operator!=(const hash& other) const noexcept(NO_EXCEPT) { return this->_val != other._val or this->_len != other._len; }
inline hash concat(const hash& other) const noexcept(NO_EXCEPT) { return sequence_hasher::concat(*this, other); }
inline hash operator+(const hash& other) const noexcept(NO_EXCEPT) { return sequence_hasher::concat(*this, other); }
};
sequence_hasher(const size_type n = 0) noexcept(NO_EXCEPT) : _n(n) {
if(sequence_hasher::base <= 0) {
if constexpr(BASE == 0) {
sequence_hasher::base = static_cast<hash_type>(uni::primitive_root<true>(sequence_hasher::mod));
}
else if constexpr(BASE < 0) {
random_engine_64bit random(std::random_device{}());
sequence_hasher::base = static_cast<hash_type>(random() % sequence_hasher::mod);
}
else {
sequence_hasher::base = BASE;
}
}
}
template<std::input_iterator I, std::sentinel_for<I> S>
sequence_hasher(I first, S last) noexcept(NO_EXCEPT) : sequence_hasher(static_cast<size_type>(std::ranges::distance(first, last))) {
this->_hashed.resize(this->_n);
this->_hashed.assign(this->_n + 1, 0);
size_type i = 0;
for(auto itr=first; itr!=last; ++i, ++itr) {
this->hashed(i + 1) = sequence_hasher::mul(this->hashed(i), sequence_hasher::base) + *itr;
if(this->hashed(i + 1) >= sequence_hasher::mod) this->hashed(i + 1) -= sequence_hasher::mod;
}
}
template<std::ranges::input_range Range>
sequence_hasher(Range&& ranges) noexcept(NO_EXCEPT) : sequence_hasher(ALL(ranges)) {}
inline size_type size() const noexcept(NO_EXCEPT) { return this->_n - this->_front; }
inline hash get(size_type l, size_type r) const noexcept(NO_EXCEPT) {
assert(0 <= l and l <= r and r <= this->size());
l = this->index(l), r = this->index(r);
hash_type res = this->hashed(r) + sequence_hasher::mod - sequence_hasher::mul(this->hashed(l), sequence_hasher::power(r - l));
if(res >= sequence_hasher::mod) res -= sequence_hasher::mod;
return { res, r - l };
}
inline hash get() const noexcept(NO_EXCEPT) { return this->get(0, this->size()); }
inline hash operator()(const size_type l, const size_type r) const noexcept(NO_EXCEPT) { return this->get(l, r); }
inline hash subseq(const size_type p, const size_type c) const noexcept(NO_EXCEPT) { return this->get(p, p+c); }
inline hash subseq(const size_type p) const noexcept(NO_EXCEPT) { return this->get(p, this->size()); }
static constexpr hash_type concat(const hash_type h0, const hash_type h1, const size_type len1) noexcept(NO_EXCEPT) {
hash_type res = sequence_hasher::mul(h0, sequence_hasher::power(len1)) + h1;
if(res >= sequence_hasher::mod) res -= sequence_hasher::mod;
return res;
}
static constexpr hash concat(const hash& h0, const hash& h1) noexcept(NO_EXCEPT) {
return { sequence_hasher::concat(h0.val(), h1.val(), h1.size()), h0.size() + h1.size() };
}
template<class T> inline sequence_hasher& push_back(const T& v) noexcept(NO_EXCEPT) {
this->_n++;
this->hashed(this->_n) = sequence_hasher::mul(this->hashed(this->_n-1), sequence_hasher::base) + hash32(v);
if(this->hashed(this->_n) >= sequence_hasher::mod) this->hashed(this->_n-1) -= sequence_hasher::mod;
return *this;
}
inline sequence_hasher& pop_back() noexcept(NO_EXCEPT) {
assert(this->_n > 0);
this->_n--;
return *this;
}
inline sequence_hasher& pop_front() noexcept(NO_EXCEPT) {
this->_front++;
assert(this->_front <= this->_n);
return *this;
}
template<std::input_iterator I, std::sentinel_for<I> S>
inline sequence_hasher& concat(I first, S last) noexcept(NO_EXCEPT) {
size_type n = this->_n;
this->_n += std::ranges::distance(first, last);
size_type i = n;
for(auto itr=first; itr!=last; ++i, ++itr) {
this->hashed(i + 1) = sequence_hasher::mul(this->hashed(i), sequence_hasher::base) + *itr;
if(this->hashed(i + 1) >= sequence_hasher::mod) this->hashed(i + 1) -= sequence_hasher::mod;
}
return *this;
}
template<class T>inline sequence_hasher& concat(const T& v) noexcept(NO_EXCEPT) { return this->concat(ALL(v)); }
inline size_type lcp(size_type l0, size_type r0, size_type l1, size_type r1) noexcept(NO_EXCEPT) {
size_type size = std::min(r0 - l0, r1 - l1);
size_type low = -1, high = size + 1;
while(high - low > 1) {
size_type mid = (low + high) / 2;
if(this->get(l0, l0 + mid) == this->get(l1, l1 + mid)) low = mid;
else high = mid;
}
return low;
}
};
} // namespace uni
#line 2 "hash/set_hasher.hpp"
#line 7 "hash/set_hasher.hpp"
#line 10 "hash/set_hasher.hpp"
#line 12 "hash/set_hasher.hpp"
namespace uni {
template<class T, int hasher_id = -1, template<class...> class Set = std::unordered_set>
struct set_hasher : protected Set<T> {
private:
using base = Set<T>;
public:
using hash_type = std::uint64_t;
using size_type = typename base::size_type;
protected:
hash_type _hash = 0;
static inline hash_type id(const T& v) noexcept(NO_EXCEPT) {
return hash64(v);
}
public:
set_hasher() noexcept(NO_EXCEPT) {}
template<std::input_iterator I, std::sentinel_for<I> S>
set_hasher(I first, S last) noexcept(NO_EXCEPT) {
for(auto itr=first; itr != last; ++itr) this->_insert(*itr);
}
template<class U>
set_hasher(const std::initializer_list<U>& init_list) noexcept(NO_EXCEPT) : set_hasher(std::begin(init_list), std::end(init_list)) {}
inline size_type empty() const noexcept(NO_EXCEPT) { return this->base::empty(); }
inline size_type size() const noexcept(NO_EXCEPT) { return this->base::size(); }
inline size_type max_size() const noexcept(NO_EXCEPT) { return this->base::max_size(); }
inline void clear() noexcept(NO_EXCEPT) { this->_hash = 0, this->base::clear(); }
using base::count;
using base::find;
using base::equal_range;
inline auto begin() const noexcept(NO_EXCEPT) { return this->base::begin(); }
inline auto end() const noexcept(NO_EXCEPT) { return this->base::end(); }
template<class... Args> auto lower_bound(const Args&... args) const noexcept(NO_EXCEPT) { return this->base::lower_bound(args...); }
template<class... Args> auto upper_bound(const Args&... args) const noexcept(NO_EXCEPT) { return this->base::upper_bound(args...); }
// return: whether inserted newly
inline bool insert(const T& v) noexcept(NO_EXCEPT) {
if(this->base::count(v)) return false;
this->base::insert(v);
this->_hash ^= set_hasher::id(v);
return true;
}
// return: number of erased elements (0 or 1)
inline size_type erase(const T& v) noexcept(NO_EXCEPT) {
if(not this->base::count(v)) return 0;
this->base::erase(v);
this->_hash ^= set_hasher::id(v);
return 1;
}
inline hash_type get() const noexcept(NO_EXCEPT) { return this->_hash; }
inline hash_type operator()() const noexcept(NO_EXCEPT) { return this->_hash; }
inline bool operator==(const set_hasher& other) const noexcept(NO_EXCEPT) { return this->_hash == other._hash; }
inline bool operator!=(const set_hasher& other) const noexcept(NO_EXCEPT) { return this->_hash != other._hash; }
};
} // namespace uni
#line 2 "include/iterable.hpp"
#line 2 "iterable/accumulation.hpp"
#line 11 "iterable/accumulation.hpp"
#line 14 "iterable/accumulation.hpp"
#line 17 "iterable/accumulation.hpp"
#line 19 "iterable/accumulation.hpp"
namespace uni {
template<class T, class Container = vector<T>>
struct accumulation : Container {
using size_type = internal::size_t;
protected:
inline size_type _positivize_index(const size_type x) const noexcept(NO_EXCEPT) {
return x < 0 ? std::size(*this) + x : x;
}
public:
accumulation() noexcept(NO_EXCEPT) {}
template<std::ranges::input_range R, class Operator = std::plus<T>>
requires std::regular_invocable<Operator, T, T>
explicit accumulation(R&& range, const T& head = T(), Operator&& op = std::plus<T>{})
: accumulation(ALL(range), head, op)
{}
template<
std::input_iterator I, std::sentinel_for<I> S,
class Operator = std::plus<T>
>
accumulation(I first, S last, const T& head = T(), Operator&& op = std::plus<T>{}) noexcept(NO_EXCEPT) {
this->resize(std::ranges::distance(first, last) + 1);
*this->begin() = head;
for(auto itr = std::ranges::begin(*this); first != last; ++first) {
const auto prev = itr++;
*itr = op(*prev, *first);
}
}
template<class Operator = std::minus<T>>
requires std::regular_invocable<Operator, T, T>
T operator()(size_type left, size_type right, Operator&& op = std::minus<T>{}) noexcept(NO_EXCEPT) {
left = _positivize_index(left), right = _positivize_index(right);
assert(0 <= left and left <= right and right < (size_type)std::size(*this));
return op((*this)[right], (*this)[left]);
}
template<class Operator = std::minus<T>>
requires std::regular_invocable<Operator, T, T>
T operator()(size_type left, size_type right, Operator&& op = std::minus<T>{}) const noexcept(NO_EXCEPT) {
left = _positivize_index(left), right = _positivize_index(right);
assert(0 <= left and left <= right and right < (size_type)std::size(*this));
return op(this->at(right), this->at(left));
}
};
template<std::input_iterator I, std::sentinel_for<I> S>
explicit accumulation(I, S) -> accumulation<typename std::iterator_traits<I>::value_type>;
template<std::ranges::input_range R>
explicit accumulation(R&&) -> accumulation<typename std::ranges::range_value_t<R>>;
template<class T, class Container = vector<vector<T>>, class Operator = std::plus<T>>
struct accumulation_2d : Container {
using size_type = internal::size_t;
protected:
inline size_type _positivize_index(const size_type x) const noexcept(NO_EXCEPT) {
return x < 0 ? std::size(*this) + x : x;
}
Operator _op;
public:
accumulation_2d() noexcept(NO_EXCEPT) {}
template<std::ranges::input_range R>
requires
std::ranges::input_range<typename std::ranges::range_value_t<R>> &&
std::regular_invocable<Operator, T, T>
explicit accumulation_2d(R&& range, const T& head = T(), Operator&& op = std::plus<T>{})
: accumulation_2d(ALL(range), head, op)
{}
template<std::input_iterator I, std::sentinel_for<I> S>
accumulation_2d(I first, S last, const T head = T{}, const Operator op = std::plus<T>{}) noexcept(NO_EXCEPT) : _op(op) {
const auto h = static_cast<size_type>(std::ranges::distance(first, last));
const auto w = static_cast<size_type>(std::ranges::distance(ALL(*first)));
{
auto row = first;
this->assign(h + 1, {});
(*this)[0].assign(w + 1, head);
REP(i, h) {
assert(w == std::ranges::ssize(*row));
(*this)[i + 1].assign(w + 1, head);
REP(j, w) (*this)[i + 1][j + 1] = first[i][j];
++row;
}
}
FOR(i, 1, h) FOR(j, w) (*this)[i][j] = op((*this)[i][j], (*this)[i - 1][j]);
FOR(i, h) FOR(j, 1, w) (*this)[i][j] = op((*this)[i][j], (*this)[i][j - 1]);
}
template<class Rev = std::minus<T>>
inline T operator()(size_type a, size_type b, size_type c, size_type d, const Rev rev = std::minus<T>{}) const noexcept(NO_EXCEPT) {
a = _positivize_index(a), b = _positivize_index(b);
c = _positivize_index(c), d = _positivize_index(d);
assert(0 <= a and a <= b and b < (size_type)std::size(*this));
assert(0 <= c and c <= d and d < (size_type)std::size((*this)[0]));
return this->_op(rev((*this)[b][d], this->_op((*this)[a][d], (*this)[b][c])), (*this)[a][c]);
}
template<class Rev = std::minus<T>>
inline T operator()(const std::pair<size_type,size_type> p, const std::pair<size_type,size_type> q, const Rev rev = std::minus<T>{}) const noexcept(NO_EXCEPT) {
return this->operator()(p.first, p.second, q.first, q.second, rev);
}
};
template<std::input_iterator I, std::sentinel_for<I> S>
explicit accumulation_2d(I, S) ->
accumulation_2d<
typename std::iterator_traits<typename std::ranges::iterator_t<typename std::iterator_traits<I>::value_type>>::value_type
>;
template<std::input_iterator I, std::sentinel_for<I> S>
explicit accumulation_2d(I, S) ->
accumulation_2d<
typename std::iterator_traits<typename uni::internal::iterator_t<typename std::iterator_traits<I>::value_type>>::value_type
>;
template<std::ranges::input_range R>
requires std::ranges::input_range<typename std::ranges::range_value_t<R>>
explicit accumulation_2d(R&&) ->
accumulation_2d<
typename std::ranges::range_value_t<typename std::ranges::range_value_t<R>>
>;
} // namespace uni
#line 2 "iterable/adjacent_difference.hpp"
#line 8 "iterable/adjacent_difference.hpp"
#line 11 "iterable/adjacent_difference.hpp"
#line 13 "iterable/adjacent_difference.hpp"
namespace uni {
template<class T, class container = valarray<T>>
struct adjacent_difference : container {
public:
explicit adjacent_difference() noexcept(NO_EXCEPT) {}
template<
std::input_iterator I, std::sentinel_for<I> S,
class Operator = std::minus<T>
>
explicit adjacent_difference(I first, S last, const bool remove_first = true, const Operator op = std::minus<T>{}) noexcept(NO_EXCEPT) {
this->resize(std::ranges::distance(first, last));
std::vector<T> diff(this->size());
std::adjacent_difference(first, last, std::ranges::begin(diff), op);
if(remove_first) diff.erase(std::ranges::begin(diff));
this->assign(std::ranges::begin(diff), std::ranges::end(diff));
}
};
template<std::input_iterator I, std::sentinel_for<I> S>
explicit adjacent_difference(I, S) -> adjacent_difference<typename std::iterator_traits<I>::value_type>;
} // namespace uni
#line 2 "iterable/applied.hpp"
#line 8 "iterable/applied.hpp"
#line 10 "iterable/applied.hpp"
#line 12 "iterable/applied.hpp"
namespace uni {
template<std::ranges::range R, class F>
inline R applied(R v, F&& func) noexcept(NO_EXCEPT) {
func(std::ranges::begin(v), std::ranges::end(v));
return v;
}
template<std::ranges::range R>
inline auto sorted(R&& v) noexcept(NO_EXCEPT) {
return applied(std::forward<R>(v), std::ranges::sort);
}
template<std::ranges::range R>
inline auto reversed(R&& v) noexcept(NO_EXCEPT) {
return applied(std::forward<R>(v), std::ranges::reverse);
}
} // namespace uni
#line 2 "iterable/count_inversion.hpp"
#line 7 "iterable/count_inversion.hpp"
#line 9 "iterable/count_inversion.hpp"
#line 12 "iterable/count_inversion.hpp"
#line 14 "iterable/count_inversion.hpp"
#line 17 "iterable/count_inversion.hpp"
namespace uni {
template<const bool STRICT = true, class T = std::int64_t>
struct inversion {
template<std::input_iterator I, std::sentinel_for<I> S>
static inline T count(I first, S last) noexcept(NO_EXCEPT) {
const internal::size_t n = std::distance(first, last);
const auto [ min, max ] = std::minmax_element(first, last);
const auto m = *max - *min + 1;
fenwick_tree<actions::range_sum<T>> cnt(m);
T res = 0;
{
internal::size_t i = 0;
I itr = first;
for(; i < n; ++i, ++itr) {
res += cnt(*itr - *min + STRICT, m).fold().val();
cnt[*itr - *min] += 1;
}
}
return res;
}
template<std::ranges::input_range R>
static inline T count(R&& range) noexcept(NO_EXCEPT) {
return inversion::count(ALL(range));
}
template<std::input_iterator I, std::sentinel_for<I> S>
static inline T count_with_compression(I first, S last) noexcept(NO_EXCEPT) {
compressed<typename std::iterator_traits<I>::value_type> comp(first, last);
return inversion::count(comp);
}
template<std::ranges::input_range R>
static inline T count_with_compression(R&& range) noexcept(NO_EXCEPT) {
return inversion::count_with_compression(ALL(range));
}
};
} // namespace uni
#line 2 "iterable/counter.hpp"
#line 4 "iterable/counter.hpp"
#line 8 "iterable/counter.hpp"
#line 10 "iterable/counter.hpp"
namespace uni {
template<class T, class Container = dynamic_auto_holder<T, internal::size_t>>
struct counter : Container {
counter() noexcept(NO_EXCEPT) = default;
template<std::input_iterator I, std::sentinel_for<I> S>
counter(I first, S last) noexcept(NO_EXCEPT) {
for(auto itr = first; itr != last; ++itr) ++(*this)[*itr];
}
template<std::ranges::input_range R>
explicit counter(R&& range) noexcept(NO_EXCEPT) : counter(ALL(range)) {}
};
template<std::input_iterator I, std::sentinel_for<I> S>
explicit counter(I, S) -> counter<std::iter_value_t<I>>;
template<std::ranges::input_range R>
explicit counter(R) -> counter<std::ranges::range_value_t<R>>;
} // namespace uni
#line 2 "iterable/inverse.hpp"
#line 6 "iterable/inverse.hpp"
#line 10 "iterable/inverse.hpp"
#line 12 "iterable/inverse.hpp"
#line 14 "iterable/inverse.hpp"
namespace uni {
template<class T, class V = vector<internal::size_t>, class container = dynamic_auto_holder<T, V>>
struct inverse : container {
explicit inverse() noexcept(NO_EXCEPT) {}
template<std::ranges::input_range R>
inverse(R&& range) noexcept(NO_EXCEPT) : inverse(std::ranges::begin(range), std::ranges::end(range)) {}
template<std::input_iterator I, std::sentinel_for<I> S>
inverse(I first, S last) noexcept(NO_EXCEPT) {
typename V::value_type index = 0;
for(auto itr = first; itr != last; ++itr, ++index) (*this)[*itr].emplace_back(index);
}
};
template<std::input_iterator I, std::sentinel_for<I> S>
explicit inverse(I, S) -> inverse<typename std::iterator_traits<I>::value_type>;
template<std::ranges::input_range R>
explicit inverse(R&&) -> inverse<std::ranges::range_value_t<R>>;
} // namespace uni
#line 2 "iterable/longest_common_subsequence.hpp"
#line 7 "iterable/longest_common_subsequence.hpp"
#line 10 "iterable/longest_common_subsequence.hpp"
#line 13 "iterable/longest_common_subsequence.hpp"
#line 15 "iterable/longest_common_subsequence.hpp"
namespace uni {
template<class container = grid<internal::size_t>>
struct lcs_sizes : container {
lcs_sizes() noexcept = default;
template<std::ranges::input_range R0, std::ranges::input_range R1>
lcs_sizes(R0&& r0, R1&& r1) noexcept(NO_EXCEPT) : container(ALL(r0), ALL(r1)) {}
template<
std::input_iterator I0, std::input_iterator I1,
std::sentinel_for<I0> S0, std::sentinel_for<I1> S1
>
lcs_sizes(I0 first0, S0 last0, I1 first1, S1 last1) noexcept(NO_EXCEPT)
: container(std::ranges::distance(first0, last0) + 1, std::ranges::distance(first1, last1) + 1)
{
internal::size_t pos0 = 0;
for(auto itr0=first0; itr0!=last0; ++pos0, ++itr0) {
internal::size_t pos1 = 0;
for(auto itr1=first1; itr1!=last1; ++pos1, ++itr1) {
if(*itr0 == *itr1) (*this)(pos0 + 1, pos1 + 1) = (*this)(pos0, pos1) + 1;
else (*this)(pos0 + 1, pos1 + 1) = std::max((*this)(pos0 + 1, pos1), (*this)(pos0, pos1 + 1));
}
}
}
};
} // namespace uni
#line 2 "iterable/longest_increasing_subsequence.hpp"
#line 6 "iterable/longest_increasing_subsequence.hpp"
#line 9 "iterable/longest_increasing_subsequence.hpp"
#line 12 "iterable/longest_increasing_subsequence.hpp"
#line 14 "iterable/longest_increasing_subsequence.hpp"
#line 16 "iterable/longest_increasing_subsequence.hpp"
namespace uni {
template<bool STRICT, class T, class container = vector<T>>
struct lis : container {
using size_type = typename internal::size_t;
std::vector<size_type> indices, positions;
lis() noexcept = default;
template<std::ranges::input_range R>
explicit lis(R&& range) noexcept(NO_EXCEPT) : lis(ALL(range)) {}
template<std::input_iterator I, std::sentinel_for<I> S>
lis(I first, S last) noexcept(NO_EXCEPT) : positions(std::ranges::distance(first, last), -1) {
this->reserve(std::ranges::distance(first, last));
size_type pos = 0;
for(auto itr=first; itr!=last; ++pos, ++itr) {
typename container::iterator bound;
if constexpr(STRICT) bound = std::ranges::lower_bound(*this, *itr);
else bound = std::ranges::upper_bound(*this, *itr);
this->positions[pos] = static_cast<size_type>(std::ranges::distance(std::ranges::begin(*this), bound));
if(std::ranges::end(*this) == bound) this->emplace_back(*itr);
else *bound = *itr;
}
size_type target = std::ranges::max(this->positions);
for(size_type i = static_cast<size_type>(this->positions.size()); --i >= 0;){
if(this->positions[i] == target) {
this->operator[](target) = *(first + i);
this->indices.emplace_back(i);
--target;
}
}
std::ranges::reverse(this->indices);
}
};
} // namespace uni
#line 2 "iterable/run_length_encoding.hpp"
#line 8 "iterable/run_length_encoding.hpp"
#line 12 "iterable/run_length_encoding.hpp"
#line 14 "iterable/run_length_encoding.hpp"
namespace uni {
template<class T, class container = vector<std::pair<T,internal::size_t>>>
struct run_length : container {
run_length() noexcept(NO_EXCEPT) = default;
template<std::input_iterator I, std::sentinel_for<I> S>
run_length(I first, S last) noexcept(NO_EXCEPT) {
this->clear();
typename container::value_type::second_type cnt = 0;
for(I itr=first, prev=itr; itr!=last; ++itr) {
if(*prev != *itr) this->emplace_back(*prev, cnt), cnt = 0;
++cnt;
prev = itr;
}
this->emplace_back(*std::ranges::prev(last), cnt);
}
template<std::ranges::input_range R>
explicit run_length(R&& range) : run_length(ALL(range)) {};
};
template<std::input_iterator I, std::sentinel_for<I> S>
run_length(I, S) -> run_length<std::iter_value_t<I>>;
template<std::ranges::input_range R>
explicit run_length(R&& range) -> run_length<std::ranges::range_value_t<R>>;
} // namespace uni
#line 2 "include/numeric.hpp"
#line 9 "include/numeric.hpp"
#line 2 "numeric/binomial_coefficient.hpp"
#line 6 "numeric/binomial_coefficient.hpp"
#line 9 "numeric/binomial_coefficient.hpp"
#line 13 "numeric/binomial_coefficient.hpp"
#line 18 "numeric/binomial_coefficient.hpp"
// Thanks to: https://nyaannyaan.github.io/library/modulo/arbitrary-mod-binomial.hpp
namespace uni {
namespace internal {
template<class T, class R = T, class Reduction = barrett_reduction_32bit>
requires (std::numeric_limits<R>::digits > 30) || modint_family<R>
struct binomial_coefficient_prime_power_mod {
using value_type = T;
using mod_type = R;
static constexpr i64 MOD_SUP = (i64{1} << 30) - 1;
static constexpr u32 MAX_BUFFER_SIZE = 30'000'000;
private:
using self = binomial_coefficient_prime_power_mod;
using reduction = Reduction;
u32 _p, _q, _m;
value_type _max;
std::valarray<u32> _fact, _inv_fact, _inv;
u32 _delta;
barrett_reduction_32bit _barrett_m, _barrett_p;
reduction _reduction_m;
u32 _one;
static constexpr std::pair<u32,u32> _factorize(u32 m) {
for(u32 i=2; i*i<=m; ++i) {
if(m % i == 0) {
u32 cnt = 0;
while(m % i == 0) m /= i, ++cnt;
assert(m == 1);
return { i, cnt };
}
}
return { m, 1 };
}
void _init() {
const u32 size = std::min(this->_m, static_cast<u32>(this->_max) + 1);
assert(size < self::MAX_BUFFER_SIZE);
this->_barrett_m = barrett_reduction_32bit(this->_m);
this->_barrett_p = barrett_reduction_32bit(this->_p);
this->_reduction_m = self::reduction(this->_m);
this->_delta = this->_reduction_m.convert_raw((this->_p == 2 && this->_q >= 3) ? 1 : this->_m - 1);
this->_one = this->_reduction_m.convert_raw(1);
this->_fact.resize(size);
this->_inv_fact.resize(size);
this->_inv.resize(size);
this->_fact[0] = this->_inv_fact[0] = this->_inv[0] = this->_one;
this->_fact[1] = this->_inv_fact[1] = this->_inv[1] = this->_one;
REP(i, 2, size) {
if(this->_barrett_p.reduce(i) == 0) {
this->_fact[i] = this->_fact[i - 1];
this->_fact[i + 1] = this->_reduction_m.multiply(this->_fact[i - 1], this->_reduction_m.convert_raw(this->_barrett_m.reduce(i + 1)));
++i;
}
else {
this->_fact[i] = this->_reduction_m.multiply(this->_fact[i - 1], this->_reduction_m.convert_raw(this->_barrett_m.reduce(i)));
}
}
this->_inv_fact[size - 1] = this->_reduction_m.pow(this->_fact[size - 1], this->_m / this->_p * (this->_p - 1) - 1);
REPD(i, 2, size - 1) {
this->_inv_fact[i] = this->_reduction_m.multiply(this->_inv_fact[i + 1], this->_reduction_m.convert_raw(this->_barrett_m.reduce(i + 1)));
if(this->_barrett_p.reduce(i) == 0) {
this->_inv_fact[i - 1] = this->_inv_fact[i];
--i;
}
}
}
public:
binomial_coefficient_prime_power_mod() noexcept = default;
explicit binomial_coefficient_prime_power_mod(const value_type max = 20'000'000) noexcept(NO_EXCEPT)
requires (1 < mod_type::mod() && mod_type::mod() < self::MOD_SUP)
: _m(mod_type::mod()), _max(max)
{
constexpr std::pair<u32,u32> pq = self::_factorize(mod_type::mod());
std::tie(this->_p, this->_q) = pq;
this->_init();
}
explicit binomial_coefficient_prime_power_mod(const mod_type p, mod_type q = 1, const value_type max = 20'000'000) noexcept(NO_EXCEPT)
requires (not modint_family<mod_type>)
: _p(static_cast<u32>(p)), _q(static_cast<u32>(q)), _max(max)
{
assert(1 < p && p < self::MOD_SUP);
assert(0 < q);
u64 m = 1;
while(q--) {
m *= this->_p;
assert(m < MOD_SUP);
}
this->_m = static_cast<u32>(m);
this->_init();
}
inline mod_type mod() const noexcept(NO_EXCEPT) { return this->_m; }
mod_type lucus(value_type n, value_type r) const noexcept(NO_EXCEPT) {
assert(0 <= n);
assert(0 <= r);
if(n < r) return 0;
u32 res = this->_one;
while(n > 0) {
u32 n0, k0;
std::tie(n, n0) = this->_barrett_p.divide(n);
std::tie(r, k0) = this->_barrett_p.divide(r);
if(n0 < k0) return 0;
res = this->_reduction_m.multiply(res, this->_fact[n0]);
res = this->_reduction_m.multiply(res, this->_reduction_m.multiply(this->_inv_fact[n0 - k0], this->_inv_fact[k0]));
}
return static_cast<mod_type>(this->_reduction_m.revert(res));
}
mod_type comb(value_type n, value_type r) const noexcept(NO_EXCEPT) {
assert(0 <= n);
assert(0 <= r);
if(this->_q == 1) return this->lucus(n, r);
if(n < r) return 0;
value_type k = n - r;
u32 e0 = 0, eq = 0, i = 0;
u32 res = this->_one;
while(n > 0) {
res = this->_reduction_m.multiply(res, this->_fact[this->_barrett_m.reduce(n)]);
res = this->_reduction_m.multiply(res, this->_inv_fact[this->_barrett_m.reduce(r)]);
res = this->_reduction_m.multiply(res, this->_inv_fact[this->_barrett_m.reduce(k)]);
n = this->_barrett_p.quotient(n);
r = this->_barrett_p.quotient(r);
k = this->_barrett_p.quotient(k);
u32 eps = static_cast<u32>(n - r - k);
e0 += eps;
if(e0 >= this->_q) return 0;
if(++i >= this->_q) eq += eps;
}
if(eq & 1) res = this->_reduction_m.multiply(res, this->_delta);
res = this->_reduction_m.multiply(res, this->_reduction_m.pow(this->_reduction_m.convert_raw(this->_p), e0));
return static_cast<mod_type>(this->_reduction_m.revert(res));
}
};
} // namespace internal
using internal::binomial_coefficient_prime_power_mod;
// (md < 10^7 && N < 2^30) || (md < 2^30 && N < 2 * 10^7)
template<class T, class R = T>
requires (std::numeric_limits<R>::digits > 30) || internal::modint_family<R>
struct binomial_coefficient {
using value_type = T;
using mod_type = R;
private:
template<class reduction = montgomery_reduction_32bit>
using internal_binomial = internal::binomial_coefficient_prime_power_mod<value_type, long long, reduction>;
u32 _mod;
value_type _max;
std::vector<u32> _mods;
std::vector<internal_binomial<>> _internals;
internal_binomial<binary_reduction_32bit> _internal_2p;
void _init() noexcept(NO_EXCEPT) {
u32 md = this->_mod;
if(md == 1) return;
assert((md < 20'000'000 && this->_max < (1 << 30)) || (md < (1 << 30) && this->_max < 30'000'000));
assert(1 <= md);
assert(md <= internal_binomial<>::MOD_SUP);
for(u32 i=2; i*i<=md; ++i) {
if(md % i == 0) {
u32 j = 0, k = 1;
while(md % i == 0) md /= i, ++j, k *= i;
this->_mods.push_back(k);
if(i == 2) {
this->_internal_2p = internal_binomial<binary_reduction_32bit>(2, j, this->_max);
this->_internals.emplace_back();
}
else {
this->_internals.emplace_back(i, j, this->_max);
assert(this->_mods.back() == this->_internals.back().mod());
}
}
}
if(md != 1) {
this->_mods.push_back(static_cast<u32>(md));
if(md == 2) this->_internal_2p = internal_binomial<binary_reduction_32bit>(2, 1, this->_max);
else this->_internals.emplace_back(md, 1, this->_max);
}
}
public:
binomial_coefficient(const value_type max = 20'000'000) noexcept(NO_EXCEPT)
requires internal::modint_family<mod_type>
: _mod(static_cast<u32>(mod_type::mod())), _max(max)
{
this->_init();
}
binomial_coefficient(const mod_type mod, const value_type max = 20'000'000) noexcept(NO_EXCEPT)
requires (not internal::modint_family<mod_type>)
: _mod(static_cast<u32>(mod)), _max(max)
{
this->_init();
}
mod_type comb(const value_type n, const value_type r) const noexcept(NO_EXCEPT) {
assert(n >= 0), assert(r >= 0);
if(this->_mod == 1) return 0;
if(n < r) return 0;
if(this->_mods.size() == 1) {
if((this->_mods.back() & 1) == 0) return static_cast<mod_type>(this->_internal_2p.comb(n, r));
else return static_cast<mod_type>(this->_internals[0].comb(n, r));
}
std::vector<long long> rem, div;
REP(i, 0, std::ranges::ssize(this->_mods)) {
div.push_back(this->_mods[i]);
if((this->_mods[i] & 1) == 0) rem.push_back(this->_internal_2p.comb(n, r));
else {
rem.push_back(this->_internals[i].comb(n, r));
}
}
return static_cast<mod_type>(atcoder::crt(rem, div).first);
}
};
} // namespace uni
#line 2 "numeric/boundary_seeker.hpp"
#line 8 "numeric/boundary_seeker.hpp"
#line 11 "numeric/boundary_seeker.hpp"
#line 14 "numeric/boundary_seeker.hpp"
#line 16 "numeric/boundary_seeker.hpp"
namespace uni {
namespace internal {
namespace boundary_seeker_impl {
template<class T>
struct integal {
protected:
std::function<bool(T)> _validate;
public:
integal(std::function<bool(T)> validate) noexcept(NO_EXCEPT) : _validate(validate) {}
template<bool INVERT = false>
T bound(const T _ok, const T _ng) const noexcept(NO_EXCEPT) {
T ok = _ok, ng = _ng;
if constexpr(INVERT) std::swap(ng, ok);
while(std::abs(ok - ng) > 1) {
T mid = ng + (ok - ng) / 2;
(INVERT ^ this->_validate(mid) ? ok : ng) = mid;
}
return ok;
}
template<bool REVERSE = false, bool INVERT = false>
T bound(const T ok) const noexcept(NO_EXCEPT) {
assert(INVERT ^ this->_validate(ok));
T ng = REVERSE ? -1 : 1;
while(INVERT ^ this->_validate(ok + ng)) ng += ng;
return this->bound<INVERT>(ok, ok + ng);
}
template<bool REVERSE = false, bool INVERT = false>
T bound() const noexcept(NO_EXCEPT) {
return this->bound<INVERT>(
REVERSE ?
numeric_limits<T>::arithmetic_infinity() / 2 :
numeric_limits<T>::arithmetic_negative_infinity() / 2
);
}
template<bool INVERT = false>
T bound_or(const T ok, const T ng, const T proxy) const noexcept(NO_EXCEPT) {
const T res = this->bound<INVERT>(ok, ng);
return this->_validate(res) ? res : proxy;
}
template<bool REVERSE = false, bool INVERT = false>
T bound_or(const T ok, const T proxy) const noexcept(NO_EXCEPT) {
const T res = this->bound<REVERSE, INVERT>(ok);
return this->_validate(res) ? res : proxy;
}
template<bool REVERSE = false, bool INVERT = false>
T bound_or(const T proxy) const noexcept(NO_EXCEPT) {
const T res = this->bound<REVERSE, INVERT>();
return this->_validate(res) ? res : proxy;
}
};
template<class T>
struct floating_point {
protected:
std::function<bool(T)> _validate;
public:
floating_point(std::function<bool(T)> validate) noexcept(NO_EXCEPT) : _validate(validate) {}
template<bool INVERT = false, internal::size_t ITERATIONS = 200>
T bound(const T _ok, const T _ng) const noexcept(NO_EXCEPT) {
T ok = _ok, ng = _ng;
if constexpr(INVERT) std::swap(ng, ok);
REP(ITERATIONS) {
T mid = ng + (ok - ng) / 2;
(INVERT ^ this->_validate(mid) ? ok : ng) = mid;
}
return ok;
}
template<bool REVERSE = false, bool INVERT = false, internal::size_t ITERATIONS = 200>
T bound(const T ok) const noexcept(NO_EXCEPT) {
assert(INVERT ^ this->_validate(ok));
T ng = REVERSE ? -1 : 1;
while(INVERT ^ this->_validate(ok + ng)) ng += ng;
return this->bound<INVERT>(ok, ok + ng);
}
template<bool REVERSE = false, bool INVERT = false, internal::size_t ITERATIONS = 200>
T bound() const noexcept(NO_EXCEPT) {
return this->bound<INVERT, ITERATIONS>(
REVERSE ?
numeric_limits<T>::arithmetic_infinity() / 2 :
numeric_limits<T>::arithmetic_negative_infinity() / 2
);
}
template<bool INVERT = false, internal::size_t ITERATIONS = 200>
T bound_or(const T ok, const T ng, const T proxy) const noexcept(NO_EXCEPT) {
const T res = this->bound<INVERT, ITERATIONS>(ok, ng);
return this->_validate(res) ? res : proxy;
}
template<bool REVERSE = false, bool INVERT = false, internal::size_t ITERATIONS = 200>
T bound_or(const T ok, const T proxy) const noexcept(NO_EXCEPT) {
const T res = this->bound<REVERSE, INVERT, ITERATIONS>(ok);
return this->_validate(res) ? res : proxy;
}
template<bool REVERSE = false, bool INVERT = false, internal::size_t ITERATIONS = 200>
T bound_or(const T proxy) const noexcept(NO_EXCEPT) {
const T res = this->bound<REVERSE, INVERT, ITERATIONS>();
return this->_validate(res) ? res : proxy;
}
};
template<class, bool>
struct seeker {};
template<class T>
struct seeker<T,true> : integal<T> {
using integal<T>::integal;
};
template<class T>
struct seeker<T,false> : floating_point<T> {
using floating_point<T>::floating_point;
};
} // namespace boundary_seeker_impl
} // namespace internal
template<class T>
using boundary_seeker = internal::boundary_seeker_impl::seeker<T,std::is_integral_v<T>>;
} // namespace uni
#line 2 "numeric/divisors.hpp"
#line 5 "numeric/divisors.hpp"
#line 8 "numeric/divisors.hpp"
namespace uni {
template<class T>
vector<T> divisors_sieve(const T k) noexcept(NO_EXCEPT) {
vector<T> res;
for(T i=1; i*i<=k; ++i) {
if(k%i == 0) {
res.emplace_back(i);
if(i*i < k) res.emplace_back(k/i);
}
}
res.sort();
return res;
}
} // namespace uni
#line 2 "numeric/extremum_seeker.hpp"
#line 6 "numeric/extremum_seeker.hpp"
#line 10 "numeric/extremum_seeker.hpp"
#line 13 "numeric/extremum_seeker.hpp"
#line 15 "numeric/extremum_seeker.hpp"
#line 17 "numeric/extremum_seeker.hpp"
namespace uni {
template<class Signature>
struct extremum_seeker;
template<class T, std::floating_point Arg>
struct extremum_seeker<T(Arg)> {
using value_type = T;
using arg_type = Arg;
private:
std::function<T(Arg)> _f;
template<const internal::size_t ITERATIONS>
std::pair<arg_type, arg_type> search(arg_type low, arg_type high, const auto comp) const noexcept(NO_EXCEPT) {
REP(ITERATIONS) {
const auto p = low + (high - low) / 3;
const auto q = high - (high - low) / 3;
if(comp(p, q)) high = q;
else low = p;
}
return { low, high };
}
public:
template<class F>
requires std::same_as<std::invoke_result_t<F, Arg>, T>
extremum_seeker(F&& f) noexcept(NO_EXCEPT) : _f(std::forward<F>(f)) {};
template<const internal::size_t ITERATIONS = 100'000>
std::pair<arg_type, arg_type> arg_min(
arg_type low = uni::numeric_limits<arg_type>::arithmetic_negative_infinity(),
arg_type high = uni::numeric_limits<arg_type>::arithmetic_infinity()
) const noexcept(NO_EXCEPT) {
const auto comp = [&](const arg_type lhs, const arg_type rhs) noexcept(NO_EXCEPT) {
return this->_f(lhs) < this->_f(rhs);
};
return this->search<ITERATIONS>(low, high, comp);
}
template<const internal::size_t ITERATIONS = 100'000>
std::pair<arg_type, arg_type> arg_max(
arg_type low = uni::numeric_limits<arg_type>::arithmetic_negative_infinity(),
arg_type high = uni::numeric_limits<arg_type>::arithmetic_infinity()
) const noexcept(NO_EXCEPT) {
const auto comp = [&](const arg_type lhs, const arg_type rhs) noexcept(NO_EXCEPT) {
return this->_f(lhs) > this->_f(rhs);
};
return this->search<ITERATIONS>(low, high, comp);
}
template<const internal::size_t ITERATIONS = 100'000>
auto min(
const arg_type _low = uni::numeric_limits<arg_type>::arithmetic_negative_infinity(),
const arg_type _high = uni::numeric_limits<arg_type>::arithmetic_infinity()
) const noexcept(NO_EXCEPT) {
const auto [ low, high ] = this->arg_min<ITERATIONS>(_low, _high);
auto res = std::min(this->_f(low), this->_f(high));
FOR(x, low, high) chmin(res, this->_f(x));
return res;
}
template<const internal::size_t ITERATIONS = 100'000>
auto max(
const arg_type _low = uni::numeric_limits<arg_type>::arithmetic_negative_infinity(),
const arg_type _high = uni::numeric_limits<arg_type>::arithmetic_infinity()
) const noexcept(NO_EXCEPT) {
const auto [ low, high ] = this->arg_max<ITERATIONS>(_low, _high);
auto res = std::max(this->_f(low), this->_f(high));
FOR(x, low, high) chmax(res, this->_f(x));
return res;
}
};
template<class T, std::integral Arg>
struct extremum_seeker<T(Arg)> {
using value_type = T;
using arg_type = Arg;
private:
std::function<T(Arg)> _f;
std::vector<arg_type> _fib = { 0, 1 };
gnu::gp_hash_table<arg_type, value_type> _cache;
auto _expand(const arg_type size) noexcept(NO_EXCEPT) {
assert(size >= 0);
this->_fib.reserve(std::bit_width(to_unsigned(size)));
if(this->_fib.back() < size) {
do {
this->_fib.emplace_back(
this->_fib[std::ranges::size(this->_fib) - 1] +
this->_fib[std::ranges::size(this->_fib) - 2]
);
} while(this->_fib.back() < size);
return std::ranges::prev(this->_fib.end());
}
return std::ranges::lower_bound(this->_fib, size);
}
auto _func(const arg_type size) noexcept(NO_EXCEPT) {
if(this->_cache.contains(size)) return this->_cache[size];
return this->_cache[size] = this->_f(size);
}
auto _search(arg_type low, const arg_type high, const auto comp) noexcept(NO_EXCEPT) {
if(low == high) return low;
auto _low = low - 1;
const auto itr = this->_expand(high - _low + 1);
auto _high = *itr + _low;
auto diff = *std::ranges::prev(itr);
while(true) {
const auto p = _high - diff;
const auto q = _low + diff;
if(p == q) return p;
if(comp(p, q)) _high = q;
else _low = p;
diff = diff - (q - p);
}
}
public:
template<class F>
requires std::same_as<std::invoke_result_t<F, Arg>, T>
extremum_seeker(F&& f, const arg_type init_size = 0) noexcept(NO_EXCEPT)
: _f(std::forward<F>(f))
{
this->_expand(init_size);
}
auto arg_min(
const arg_type low = uni::numeric_limits<arg_type>::arithmetic_negative_infinity(),
const arg_type high = uni::numeric_limits<arg_type>::arithmetic_infinity()
) noexcept(NO_EXCEPT) {
const auto comp = [&](const arg_type lhs, const arg_type rhs) noexcept(NO_EXCEPT) {
if(high < rhs) return true;
return this->_func(lhs) < this->_func(rhs);
};
return this->_search(low, high, comp);
}
auto arg_max(
const arg_type low = uni::numeric_limits<arg_type>::arithmetic_negative_infinity(),
const arg_type high = uni::numeric_limits<arg_type>::arithmetic_infinity()
) noexcept(NO_EXCEPT) {
const auto comp = [&](const arg_type lhs, const arg_type rhs) noexcept(NO_EXCEPT) {
if(high < rhs) return true;
return this->_func(lhs) > this->_func(rhs);
};
return this->_search(low, high, comp);
}
inline auto min(
const arg_type _low = uni::numeric_limits<arg_type>::arithmetic_negative_infinity(),
const arg_type high = uni::numeric_limits<arg_type>::arithmetic_infinity()
) noexcept(NO_EXCEPT) {
return this->_func(this->arg_min(_low, high));
}
inline auto max(
const arg_type _low = uni::numeric_limits<arg_type>::arithmetic_negative_infinity(),
const arg_type high = uni::numeric_limits<arg_type>::arithmetic_infinity()
) noexcept(NO_EXCEPT) {
return this->_func(this->arg_max(_low, high));
}
};
} // namespace uni
#line 2 "numeric/factorial.hpp"
#line 5 "numeric/factorial.hpp"
#line 7 "numeric/factorial.hpp"
#line 9 "numeric/factorial.hpp"
#line 11 "numeric/factorial.hpp"
namespace uni {
namespace internal {
template<class T>
struct factorial_base {
using value_type = T;
using size_type = internal::size_t;
static constexpr value_type calc(const size_type& n) noexcept(NO_EXCEPT) {
assert(n >= 0);
value_type ans = 1;
FOR(k, 1, n) ans *= k;
return ans;
}
};
} // namespace internal
template<class>
struct factorial {};
template<std::integral T>
struct factorial<T> : internal::factorial_base<T> {
using value_type = T;
using size_type = internal::size_t;
private:
size_type _n;
std::valarray<value_type> _fact;
public:
factorial(const size_type n) noexcept(NO_EXCEPT) : _n(n), _fact(n + 1) {
this->_fact[0] = this->_fact[1] = 1;
FOR(i, 2, n) this->_fact[i] = this->_fact[i - 1] * i;
}
inline value_type fact(const size_type k) noexcept(NO_EXCEPT) {
assert(0 <= k and k <= this->_n);
return this->_fact[k];
}
inline value_type operator()(const size_type k) noexcept(NO_EXCEPT) {
return this->fact(k);
}
auto _debug() const { return this->_fact; }
};
template<uni::internal::modint_family T>
struct factorial<T> : internal::factorial_base<T> {
using value_type = T;
using size_type = internal::size_t;
private:
size_type _n;
std::valarray<value_type> _fact, _ifact, _inv;
public:
factorial(const size_type n) noexcept(NO_EXCEPT) : _n(n), _fact(n + 1), _ifact(n + 1), _inv(n + 1) {
constexpr auto P = T::mod();
this->_fact[0] = this->_fact[1] = 1;
this->_ifact[0] = this->_ifact[1] = 1;
this->_inv[1] = 1;
FOR(i, 2, n) {
this->_inv[i] = -this->_inv[P % i] * (P / i);
this->_fact[i] = this->_fact[i - 1] * i;
this->_ifact[i] = this->_ifact[i - 1] * this->_inv[i];
}
}
inline value_type fact(const size_type k) noexcept(NO_EXCEPT) {
assert(0 <= k and k <= this->_n);
return this->_fact[k];
}
inline value_type operator()(const size_type k) noexcept(NO_EXCEPT) {
return this->fact(k);
}
inline value_type ifact(const size_type k) noexcept(NO_EXCEPT) {
assert(0 <= k and k <= this->_n);
return this->_ifact[k];
}
inline value_type inv(const size_type k) noexcept(NO_EXCEPT) {
assert(0 <= k and k <= this->_n);
return this->_inv[k];
}
inline value_type bimom(const size_type n, const size_type r) noexcept(NO_EXCEPT) {
assert(0 <= r and r <= n and n <= this->_n);
return this->fact(n) * this->ifact(r) * this->ifact(n - r);
}
auto _debug() const { return this->_fact; }
};
} // namespace uni
#line 2 "numeric/hilbert_order.hpp"
#line 4 "numeric/hilbert_order.hpp"
template<class T> T hilbert_order(const T n, T i, T j) {
T p, q, d = 0;
for(T t=n>>1; t>0; t>>=1) {
p = (i&t) > 0, q = (j&t) > 0;
d += t * t * ((p * 3) ^ q);
if(q > 0) continue;
if(p > 0) {
i = n - i - 1;
j = n - j - 1;
}
std::swap(i, j);
}
return d;
}
template<class T> T hilbert_order(const T n,const std::pair<T,T> p) {
return hilbert_order(n, p.first, p.second);
}
#line 2 "numeric/interval_scanner.hpp"
#line 2 "numeric/internal/two_pointer_technique.hpp"
#line 10 "numeric/internal/two_pointer_technique.hpp"
#line 12 "numeric/internal/two_pointer_technique.hpp"
#line 15 "numeric/internal/two_pointer_technique.hpp"
namespace uni {
namespace internal {
namespace interval_scanner_impl {
template<class T> using interval = std::pair<T, T>;
template<class T> using intervals = std::vector<std::pair<T, T>>;
template<class T>
struct base {
protected:
std::function<bool(T)> _validate;
public:
base(std::function<bool(T)> validate) : _validate(validate) {}
void scan(T, T, T) {
static_assert(internal::EXCEPTION_ON_TYPE<T>, "not implemented: scan()");
}
void split(const T first, const T last, intervals<T> *intervals) const {
std::valarray<bool> _valid(false, last - first);
for(auto itr=first,index=0; itr!=last; ++itr, ++index) _valid[index] = _validate(itr);
auto can_begin = [&](const T itr) {
const auto index = itr - first;
if(itr == first) return _valid[index];
if(itr == last) return false;
if(not _valid[index-1] and _valid[index]) return true;
return false;
};
auto is_end = [&](const T itr) {
const auto index = itr - first;
if(itr == first) return false;
if(itr == last) return _valid[index-1];
if(_valid[index-1] and not _valid[index]) return true;
return false;
};
{
intervals->clear();
T start = first;
for(auto itr=first; ; ++itr) {
if(can_begin(itr)) start = itr;
if(is_end(itr)) intervals->emplace_back(start, itr);
if(itr == last) break;
}
}
}
void scan_all(const T first, const T last) const {
intervals<T> targets;
this->split(first, last, &targets);
ITR(start, end, targets) this->scan(first, start, end);
}
};
} // namespace interval_scanner_impl
} // namespace internal
template<class T>
struct exclusive_interval_scanner : internal::interval_scanner_impl::base<T> {
private:
std::function<void(T)> _init;
std::function<bool(T)> _can_expand;
std::function<void(T)> _expand, _contract;
std::function<void(T, T)> _apply;
public:
using interval = internal::interval_scanner_impl::interval<T>;
using intervals = internal::interval_scanner_impl::intervals<T>;
exclusive_interval_scanner(
std::function<bool(T)> validate,
std::function<void(T)> init,
std::function<bool(T)> can_expand,
std::function<void(T)> expand,
std::function<void(T)> contract,
std::function<void(T, T)> apply
)
: internal::interval_scanner_impl::base<T>(validate), _init(init), _can_expand(can_expand),
_expand(expand), _contract(contract), _apply(apply)
{}
template<const bool FOLLOWING = true>
void scan(const T start, const T end) const {
T l_itr=start, r_itr=start;
while(l_itr < end) {
if (FOLLOWING and r_itr <= l_itr) {
r_itr = l_itr+1;
_init(l_itr);
}
while(r_itr < end && _can_expand(r_itr)) {
_expand(r_itr++);
}
_apply(l_itr, r_itr);
_contract(l_itr++);
}
};
template<const bool FOLLOWING = true>
void scan_all(const T first, const T last) const {
intervals targets;
this->split(first, last, &targets);
ITR(start, end, targets) this->scan<FOLLOWING>(start, end);
}
};
template<class T>
struct inclusive_interval_scanner : internal::interval_scanner_impl::base<T> {
protected:
std::function<void()> _init;
std::function<bool()> _valid;
std::function<void(T)> _expand, _contract;
std::function<void(T, T)> _apply;
public:
using interval = internal::interval_scanner_impl::interval<T>;
using intervals = internal::interval_scanner_impl::intervals<T>;
inclusive_interval_scanner(
std::function<bool(T)> validate,
std::function<void()> init,
std::function<bool()> valid,
std::function<void(T)> expand,
std::function<void(T)> contract,
std::function<void(T, T)> apply
) : internal::interval_scanner_impl::base<T>(validate), _init(init), _valid(valid), _expand(expand), _contract(contract), _apply(apply) {}
template<const bool INVERSE = false, const bool FOLLOWING = true, const bool CONFIRMATION = true>
void scan(const T start, const T end) const {
T l_itr = start, r_itr = start;
_init();
while(l_itr < end) {
if(FOLLOWING and r_itr < l_itr) {
r_itr = l_itr;
_init();
}
if(r_itr < end and (INVERSE ^ _valid())) {
_expand(r_itr++);
}
else {
_contract(l_itr++);
}
if(!CONFIRMATION or _valid()) _apply(l_itr, r_itr);
}
}
template<const bool INVERSE = false, const bool FOLLOWING = true, const bool CONFIRMATION = true>
void scan_all(const T first, const T last) const {
intervals targets;
this->split(first, last, &targets);
ITR(start, end, targets) this->scan<INVERSE,FOLLOWING,CONFIRMATION>(start, end);
}
};
} // namespace uni
#line 2 "numeric/internal/mo.hpp"
#line 12 "numeric/internal/mo.hpp"
#line 16 "numeric/internal/mo.hpp"
#line 19 "numeric/internal/mo.hpp"
#line 22 "numeric/internal/mo.hpp"
#line 26 "numeric/internal/mo.hpp"
namespace uni {
template<class R, class EF, class PF, class EB = EF, class PB = PF>
class interval_plannner {
using size_type = internal::size_t;
public:
EF _expand_front; EB _expand_back;
PF _contract_front; PB _contract_back;
R _evaluate;
using evaluator_result_t = std::invoke_result_t<R>;
interval_plannner(
EF expand_front, EB expand_back,
PF contract_front, PB contract_back,
R evaluate
) noexcept(NO_EXCEPT)
: _expand_front(expand_front), _expand_back(expand_back),
_contract_front(contract_front), _contract_back(contract_back),
_evaluate(evaluate)
{}
interval_plannner(EF expand, PF contract, R evaluate) noexcept(NO_EXCEPT)
: interval_plannner(expand, expand, contract, contract, evaluate)
{}
template<
std::input_iterator QI, std::sentinel_for<QI> QS,
std::output_iterator<evaluator_result_t> RI
>
void scan(const QI query_first, const QS query_last, const RI res_first) noexcept(NO_EXCEPT) {
const auto q = std::ranges::distance(query_first, query_last);
size_type n = 0;
for(auto query=query_first; query!=query_last; ++query) {
chmax(n, std::ranges::max(query->first, query->second));
}
n = std::bit_ceil(uni::to_unsigned(n));
std::vector<i64> orders(q);
{
auto query = query_first;
auto order = orders.begin();
for(; query!=query_last; ++query, ++order) {
*order = hilbert_order<i64>(n, *query);
}
}
std::vector<size_type> indices(q); std::iota(ALL(indices), 0);
std::ranges::sort(
indices,
[&orders](const size_type i, const size_type j) { return orders[i] < orders[j]; }
);
size_type l = 0, r = 0;
ITR(i, indices) {
while(l > query_first[i].first) _expand_front(--l);
while(r < query_first[i].second) _expand_back(r++);
while(l < query_first[i].first) _contract_front(l++);
while(r > query_first[i].second) _contract_back(--r);
res_first[i] = _evaluate();
}
}
template<std::input_iterator QI, std::sentinel_for<QI> QS>
auto scan(const QI query_first, const QS query_last) noexcept(NO_EXCEPT) {
valarray<evaluator_result_t> res(std::ranges::distance(query_first, query_last));
this->scan(query_first, query_last, std::ranges::begin(res));
return res;
}
template<std::ranges::input_range Q>
auto scan(const Q& queries) noexcept(NO_EXCEPT) {
valarray<evaluator_result_t> res(std::ranges::distance(queries));
this->scan(std::ranges::begin(queries), std::ranges::end(queries), std::ranges::begin(res));
return res;
}
};
} // namespace uni
#line 2 "numeric/leveler.hpp"
#line 7 "numeric/leveler.hpp"
#line 10 "numeric/leveler.hpp"
#line 13 "numeric/leveler.hpp"
#line 15 "numeric/leveler.hpp"
#line 18 "numeric/leveler.hpp"
namespace uni {
template<class T = internal::size_t>
struct leveler {
using value_type = T;
using size_type = internal::size_t;
private:
uni::valarray<value_type> _bases;
size_type _dim;
value_type _max;
inline value_type _compute_max() const noexcept(NO_EXCEPT) {
return std::reduce(std::begin(this->_bases), std::end(this->_bases), 1, std::multiplies<value_type>{});
}
public:
leveler(const std::initializer_list<value_type> bases) noexcept(NO_EXCEPT) : _bases(bases), _dim(std::ranges::size(bases)) {
this->_max = this->_compute_max();
}
template<class I>
leveler(I first, I last) noexcept(NO_EXCEPT) : _bases(first, last), _dim(std::ranges::distance(first, last)) {
this->_max = this->_compute_max();
}
template<std::ranges::forward_range R>
leveler(R&& range) noexcept(NO_EXCEPT) : leveler(std::ranges::begin(range), std::ranges::end(range)) {}
template<std::integral... Values>
leveler(const Values... bases) noexcept(NO_EXCEPT) : leveler(std::initializer_list<value_type>{ bases... }) {}
inline size_type dimension() const noexcept(NO_EXCEPT) { return this->_dim; }
inline value_type sup() const noexcept(NO_EXCEPT) { return this->_max; }
inline value_type convert(const std::initializer_list<value_type> inds) const noexcept(NO_EXCEPT) {
return this->convert(inds | std::views::all);
}
template<std::ranges::forward_range R>
inline value_type convert(R&& range) const noexcept(NO_EXCEPT) {
assert(std::ranges::distance(range) == std::ranges::ssize(this->_bases));
value_type res = 0;
{
auto size = std::ranges::begin(this->_bases);
ITR(v, range) {
assert(0 <= v and v < *size);
res *= *(size++);
res += v;
}
}
return res;
}
template<std::integral... Values>
inline value_type convert(const Values... inds) const noexcept(NO_EXCEPT) {
return this->convert({ inds... });
}
inline uni::valarray<value_type> revert(value_type id) const noexcept(NO_EXCEPT) {
assert(0 <= id and id < this->sup());
uni::valarray<value_type> res(std::size(this->_bases));
REPD(i, std::size(this->_bases)) {
res[i] = id % this->_bases[i];
id /= this->_bases[i];
}
return res;
}
auto _debug() const { return this->_bases; }
};
}
#line 2 "numeric/matrix.hpp"
#line 6 "numeric/matrix.hpp"
#line 9 "numeric/matrix.hpp"
#line 12 "numeric/matrix.hpp"
#line 14 "numeric/matrix.hpp"
#line 16 "numeric/matrix.hpp"
namespace uni {
namespace internal {
template<class Base>
struct matrix_core : Base {
using Base::Base;
using value_type = typename Base::value_type;
using size_type = typename Base::size_type;
using vector_type = typename Base::row_type;
static constexpr auto identity(const size_type n, const value_type& val = 1) noexcept(NO_EXCEPT) {
matrix_core res(n);
REP(i, n) res(i, i) = val;
return res;
}
inline constexpr bool square() const noexcept(NO_EXCEPT) { return this->height() == this->width(); }
constexpr auto& operator+=(const value_type& rhs) noexcept(NO_EXCEPT) {
REP(i, this->height()) REP(j, this->width()) this->operator()(i, j) += rhs;
return *this;
}
template<class... Ts>
constexpr auto& operator+=(const matrix_core<Ts...>& rhs) noexcept(NO_EXCEPT) {
REP(i, this->height()) REP(j, this->width()) this->operator()(i, j) += rhs(i, j);
return *this;
}
template<weakly_addition_assignable<matrix_core> T>
inline constexpr auto operator+(const T& rhs) const noexcept(NO_EXCEPT) {
return matrix_core(*this) += rhs;
}
constexpr auto& operator-=(const value_type& rhs) noexcept(NO_EXCEPT) {
REP(i, this->height()) REP(j, this->width()) this->operator()(i, j) -= rhs;
return *this;
}
template<class... Ts>
constexpr auto& operator-=(const matrix_core<Ts...>& rhs) noexcept(NO_EXCEPT) {
REP(i, this->height()) REP(j, this->width()) this->operator()(i, j) -= rhs(i, j);
return *this;
}
template<weakly_subtraction_assignable<matrix_core> T>
inline constexpr auto operator-(const T& rhs) const noexcept(NO_EXCEPT) {
return matrix_core(*this) -= rhs;
}
template<class... Ts>
constexpr auto operator*(const matrix_core<Ts...>& rhs) const noexcept(NO_EXCEPT) {
assert(this->width() == rhs.height());
matrix_core res(this->height(), rhs.width());
REP(i, this->height()) REP(j, rhs.width()) REP(k, this->width()) {
res(i, j) += (*this)(i, k) * rhs(k, j);
}
return res;
}
template<std::ranges::input_range Vector>
requires
(!internal::derived_from_template<Vector, matrix_core>) &&
internal::weakly_multipliable<value_type, std::ranges::range_value_t<Vector>>
constexpr auto operator*(const Vector& rhs) const noexcept(NO_EXCEPT) {
debug(*this, rhs);
assert(this->width() == std::ranges::ssize(rhs));
Vector res(this->height());
REP(i, this->height()) REP(j, this->width()) res[i] += this->operator()(i, j) * rhs[j];
return res;
}
template<std::ranges::input_range Vector>
requires
(!internal::derived_from_template<Vector, matrix_core>) &&
internal::weakly_multipliable<std::ranges::range_value_t<Vector>, value_type>
friend constexpr auto operator*(const Vector& lhs, const matrix_core& rhs) noexcept(NO_EXCEPT) {
debug(lhs, rhs);
assert(std::ranges::ssize(lhs) == rhs.height());
Vector res(rhs.width());
REP(i, rhs.height()) REP(j, rhs.width()) res[j] += lhs[j] * rhs[i][j];
return res;
}
constexpr auto operator*(const value_type& rhs) noexcept(NO_EXCEPT) {
auto res = *this;
REP(i, res.height()) REP(j, res.width()) res(i, j) *= rhs;
return res;
}
template<multipliable<matrix_core> T>
constexpr auto& operator*=(const T& rhs) noexcept(NO_EXCEPT) {
matrix_core res = *this * rhs;
this->assign(res);
return *this;
}
constexpr auto& operator/=(const value_type& rhs) noexcept(NO_EXCEPT) {
REP(i, this->height()) REP(j, this->width()) this->operator()(i, j) /= rhs;
return *this;
}
inline constexpr auto operator/(const value_type& rhs) const noexcept(NO_EXCEPT) {
return matrix_core(*this) /= rhs;
}
constexpr auto& operator%=(const value_type& rhs) noexcept(NO_EXCEPT) {
REP(i, this->height()) REP(j, this->width()) this->operator()(i, j) %= rhs;
return *this;
}
inline constexpr auto operator%(const value_type& rhs) const noexcept(NO_EXCEPT) {
return matrix_core(*this) %= rhs;
}
template<std::integral K>
constexpr auto pow(const K n) const noexcept(NO_EXCEPT) {
assert(this->height() == this->width());
if constexpr(std::signed_integral<K>) assert(n >= 0);
return uni::pow(*this, n, {}, matrix_core::identity(this->height()));
}
constexpr auto find_pivot(const size_type rank, const size_type col) const noexcept(NO_EXCEPT) {
size_type pivot = -1;
REP(i, rank, this->height()) {
if(this->operator()(i, col) != 0) {
pivot = i;
break;
}
}
return pivot;
}
template<bool DIAGONALIZE = false>
constexpr void sweep(const size_type rank, const size_type col, const size_type pivot) noexcept(NO_EXCEPT)
requires modint_family<value_type>
{
std::swap(this->operator[](pivot), this->operator[](rank));
if constexpr(DIAGONALIZE) {
const auto inv = this->operator()(rank, col).inv();
REP(j, this->width()) this->operator()(rank, j) *= inv;
}
REP(i, (DIAGONALIZE ? 0 : rank + 1), this->height()) {
if(i != rank && this->operator()(i, col) != 0) {
const auto fac = this->operator()(i, col);
REP(j, this->width()) this->operator()(i, j) -= this->operator()(rank, j) * fac;
}
}
}
template<size_type IGNORE_WIDTH = 0, bool DIAGONALIZE = false>
inline constexpr auto transform_to_upper_triangular() noexcept(NO_EXCEPT)
requires modint_family<value_type>
{
size_type rank = 0;
REP(j, this->width() - IGNORE_WIDTH) {
const auto pivot = this->find_pivot(rank, j);
if(pivot == -1) continue;
this->template sweep<DIAGONALIZE>(rank++, j, pivot);
}
return rank;
}
template<size_type IGNORE_WIDTH>
inline constexpr auto transform_to_lower_triangular() noexcept(NO_EXCEPT)
requires modint_family<value_type>
{
const auto rank = this->template transform_to_upper_triangular<IGNORE_WIDTH>();
this->transpose();
return rank;
}
template<std::ranges::input_range Vector, class Sol = void, class System = void>
constexpr std::optional<size_type> solve_linear_equation(
const Vector& v,
Sol *const sol = nullptr,
System *const system = nullptr
)
const noexcept(NO_EXCEPT)
requires modint_family<value_type>
{
static_assert(!(std::same_as<Sol, void>) || (std::same_as<System, void>));
assert(this->height() == std::ranges::ssize(v));
matrix_core mat(this->height(), this->width() + 1);
REP(i, this->height()) {
REP(j, this->width()) mat(i, j) = this->operator()(i, j);
mat(i, this->width()) = v[i];
}
const auto rank = mat.transform_to_upper_triangular<1, true>();
REP(i, rank, this->height()) if(mat(i, this->width()) != value_type::zero) return {};
if constexpr(!std::same_as<Sol, void>) {
static_assert(std::ranges::output_range<Sol, value_type>);
static_assert(std::ranges::output_range<std::ranges::range_value_t<System>, value_type>);
assert(!sol || system);
if(sol) {
sol->assign(this->width(), value_type::zero);
std::vector<size_type> pivots(system ? this->width() : 0, -1);
for(size_type i = 0, j = 0; i < rank; ++i) {
while(mat(i, j) == value_type::zero) ++j;
sol->operator[](j) = mat(i, this->width());
if constexpr(!std::same_as<System, void>) if(system) {
pivots[j] = i;
}
}
if constexpr(!std::same_as<System, void>) if(system) {
REP(j, this->width()) {
if(pivots[j] != -1) continue;
typename System::vector_type x(this->width());
x[j] = value_type::one;
REP(k, j) if(pivots[k] != -1) x[k] = -mat(pivots[k], j);
system->push_back(x);
}
system->resize(system->size(), this->width());
}
}
}
return rank;
}
value_type determinant() const noexcept(NO_EXCEPT)
requires modint_family<value_type>
{
assert(this->square());
auto mat = *this;
value_type det = value_type::one;
REP(j, this->height()) {
const auto pivot = mat.find_pivot(j, j);
if(j < pivot) std::swap(mat[pivot], mat[j]), det = -det;
if(mat(j, j) == 0) return 0;
REP(i, j + 1, this->height()) {
while(mat(i, j) != 0) {
const auto c = static_cast<value_type>(-to_signed(mat(j, j).val() / mat(i, j).val()));
REP(k, j, this->height()) mat(j, k) += mat(i, k) * c;
std::swap(mat[i], mat[j]), det = -det;
}
}
}
REP(i, mat.height()) det *= mat(i, i);
return det;
}
};
} // namespace internal
template<class T, class Base = grid<T>>
using matrix = internal::matrix_core<Base>;
template<class T>
using valmatrix = internal::matrix_core<valgrid<T>>;
template<class T>
using unfolded_matrix = internal::matrix_core<unfolded_grid<T>>;
template<class T>
using unfolded_valmatrix = internal::matrix_core<unfolded_valgrid<T>>;
} // namespace uni
#line 2 "numeric/numerical_sequence.hpp"
#line 6 "numeric/numerical_sequence.hpp"
#line 8 "numeric/numerical_sequence.hpp"
namespace uni {
namespace numerical_sequence {
namespace internal {
using size_t = std::int64_t;
template<class T>
struct single_constant {
using value_type = T;
private:
value_type _val;
public:
constexpr single_constant() = default;
constexpr single_constant(const value_type& val) noexcept(NO_EXCEPT) : _val(val) {}
inline constexpr const value_type& val() const noexcept(NO_EXCEPT) { return this->_val; }
inline constexpr operator value_type() const noexcept(NO_EXCEPT) { return this->_val; }
};
} // namespace internl
template<class T>
struct term {
using size_type = internal::size_t;
using value_type = T;
private:
size_type _index;
value_type _val;
public:
constexpr term() = default;
constexpr explicit term(const size_type index, const value_type& val) noexcept(NO_EXCEPT) : _index(index), _val(val) {}
inline constexpr size_type index() const noexcept(NO_EXCEPT) { return this->_index; }
inline constexpr const value_type& val() const noexcept(NO_EXCEPT) { return this->_val; }
};
template<class T, internal::size_t INDEX>
struct static_term : internal::single_constant<T> {
using internal::single_constant<T>::single_constant;
using size_type = internal::size_t;
using value_type = T;
inline constexpr size_type index() const noexcept(NO_EXCEPT) { return INDEX; }
inline constexpr operator term<value_type>() const noexcept(NO_EXCEPT) { return term(INDEX, this->_val); }
};
template<class T>
struct common_difference : internal::single_constant<T> {
using internal::single_constant<T>::single_constant;
};
template<class T>
struct common_ratio : internal::single_constant<T> {
using internal::single_constant<T>::single_constant;
};
template<class T>
struct arithmetic {
using size_type = internal::size_t;
using value_type = T;
protected:
value_type _begin, _diff;
public:
constexpr arithmetic() = default;
constexpr arithmetic(const static_term<value_type,0>& begin, const common_difference<value_type>& diff)
: _begin(static_cast<value_type>(begin.val())), _diff(diff.val()) {}
constexpr arithmetic(const common_difference<value_type>& diff, const static_term<value_type,0>& begin) : arithmetic(begin, diff) {}
constexpr arithmetic(const term<value_type>& p, const common_difference<value_type>& diff) noexcept(NO_EXCEPT)
: arithmetic(diff, static_cast<value_type>(p.val() - diff * p.index()))
{}
constexpr arithmetic(const common_difference<value_type>& diff, const term<value_type>& p) noexcept(NO_EXCEPT) : arithmetic(p, diff) {}
constexpr arithmetic(const term<value_type> p, const term<value_type> q) noexcept(NO_EXCEPT)
: arithmetic(p, common_difference(static_cast<value_type>((p.val() - q.val()) / (p.index() - q.index()))))
{}
inline constexpr term<value_type> operator[](const size_type k) const noexcept(NO_EXCEPT) {
return term(k, static_cast<value_type>(this->_begin + this->_diff * k));
}
inline constexpr value_type sum(const size_type k) const noexcept(NO_EXCEPT) {
return static_cast<value_type>((this->_begin * k) + (k - 1) * k / 2 * this->_diff);
}
inline constexpr value_type sum(const size_type l, const size_type r) const noexcept(NO_EXCEPT) {
return this->sum(r) - this->sum(l);
}
};
template<class T>
struct geometric {
using size_type = internal::size_t;
using value_type = T;
protected:
value_type _begin, _ratio;
public:
constexpr geometric() = default;
constexpr geometric(const static_term<value_type,0> begin, const common_ratio<T> ratio) noexcept(NO_EXCEPT) : _begin(begin), _ratio(ratio) {};
inline constexpr term<value_type> operator[](const size_type k) const noexcept(NO_EXCEPT) {
return term(k, this->_begin * uni::pow(this->_diff, k));
}
inline constexpr value_type sum(const size_type k) const noexcept(NO_EXCEPT) {
if(this->_ratio == 1) return this->_begin * this->k;
else {
return this->_begin * (uni::pow(this->_ratio, k) - 1) / (this->_ratio - 1);
}
return ;
}
inline constexpr value_type sum(const size_type l, const size_type r) const noexcept(NO_EXCEPT) {
return this->sum(r) - this->sum(l);
}
};
} // namespace numerical_sequence
} // namespace uni
#line 2 "numeric/prime_counter.hpp"
#line 6 "numeric/prime_counter.hpp"
#line 10 "numeric/prime_counter.hpp"
#line 12 "numeric/prime_counter.hpp"
#line 14 "numeric/prime_counter.hpp"
namespace uni {
static inline i64 float_div(const i64 n, const i64 p) {
return static_cast<i64>(static_cast<double>(n) / static_cast<double>(p));
};
// Thanks to: https://nyaannyaan.github.io/library/multiplicative-function/prime-counting-faster.hpp
__attribute__((target("avx2"), optimize("O3", "unroll-loops")))
i64 count_primes(const u64 n) noexcept(NO_EXCEPT) {
if(n == 0 || n == 1) return 0;
const i64 sqrt_n = uni::sqrt_floor(n);
const i64 m = float_div(n, sqrt_n);
std::vector<i64> hl(m);
REP(i, 1, m) hl[i] = float_div(n, i) - 1;
std::vector<i32> hs(sqrt_n + 1);
std::iota(ALL(hs), -1);
for(i32 x=2, pi=0; x <= sqrt_n; ++x) {
if(hs[x] == hs[x - 1]) continue;
const i64 x2 = static_cast<i64>(x) * x;
const i64 imax = std::min(m, float_div(n, x2) + 1);
i64 ix = x;
REP(i, 1, imax) {
hl[i] -= (ix < m ? hl[ix] : hs[float_div(n, ix)]) - pi;
ix += x;
}
FORD(k, x2, sqrt_n) hs[k] -= hs[float_div(k, x)] - pi;
++pi;
}
return hl[1];
}
inline i64 count_primes(const i64 l, const i64 r) noexcept(NO_EXCEPT) {
assert(l <= r);
return count_primes(r) - count_primes(l - 1);
}
} // namespace uni
#line 2 "numeric/prime_sieve.hpp"
#line 5 "numeric/prime_sieve.hpp"
#line 8 "numeric/prime_sieve.hpp"
#line 11 "numeric/prime_sieve.hpp"
#line 14 "numeric/prime_sieve.hpp"
namespace uni {
template<class container = valarray<bool>> struct prime_flags : container {
prime_flags(const internal::size_t max) noexcept(NO_EXCEPT) : container(max+1, true) {
(*this)[0] = (*this)[1] = false;
for(internal::size_t p=2; p*p<=max; p++) if((*this)[p]) {
for(internal::size_t i=p*p; i<=max; i+=p) (*this)[i] = false;
}
}
};
template<class T, class container = vector<T>> struct prime_sieve : container {
protected:
std::vector<bool> is_prime;
public:
prime_sieve() noexcept(NO_EXCEPT) {}
prime_sieve(const T max) noexcept(NO_EXCEPT) : is_prime(max+1, true) {
is_prime[0] = is_prime[1] = false;
FOR(p, T{2}, max) {
if(is_prime[p]) {
for(T i = mul_overflow(p,p).value_or(max+1); i<=max; i+=p) is_prime[i] = false;
this->emplace_back(p);
}
}
}
inline bool operator()(const T index) const noexcept(NO_EXCEPT) {
return is_prime[index];
}
};
} // namespace uni
#line 2 "numeric/quotient_enumerator.hpp"
#line 6 "numeric/quotient_enumerator.hpp"
#line 10 "numeric/quotient_enumerator.hpp"
#line 12 "numeric/quotient_enumerator.hpp"
namespace uni {
template<class T, bool CEIL = false>
struct quotient_enumerator {
using value_type = std::tuple<T,T,T>; // (q, l, r)
using size_type = T;
private:
T _n = 0, _n_impl = 0;
size_type _size = -1;
protected:
using iterator_interface = internal::bidirectional_iterator_interface<const value_type>;
public:
// Enumerate tuple of (q, l, r), which means (floor/ceil)(_n/k) == q (l <= k <= r).
quotient_enumerator(const T n) noexcept(NO_EXCEPT) : _n(n), _n_impl(n - CEIL) { assert(n > 0); }
struct iterator;
using const_iterator = iterator;
inline auto begin() noexcept(NO_EXCEPT) { return iterator(this->_n_impl, 1); }
inline auto end() noexcept(NO_EXCEPT) { return iterator(this->_n_impl, this->_n + 1); }
inline auto rbegin() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
inline auto size() noexcept(NO_EXCEPT) {
if(this->_size < 0) {
size_type r = uni::sqrt_floor(this->_n_impl);
this->_size = 2 * r - (this->_n_impl < r * (r + 1)) + CEIL;
}
return this->_size;
}
struct iterator : virtual iterator_interface {
using value_type = quotient_enumerator::value_type;
using reference = value_type;
protected:
T _n_impl = 0;
T _q = 0, _l = 0, _r = 0;
void _set_l(const T l) noexcept(NO_EXCEPT) {
this->_l = l, this->_q = this->_n_impl / l;
if(this->_q == 0) {
if(CEIL) {
if(l == this->_n_impl + 1) this->_r = l;
}
return;
}
this->_r = this->_n_impl / this->_q;
}
void _set_r(const T r) noexcept(NO_EXCEPT) {
this->_r = r, this->_q = this->_n_impl / r;
this->_l = this->_n_impl / (this->_q + 1) + 1;
}
public:
iterator() noexcept = default;
iterator(const T n, const T l) noexcept(NO_EXCEPT) : _n_impl(n) { this->_set_l(l); }
friend inline bool operator==(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT) { return lhs._l == rhs._l; }
inline value_type operator*() const noexcept(NO_EXCEPT) { return { this->_q + CEIL, this->_l, this->_r }; }
inline auto& operator++() noexcept(NO_EXCEPT) { this->_set_l(this->_r + 1); return *this; }
inline auto& operator--() noexcept(NO_EXCEPT) { this->_set_r(this->_l - 1); return *this; }
inline auto operator++(int) noexcept(NO_EXCEPT) { const auto res = *this; this->_set_l(this->_r + 1); return res; }
inline auto operator--(int) noexcept(NO_EXCEPT) { const auto res = *this; this->_set_r(this->_l - 1); return res; }
};
};
} // namespace uni
namespace std::ranges {
template<class T>
inline constexpr bool enable_borrowed_range<uni::quotient_enumerator<T>> = true;
} // namespace std::ranges
#line 2 "numeric/repeater.hpp"
#line 7 "numeric/repeater.hpp"
#line 11 "numeric/repeater.hpp"
#line 13 "numeric/repeater.hpp"
namespace uni {
template<class T, internal::size_t SUP, internal::size_t DEFAULT_DEPTH = 64>
struct repeater {
using value_type = T;
using size_type = internal::size_t;
private:
std::vector<std::array<T, SUP>> _app;
inline void _extend(const std::size_t k) noexcept(NO_EXCEPT) {
const auto size = this->_app.size();
const auto w = to_unsigned(std::bit_width(k));
if(w <= size) return;
this->_app.resize(w);
REP(d, size, w) {
REP(n, SUP) {
this->_app[d][n] = this->_app[d - 1][this->_app[d - 1][n]];
}
}
}
template<std::unsigned_integral K>
struct applyer {
private:
K _k;
repeater* _super;
public:
applyer(const K k, repeater *const super) noexcept(NO_EXCEPT) : _k(k), _super(super) {}
inline K times() const noexcept(NO_EXCEPT) { return this->_k; }
inline value_type operator()(value_type val) const noexcept(NO_EXCEPT) {
REP(d, this->_super->_app.size()) {
if(uni::bit(this->_k, d)) val = this->_super->_app[d][val];
}
return val;
}
};
public:
template<class F>
requires std::convertible_to<std::invoke_result_t<F, T>, T>
explicit repeater(F&& f) noexcept(NO_EXCEPT) : _app(1) {
this->_app.reserve(DEFAULT_DEPTH);
REP(n, SUP) this->_app[0][n] = static_cast<value_type>(f(n));
};
template<std::ranges::sized_range R>
explicit repeater(R&& f) noexcept(NO_EXCEPT) : _app(1) {
assert(std::ranges::size(f) <= SUP);
this->_app.reserve(DEFAULT_DEPTH);
std::ranges::copy(f, std::ranges::begin(this->_app[0]));
};
template<std::integral K>
inline auto operator[](K k) noexcept(NO_EXCEPT) {
if(std::signed_integral<K>) assert(0 <= k);
this->_extend(static_cast<std::size_t>(k));
return applyer{ to_unsigned(k), this };
}
};
} // namespace uni
#line 2 "numeric/stern_brocot_tree.hpp"
#line 6 "numeric/stern_brocot_tree.hpp"
#line 8 "numeric/stern_brocot_tree.hpp"
#line 10 "numeric/stern_brocot_tree.hpp"
#line 12 "numeric/stern_brocot_tree.hpp"
namespace uni {
// Thanks to: https://maspypy.github.io/library/nt/stern_brocot_tree.hpp
template<
class Value = i32,
class Middle = i64,
class Large = i128,
class Fraction = spair<Value>, std::ranges::range Path = uni::vector<Value>
>
struct stern_brocot_tree {
using value_type = Value;
using middle_type = Middle;
using large_type = middle_type;
using path_type = Path;
using fraction_type = Fraction;
static constexpr std::tuple<path_type, fraction_type, fraction_type> path_and_rang(const fraction_type x) {
path_type path;
fraction_type l = { 0, 1 }, r = { 1, 0 };
fraction_type m = { 1, 1 };
middle_type det_l = l.first * x.second - l.second * x.first;
middle_type det_r = r.first * x.second - r.second * x.first;
middle_type det_m = det_l + det_r;
while(true) {
if(det_m == 0) break;
middle_type k = uni::div_ceil(-det_m, det_r);
path.emplace_back(k);
l = { l.first + k * r.first, l.second + k * r.second };
m = { l.first + r.first, l.second + r.second };
det_l += k * det_r;
det_m += k * det_r;
if(det_m == 0) break;
k = uni::div_ceil(det_m, -det_l);
path.emplace_back(k);
r = { r.first + k * l.first, r.second + k * l.second };
m = { l.first + r.first, l.second + r.second };
det_r += k * det_l;
det_m += k * det_l;
}
return { path, l, r };
}
static constexpr path_type path(const fraction_type x) {
const auto [ path, l, r ] = path_and_rang(x);
return path;
}
static constexpr spair<fraction_type> range(const fraction_type x) {
const auto [ path, l, r ] = path_and_rang(x);
return { l, r };
}
// x in range(y)
static constexpr bool in_subtree(const fraction_type x, const fraction_type y) {
const auto [ l, r ] = range(y);
const bool ok_l = static_cast<middle_type>(x.first) * l.second - static_cast<middle_type>(x.second) * l.first > 0;
const bool ok_r = static_cast<middle_type>(r.first) * x.second - static_cast<middle_type>(r.second) * x.first > 0;
return ok_l && ok_r;
}
template<class T = middle_type, class Frac = spair<middle_type>>
static constexpr Frac from_path(const path_type &p) {
Frac l = { 0, 1 }, r = { 1, 0 };
FOR(i, std::ranges::size(p)) {
middle_type k = p[i];
if((i & 1) == 0) {
l.first += static_cast<T>(k) * r.first;
l.second += static_cast<T>(k) * r.second;
}
if((i & 1) == 1) {
r.first += static_cast<T>(k) * l.first;
r.second += static_cast<T>(k) * l.second;
}
}
return { l.first + r.first, l.second + r.second };
}
static constexpr spair<fraction_type> children(const fraction_type x) {
const auto [ l, r ] = range(x);
const fraction_type lc = { l.first + x.first, l.second + x.second };
const fraction_type rc = { x.first + r.first, x.second + r.second };
return { lc, rc };
}
static constexpr fraction_type lowest_common_ancestor(const fraction_type x, const fraction_type y) {
const auto px = path(x);
const auto py = path(y);
path_type path;
FOR(i, uni::min(std::ranges::ssize(px), std::ranges::ssize(py))) {
middle_type k = uni::min(px[i], py[i]);
path.emplace_back(k);
if(k < px[i] || k < py[i]) break;
}
return from_path(path);
}
static constexpr fraction_type ancestor(const fraction_type x, middle_type dep) {
fraction_type l = { 0, 1 }, r = { 1, 0 };
fraction_type m = { 1, 1 };
middle_type det_l = l.first * x.second - l.second * x.first;
middle_type det_r = r.first * x.second - r.second * x.first;
middle_type det_m = det_l + det_r;
while(true) {
if(det_m == 0 || dep == 0) break;
middle_type k = uni::min(dep, uni::div_ceil(-det_m, det_r));
l = { l.first + k * r.first, l.second + k * r.second };
m = { l.first + r.first, l.second + r.second };
det_l += k * det_r;
det_m += k * det_r;
dep -= k;
if(det_m == 0 || dep == 0) break;
k = uni::min(dep, uni::div_ceil(det_m, -det_l));
r = {r.first + k * l.first, r.second + k * l.second };
m = { l.first + r.first, l.second + r.second };
det_r += k * det_l;
det_m += k * det_l;
dep -= k;
}
if(dep == 0) return m;
return { -1, -1 };
}
static constexpr std::string to_string(const path_type &p) {
std::string res;
char c = 'L';
ITR(x, p) {
c = 'L' + 'R' - c;
if(x == 0) continue;
res += c;
res += " " + std::to_string(x);
}
return res;
}
};
} // namespace uni
#line 2 "numeric/subset_enumerator.hpp"
#line 6 "numeric/subset_enumerator.hpp"
#line 10 "numeric/subset_enumerator.hpp"
#line 13 "numeric/subset_enumerator.hpp"
namespace uni {
template<std::unsigned_integral T>
struct subset_enumerator {
using value_type = T;
using size_type = internal::size_t;
private:
T _n = 0;
protected:
using iterator_interface = internal::bidirectional_iterator_interface<const value_type>;
public:
// Enumerate tuple of (q, l, r), which means (floor/ceil)(_n/k) == q (l <= k <= r).
subset_enumerator(const T n) noexcept(NO_EXCEPT) : _n(n) { assert(n >= 0); }
struct iterator;
using const_iterator = iterator;
inline auto begin() noexcept(NO_EXCEPT) { return iterator(this->_n, this->_n); }
inline auto end() noexcept(NO_EXCEPT) { return iterator(this->_n, 0, true); }
inline auto rbegin() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
inline auto size() noexcept(NO_EXCEPT) { return static_cast<size_type>(1) << std::popcount(this->_n); }
struct iterator : iterator_interface {
protected:
value_type _n = 0, _v = 0;
bool _end = false;
public:
iterator() noexcept = default;
iterator(const T n, const T v, const bool end = false) noexcept(NO_EXCEPT) : _n(n), _v(v), _end(end) {};
friend inline bool operator==(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT) {
if(rhs._end) return lhs._end;
if(lhs._end) return false;
return lhs._v == rhs._v;
};
friend inline auto operator<=>(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT) {
if(rhs._end) {
if(lhs._end) return std::partial_ordering::equivalent;
return std::partial_ordering::less;
}
if(lhs._end) {
return std::partial_ordering::greater;
}
return comapre_as_bitset(rhs._v, lhs._v);
};
inline auto operator*() const noexcept(NO_EXCEPT) { return this->_v; }
inline auto& operator++() noexcept(NO_EXCEPT) {
if(this->_v == 0) {
this->_end = true;
}
else {
this->_v = (this->_v - 1) & this->_n;
}
return *this;
}
inline auto& operator--() noexcept(NO_EXCEPT) {
if(this->_end) {
this->_end = false;
}
else {
const auto lsb = lowest_bit_pos(this->_n & ~this->_v);
this->_v = ((this->_v >> lsb) | 1) << lsb;
}
return *this;
}
inline auto operator++(int) noexcept(NO_EXCEPT) { auto res = *this; ++res; return res; }
inline auto operator--(int) noexcept(NO_EXCEPT) { auto res = *this; --res; return res; }
};
};
} // namespace uni
namespace std::ranges {
template<class T>
inline constexpr bool enable_borrowed_range<uni::subset_enumerator<T>> = true;
} // namespace std::ranges
#line 2 "numeric/subset_superset_transform.hpp"
#line 6 "numeric/subset_superset_transform.hpp"
#line 8 "numeric/subset_superset_transform.hpp"
namespace uni {
namespace superset_transform {
template<std::ranges::random_access_range R, std::unsigned_integral Bit = std::uint32_t>
void zeta(R& range) {
const auto n = std::ranges::size(range);
assert(std::has_single_bit(n));
for(Bit i = 1; i < n; i <<= 1) {
for(Bit j = 0; j < n; ++j) {
if((j & i) == 0) {
range[j] += range[j | i];
}
}
}
}
template<std::ranges::random_access_range R, std::unsigned_integral Bit = std::uint32_t>
void mobius(R& range) {
const auto n = std::ranges::size(range);
assert(std::has_single_bit(n));
for(Bit i = 1; i < n; i <<= 1) {
for(Bit j = 0; j < n; ++j) {
if((j & i) == 0) {
range[j] -= range[j | i];
}
}
}
}
} // namespace superset_transform
namespace subset_transform {
template<std::ranges::random_access_range R, std::unsigned_integral Bit = std::uint32_t>
void zeta(R& range) {
const auto n = std::ranges::size(range);
assert(std::has_single_bit(n));
for(Bit i = 1; i < n; i <<= 1) {
for(Bit j = 0; j < n; ++j) {
if((j & i) == 0) {
range[j | i] += range[j];
}
}
}
}
template<std::ranges::random_access_range R, std::unsigned_integral Bit = std::uint32_t>
void mobius(R& range) {
const auto n = std::ranges::size(range);
assert(std::has_single_bit(n));
for(Bit i = 1; i < n; i <<= 1) {
for(Bit j = 0; j < n; ++j) {
if((j & i) == 0) {
range[j | i] -= range[j];
}
}
}
}
} // namespace subset_transform
} // namespace uni
#line 2 "include/snippets.hpp"
#line 2 "snippet/fast_io.hpp"
#line 5 "snippet/fast_io.hpp"
#line 7 "snippet/fast_io.hpp"
#ifdef __GNUC__
__attribute__((constructor)) inline void fast_io() noexcept(NO_EXCEPT) { std::ios::sync_with_stdio(false), std::cin.tie(nullptr); }
#else
inline void fast_io() noexcept(NO_EXCEPT) { std::ios::sync_with_stdio(false), std::cin.tie(nullptr); }
#endif
#line 2 "include/views.hpp"
#line 2 "view/repeat.hpp"
#line 8 "view/repeat.hpp"
#line 12 "view/repeat.hpp"
#line 2 "view/internal/box.hpp"
#line 6 "view/internal/box.hpp"
#line 9 "view/internal/box.hpp"
namespace uni {
namespace internal {
#if CPP23
template<class T>
concept boxable = std::copy_constructible<T> && std::is_object_v<T>;
#else
template<class T>
concept boxable = std::copy_constructible<T> && std::is_object_v<T>;
#endif
template<boxable T> struct box : std::optional<T> {
using std::optional<T>::optional;
constexpr box()
noexcept(std::is_nothrow_default_constructible_v<T>)
requires std::default_initializable<T>
: std::optional<T> { std::in_place }
{}
box(const box&) = default;
box(box&&) = default;
using std::optional<T>::operator=;
constexpr box& operator=(const box& other) noexcept(
std::is_nothrow_copy_constructible_v<T>)
requires(!std::copyable<T>) && std::copy_constructible<T>
{
if(this != std::addressof(other)) {
if((bool)other) this->emplace(*other);
else this->reset();
}
return *this;
}
constexpr box& operator=(box&& other) noexcept(std::is_nothrow_move_constructible_v<T>)
requires(!std::movable<T>)
{
if(this != std::addressof(other)) {
if((bool)other)
this->emplace(std::move(*other));
else
this->reset();
}
return *this;
}
};
template<class T>
concept boxable_copyable =
std::copy_constructible<T> &&
(
std::copyable<T> ||
(std::is_nothrow_move_constructible_v<T> && std::is_nothrow_copy_constructible_v<T>)
);
template<class T>
concept boxable_movable =
(!std::copy_constructible<T>) &&
(std::movable<T> || std::is_nothrow_move_constructible_v<T>);
template<boxable T>
requires boxable_copyable<T> || boxable_movable<T>
struct box<T> {
private:
[[no_unique_address]] T _value = T();
public:
box() requires std::default_initializable<T> = default;
constexpr explicit box(const T& value) noexcept(std::is_nothrow_copy_constructible_v<T>)
requires std::copy_constructible<T>
: _value(value)
{}
constexpr explicit box(T&& value) noexcept(std::is_nothrow_move_constructible_v<T>)
: _value(std::move(value)) {}
template<class... Args>
requires std::constructible_from<T, Args...>
constexpr explicit box(std::in_place_t, Args&&... args) noexcept(std::is_nothrow_constructible_v<T, Args...>)
: _value(std::forward<Args>(args)...) {}
box(const box& ) = default;
box(box&& ) = default;
box& operator=(const box& ) requires std::copyable<T> = default;
box& operator=(box&& ) requires std::movable<T> = default;
constexpr box& operator=(const box& other) noexcept
requires(!std::copyable<T>) && std::copy_constructible<T>
{
static_assert(std::is_nothrow_copy_constructible_v<T>);
if(this != std::addressof(other)) {
this->_value.~T();
std::construct_at(std::addressof(this->_value), *other);
}
return *this;
}
constexpr box& operator=(box&& other) noexcept
requires(!std::movable<T>)
{
static_assert(std::is_nothrow_move_constructible_v<T>);
if(this != std::addressof(other)) {
this->_value.~T();
std::construct_at(std::addressof(this->_value), std::move(*other));
}
return *this;
}
constexpr bool has_value() const noexcept { return true; };
constexpr T& operator*() noexcept { return this->_value; }
constexpr const T& operator*() const noexcept { return this->_value; }
constexpr T* operator->() noexcept { return std::addressof(this->_value); }
constexpr const T* operator->() const noexcept { return std::addressof(this->_value); }
};
} // namespace internal
} // namespace uni
#line 15 "view/repeat.hpp"
#line 18 "view/repeat.hpp"
namespace uni {
template <std::move_constructible T, std::semiregular Bound = std::unreachable_sentinel_t>
requires
std::is_object_v<T> && std::same_as<T, std::remove_cv_t<T>> &&
(
std::is_integral_v<Bound> ||
std::same_as<Bound, std::unreachable_sentinel_t>
)
struct repeat_view : public std::ranges::view_interface<repeat_view<T, Bound>> {
private:
internal::box<T> _value;
[[no_unique_address]] Bound _bound = Bound();
struct iterator;
template <typename Range>
friend constexpr auto take_of_repeat_view(Range&&, std::ranges::range_difference_t<Range>);
template <typename Range>
friend constexpr auto drop_of_repeat_view(Range &&, std::ranges::range_difference_t<Range>);
public:
repeat_view() requires std::default_initializable<T> = default;
constexpr explicit repeat_view(const T& val, Bound bound = Bound())
requires std::copy_constructible<T> : _value(val), _bound(bound) {
if constexpr(!std::same_as<Bound, std::unreachable_sentinel_t>) assert(bound >= 0);
}
constexpr explicit repeat_view(T&& val, Bound bound = Bound())
: _value(std::move(val)), _bound(bound)
{}
template <typename... Args, typename... BoundArgs>
requires std::constructible_from<T, Args...> && std::constructible_from<Bound, BoundArgs...>
constexpr explicit repeat_view(
std::piecewise_construct_t, std::tuple<Args...> args,
std::tuple<BoundArgs...> bound_args = std::tuple<>{}
)
: _value(std::make_from_tuple<T>(std::move(args))),
_bound(std::make_from_tuple<Bound>(std::move(bound_args)))
{}
constexpr iterator begin() const {
return iterator(std::addressof(*this->_value));
}
constexpr iterator end() const
requires(!std::same_as<Bound, std::unreachable_sentinel_t>)
{
return iterator(std::addressof(*this->_value), this->_bound);
}
constexpr std::unreachable_sentinel_t end() const noexcept {
return std::unreachable_sentinel;
}
constexpr auto size() const
requires(!std::same_as<Bound, std::unreachable_sentinel_t>)
{
return to_unsigned(this->_bound);
}
};
template <typename T, typename Bound>
repeat_view(T, Bound) -> repeat_view<T, Bound>;
template <std::move_constructible T, std::semiregular Bound>
requires
std::is_object_v<T> && std::same_as<T, std::remove_cv_t<T>> &&
(std::is_integral_v<Bound> || std::same_as<Bound, std::unreachable_sentinel_t>)
struct repeat_view<T, Bound>::iterator {
private:
using index_type = std::conditional_t<std::same_as<Bound, std::unreachable_sentinel_t>, std::ptrdiff_t, Bound>;
const T* _value = nullptr;
index_type _crrent = index_type();
constexpr explicit iterator(const T* val, index_type bound = index_type())
: _value(val), _crrent(bound)
{
if constexpr(!std::same_as<Bound, std::unreachable_sentinel_t>) assert(bound >= 0);
}
friend repeat_view;
public:
using iterator_concept = std::random_access_iterator_tag;
using iterator_category = std::random_access_iterator_tag;
using value_type = T;
using difference_type =
std::conditional_t<
std::is_integral_v<index_type>,
index_type,
internal::iota_diff_t<index_type>
>;
iterator() = default;
constexpr const T& operator*() const noexcept { return *this->_value; }
constexpr iterator& operator++() {
++this->_crrent;
return *this;
}
constexpr iterator operator++(int) {
auto _tmp = *this;
++*this;
return _tmp;
}
constexpr iterator& operator--() {
if constexpr(!std::same_as<Bound, std::unreachable_sentinel_t>) assert(this->_crrent > 0);
--this->_crrent;
return *this;
}
constexpr iterator operator--(int) {
auto _tmp = *this;
--*this;
return _tmp;
}
constexpr iterator& operator+=(difference_type diff) {
if constexpr(!std::same_as<Bound, std::unreachable_sentinel_t>) assert(this->_crrent + diff >= 0);
this->_crrent += diff;
return *this;
}
constexpr iterator& operator-=(difference_type diff) {
if constexpr(!std::same_as<Bound, std::unreachable_sentinel_t>) assert(this->_crrent - diff >= 0);
this->_crrent -= diff;
return *this;
}
constexpr const T& operator[](difference_type diff) const noexcept {
return *(*this + diff);
}
friend constexpr bool operator==(const iterator& lhs, const iterator& rhs) {
return lhs._crrent == rhs._crrent;
}
friend constexpr auto operator<=>(const iterator& lhs, const iterator& rhs) {
return lhs._crrent <=> rhs._crrent;
}
friend constexpr iterator operator+(iterator itr, difference_type diff) {
return itr += diff;
}
friend constexpr iterator operator+(difference_type diff, iterator itr) {
return itr + diff;
}
friend constexpr iterator operator-(iterator itr, difference_type diff) {
return itr -= diff;
}
friend constexpr difference_type operator-(const iterator& lhs, const iterator& rhs) {
return (
static_cast<difference_type>(lhs._crrent) -
static_cast<difference_type>(rhs._crrent)
);
}
};
namespace views {
namespace internal {
template<typename _Range>
inline constexpr bool is_repeat_view = false;
template <class T, class Bound>
inline constexpr bool is_repeat_view<repeat_view<T, Bound>> = true;
template <class T>
concept can_repeat_view = requires { repeat_view(std::declval<T>()); };
template <class T, class Bound>
concept can_bounded_repeat_view =
requires { repeat_view(std::declval<T>(), std::declval<Bound>()); };
} // namespace internal
struct Repeat {
template <class T>
requires internal::can_repeat_view<T>
constexpr auto operator() [[nodiscard]] (T&& val) const {
return repeat_view(std::forward<T>(val));
}
template <class T, class Bound>
requires internal::can_bounded_repeat_view<T, Bound>
constexpr auto operator()
[[nodiscard]] (T&& val, Bound bound) const {
return repeat_view(std::forward<T>(val), bound);
}
};
inline constexpr Repeat repeat;
namespace internal {
template<class Range>
constexpr auto take_of_repeat_view(Range&& range, std::ranges::range_difference_t<Range> diff) {
using T = std::remove_cvref_t<Range>;
static_assert(is_repeat_view<T>);
if constexpr(std::ranges::sized_range<T>) return views::repeat(*range._value, std::min(std::ranges::distance(range), diff));
else return views::repeat(*range._value, diff);
}
template<class Range>
constexpr auto drop_of_repeat_view(Range&& range, std::ranges::range_difference_t<Range> diff) {
using T = std::remove_cvref_t<Range>;
static_assert(is_repeat_view<T>);
if constexpr(std::ranges::sized_range<T>) {
auto size = std::ranges::distance(range);
return views::repeat(*range._value, size - std::min(size, diff));
}
else {
return range;
}
}
} // namespace internal
} // namespace views
} // namespace uni
#line 2 "view/slide.hpp"
#line 6 "view/slide.hpp"
#line 9 "view/slide.hpp"
#line 11 "view/slide.hpp"
namespace uni {
namespace internal {
template<class View>
concept slide_caches_nothing = std::ranges::random_access_range<View> && std::ranges::sized_range<View>;
template<class View>
concept slide_caches_last = !slide_caches_nothing<View> && std::ranges::bidirectional_range<View> && std::ranges::common_range<View>;
template<class View>
concept slide_caches_first = !slide_caches_nothing<View> && !slide_caches_last<View>;
} // namespace internal
template<std::ranges::forward_range View>
requires std::ranges::view<View>
struct slide_view : std::ranges::view_interface<slide_view<View>> {
private:
View _base;
std::ranges::range_difference_t<View> _n;
[[no_unique_address]] internal::maybe_present_t<internal::slide_caches_first<View>, internal::cached_position<View>, 0> _cache_begin;
[[no_unique_address]] internal::maybe_present_t<internal::slide_caches_last<View>, internal::cached_position<View>, 1> _cache_end;
template<bool> struct iterator;
struct sentinel;
public:
constexpr explicit slide_view(View base, std::ranges::range_difference_t<View> n)
: _base(std::move(base)), _n(n)
{
assert(n > 0);
}
constexpr auto begin()
requires(!(internal::simple_view<View> && internal::slide_caches_nothing<const View>))
{
if constexpr(internal::slide_caches_first<View>) {
std::ranges::iterator_t<View> itr;
if(this->_cache_begin.has_value()) {
itr = this->_cache_begin.get(this->_base);
}
else {
itr = std::ranges::next(std::ranges::begin(this->_base), this->_n - 1, std::ranges::end(this->_base));
this->_cache_begin.set(this->_base, itr);
}
return iterator<false>(std::ranges::begin(this->_base), std::move(itr), this->_n);
}
else {
return iterator<false>(std::ranges::begin(this->_base), this->_n);
}
}
constexpr auto begin() const
requires internal::slide_caches_nothing<const View>
{
return iterator<true>(std::ranges::begin(this->_base), this->_n);
}
constexpr auto end()
requires (!(internal::simple_view<View> && internal::slide_caches_nothing<const View>))
{
if constexpr(internal::slide_caches_nothing<View>) {
return iterator<false>(std::ranges::begin(this->_base) + std::ranges::range_difference_t<View>(this->size()), this->_n);
}
else if constexpr(internal::slide_caches_last<View>) {
std::ranges::iterator_t<View> itr;
if(this->_cache_end.has_value()) {
itr = this->_cache_end.get(this->_base);
}
else {
itr = std::ranges::prev(std::ranges::end(this->_base), this->_n - 1, std::ranges::begin(this->_base));
this->_cache_end.set(this->_base, itr);
}
return iterator<false>(std::move(itr), this->_n);
}
else if constexpr(std::ranges::common_range<View>) {
return iterator<false>(std::ranges::end(this->_base), std::ranges::end(this->_base), this->_n);
}
else {
return sentinel(std::ranges::end(this->_base));
}
}
constexpr auto end() const
requires internal::slide_caches_nothing<const View>
{
return this->begin() + std::ranges::range_difference_t<const View>(this->size());
}
constexpr auto size()
requires std::ranges::sized_range<View>
{
auto size = std::ranges::distance(this->_base) - this->_n + 1;
if(size < 0) size = 0;
return to_unsigned(size);
}
constexpr auto size() const
requires std::ranges::sized_range<const View>
{
auto size = std::ranges::distance(this->_base) - this->_n + 1;
if(size < 0) size = 0;
return to_unsigned(size);
}
};
template<class Range>
slide_view(Range &&, std::ranges::range_difference_t<Range>) -> slide_view<std::views::all_t<Range>>;
template<std::ranges::forward_range View>
requires std::ranges::view<View>
template<bool CONST>
struct slide_view<View>::iterator {
private:
using Base = internal::maybe_const_t<CONST, View>;
static constexpr bool LAST_PRESENT = internal::slide_caches_first<Base>;
std::ranges::iterator_t<Base> _current = std::ranges::iterator_t<Base>();
[[no_unique_address]] internal::maybe_present_t<LAST_PRESENT, std::ranges::iterator_t<Base>> _last = decltype(_last)();
std::ranges::range_difference_t<Base> _n = 0;
constexpr iterator(std::ranges::iterator_t<Base> current, std::ranges::range_difference_t<Base> n)
requires (!LAST_PRESENT)
: _current(current), _n(n)
{}
constexpr iterator(std::ranges::iterator_t<Base> current, std::ranges::iterator_t<Base> last, std::ranges::range_difference_t<Base> n)
requires (LAST_PRESENT)
: _current(current), _last(last), _n(n)
{}
friend slide_view;
friend slide_view::sentinel;
public:
using iterator_category = std::input_iterator_tag;
using iterator_concept = internal::most_primitive_iterator_concept<false, Base>;
using value_type = decltype(std::views::counted(_current, _n));
using difference_type = std::ranges::range_difference_t<Base>;
iterator() = default;
constexpr iterator(iterator<!CONST> itr)
requires CONST && std::convertible_to<std::ranges::iterator_t<View>, std::ranges::iterator_t<Base>>
: _current(std::move(itr._current)), _n(itr._n)
{}
constexpr auto operator*() const {
return std::views::counted(_current, _n);
}
constexpr iterator &operator++() {
++this->_current;
if constexpr(LAST_PRESENT) ++this->_last;
return *this;
}
constexpr iterator operator++(int) {
const auto temp = *this;
return ++*this, temp;
}
constexpr iterator &operator--()
requires std::ranges::bidirectional_range<Base>
{
--this->_current;
if constexpr(LAST_PRESENT) --this->_last;
return *this;
}
constexpr iterator operator--(int)
requires std::ranges::bidirectional_range<Base>
{
auto temp = *this;
return --*this, temp;
}
constexpr iterator &operator+=(const difference_type rhs)
requires std::ranges::random_access_range<Base>
{
this->_current += rhs;
if constexpr(LAST_PRESENT) this->_last += rhs;
return *this;
}
constexpr iterator &operator-=(const difference_type rhs)
requires std::ranges::random_access_range<Base>
{
this->_current -= rhs;
if constexpr(LAST_PRESENT) this->_last -= rhs;
return *this;
}
constexpr auto operator[](const difference_type count) const
requires std::ranges::random_access_range<Base>
{
return std::views::counted(this->_current + count, this->_n);
}
friend constexpr bool operator==(const iterator &lhs, const iterator &rhs) {
if constexpr(LAST_PRESENT) return lhs._last == rhs._last;
else return lhs._current == rhs._current;
}
friend constexpr auto operator<=>(const iterator &lhs, const iterator &rhs)
requires std::ranges::random_access_range<Base> && std::three_way_comparable<std::ranges::iterator_t<Base>>
{
return lhs._current <=> rhs._current;
}
friend constexpr iterator operator+(iterator itr, const difference_type count)
requires std::ranges::random_access_range<Base>
{
auto res = itr;
return res += count, res;
}
friend constexpr iterator operator+(const difference_type count, const iterator &itr)
requires std::ranges::random_access_range<Base>
{
auto res = itr;
return res += count, res;
}
friend constexpr iterator operator-(const iterator &itr, difference_type count)
requires std::ranges::random_access_range<Base>
{
auto res = itr;
return res -= count, res;
}
friend constexpr difference_type operator-(const iterator &lhs, const iterator &rhs)
requires std::sized_sentinel_for<std::ranges::iterator_t<Base>, std::ranges::iterator_t<Base>>
{
if constexpr(LAST_PRESENT) return lhs._last - rhs._last;
else return lhs._current - rhs._current;
}
};
template<std::ranges::forward_range View>
requires std::ranges::view<View>
struct slide_view<View>::sentinel {
private:
std::ranges::sentinel_t<View> _end = std::ranges::sentinel_t<View>();
constexpr explicit sentinel(std::ranges::sentinel_t<View> end) : _end(end) {}
friend slide_view;
public:
sentinel() = default;
friend constexpr bool operator==(const iterator<false> &lhs, const sentinel &rhs) {
return lhs._last == rhs._end;
}
friend constexpr std::ranges::range_difference_t<View>
operator-(const iterator<false> &lhs, const sentinel &rhs)
requires std::sized_sentinel_for<std::ranges::sentinel_t<View>, std::ranges::iterator_t<View>>
{
return lhs._last - rhs._end;
}
friend constexpr std::ranges::range_difference_t<View>
operator-(const sentinel &rhs, const iterator<false> &lhs)
requires std::sized_sentinel_for<std::ranges::sentinel_t<View>, std::ranges::iterator_t<View>>
{
return rhs._end - lhs._last;
}
};
namespace views {
namespace internal {
template<class Range, class Diff>
concept can_slide_view = requires { slide_view(std::declval<Range>(), std::declval<Diff>()); };
} // namespace internal
struct Slide : adaptor::range_adaptor<Slide> {
template<std::ranges::viewable_range Range, class Diff = std::ranges::range_difference_t<Range>>
requires internal::can_slide_view<Range, Diff>
constexpr auto operator() [[nodiscard]] (Range &&res, std::type_identity_t<Diff> n) const {
return slide_view(std::forward<Range>(res), n);
}
using adaptor::range_adaptor<Slide>::operator();
static constexpr int arity = 2;
static constexpr bool has_simple_extra_args = true;
};
inline constexpr Slide slide;
} // namespace views
} // namespace uni
namespace std::ranges {
template<class View>
inline constexpr bool enable_borrowed_range<uni::slide_view<View>> = enable_borrowed_range<View>;
}
#line 2 "view/stride.hpp"
#line 8 "view/stride.hpp"
#line 12 "view/stride.hpp"
#line 14 "view/stride.hpp"
#line 16 "view/stride.hpp"
namespace uni {
template<std::ranges::input_range View>
requires std::ranges::view<View>
struct stride_view : std::ranges::view_interface<stride_view<View>> {
private:
View _base;
std::ranges::range_difference_t<View> _stride;
template<bool Const> using Base = internal::maybe_const_t<Const, View>;
template<bool Const> struct iterator_tag {};
template<bool Const>
requires std::ranges::forward_range<Base<Const>>
struct iterator_tag<Const> {
private:
static constexpr auto _iterator_category() noexcept {
using category = typename std::iterator_traits<std::ranges::iterator_t<Base<Const>>>::iterator_category;
if constexpr(std::derived_from<category, std::random_access_iterator_tag>)
return std::random_access_iterator_tag{};
else
return category{};
}
public:
using iterator_category = decltype(_iterator_category());
};
public:
template<bool> class iterator;
constexpr explicit stride_view(View base, const std::ranges::range_difference_t<View> stride) noexcept(NO_EXCEPT)
: _base(std::move(base)), _stride(stride) { assert(stride > 0); }
inline constexpr View base() const & noexcept(NO_EXCEPT) requires std::copy_constructible<View>
{
return this->_base;
}
inline constexpr View base() && noexcept(NO_EXCEPT) { return std::move(this->_base); }
inline constexpr std::ranges::range_difference_t<View> stride() const noexcept {
return this->_stride;
}
inline constexpr auto begin() noexcept(NO_EXCEPT)
requires(!internal::simple_view<View>)
{
return iterator<false>(this, std::ranges::begin(this->_base));
}
inline constexpr auto begin() const noexcept(NO_EXCEPT)
requires std::ranges::range<const View>
{
return iterator<true>(this, std::ranges::begin(this->_base));
}
inline constexpr auto end() noexcept(NO_EXCEPT)
requires(!internal::simple_view<View>)
{
if constexpr(std::ranges::common_range<View> && std::ranges::sized_range<View> &&
std::ranges::forward_range<View>) {
const auto missing = (this->_stride - std::ranges::distance(this->_base) % this->_stride) % this->_stride;
return iterator<false>(this, std::ranges::end(this->_base), missing);
} else if constexpr(std::ranges::common_range<View> && !std::ranges::bidirectional_range<View>)
return iterator<false>(this, std::ranges::end(this->_base));
else
return std::default_sentinel;
}
inline constexpr auto end() const noexcept(NO_EXCEPT)
requires std::ranges::range<const View>
{
if constexpr(std::ranges::common_range<const View> && std::ranges::sized_range<const View> && std::ranges::forward_range<const View>)
{
const auto missing = (this->_stride - std::ranges::distance(this->_base) % this->_stride) % this->_stride;
return iterator<true>(this, std::ranges::end(this->_base), missing);
}
else if constexpr(std::ranges::common_range<const View> && !std::ranges::bidirectional_range<const View>)
return iterator<true>(this, std::ranges::end(this->_base));
else
return std::default_sentinel;
}
inline constexpr auto size() noexcept(NO_EXCEPT)
requires std::ranges::sized_range<View>
{
return to_unsigned(div_ceil(std::ranges::distance(this->_base), this->_stride));
}
inline constexpr auto size() const noexcept(NO_EXCEPT)
requires std::ranges::sized_range<const View>
{
return to_unsigned(div_ceil(std::ranges::distance(this->_base), this->_stride));
}
};
template<class Range>
stride_view(Range&& , std::ranges::range_difference_t<Range>) -> stride_view<std::views::all_t<Range>>;
template<std::ranges::input_range View>
requires std::ranges::view<View>
template<bool Const>
struct stride_view<View>::iterator : iterator_tag<Const> {
private:
using Parent = internal::maybe_const_t<Const, stride_view>;
using Base = stride_view::Base<Const>;
std::ranges::iterator_t<Base> _current = std::ranges::iterator_t<Base>();
std::ranges::sentinel_t<Base> _end = std::ranges::sentinel_t<Base>();
std::ranges::range_difference_t<Base> _stride = 0;
std::ranges::range_difference_t<Base> _missing = 0;
constexpr iterator(Parent *const parent, const std::ranges::iterator_t<Base> current, const std::ranges::range_difference_t<Base> missing = 0) noexcept(NO_EXCEPT)
: _current(std::move(current)), _end(std::ranges::end(parent->_base)), _stride(parent->_stride), _missing(missing)
{}
friend stride_view;
public:
using difference_type = std::ranges::range_difference_t<Base>;
using value_type = std::ranges::range_value_t<Base>;
using iterator_concept = typename internal::iterator_concept<Base>;
iterator() noexcept(NO_EXCEPT) requires std::default_initializable<std::ranges::iterator_t<Base>> = default;
constexpr iterator(iterator<!Const> itr) noexcept(NO_EXCEPT)
requires
Const && std::convertible_to<std::ranges::iterator_t<View>, std::ranges::iterator_t<Base>> &&
std::convertible_to<std::ranges::sentinel_t<View>, std::ranges::sentinel_t<Base>>
: _current(std::move(itr._current)), _end(std::move(itr._end)), _stride(itr._stride), _missing(itr._missing)
{}
inline constexpr std::ranges::iterator_t<Base> base() && noexcept(NO_EXCEPT) { return std::move(this->_current); }
inline constexpr const std::ranges::iterator_t<Base>& base() const & noexcept {
return this->_current;
}
inline constexpr decltype(auto) operator*() const noexcept(NO_EXCEPT)
{
return *this->_current;
}
inline constexpr iterator& operator++() noexcept(NO_EXCEPT)
{
assert(this->_current != _end);
this->_missing = std::ranges::advance(this->_current, this->_stride, this->_end);
return *this;
}
inline constexpr void operator++(int) noexcept(NO_EXCEPT) { ++*this; }
inline constexpr iterator operator++(int) noexcept(NO_EXCEPT)
requires std::ranges::forward_range<Base>
{
const auto res = *this; ++*this; return res;
}
inline constexpr iterator& operator--() noexcept(NO_EXCEPT)
requires std::ranges::bidirectional_range<Base>
{
std::ranges::advance(this->_current, this->_missing - this->_stride);
this->_missing = 0;
return *this;
}
inline constexpr iterator operator--(int) noexcept(NO_EXCEPT)
requires std::ranges::bidirectional_range<Base>
{
const auto res = *this; --*this; return res;
}
inline constexpr iterator& operator+=(const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
if(diff > 0) {
assert(std::ranges::distance(this->_current, this->_end) > this->_stride * (diff - 1));
this->_missing = std::ranges::advance(this->_current, this->_stride * diff, this->_end);
}
if(diff < 0) {
std::ranges::advance(this->_current, this->_stride * diff + this->_missing);
this->_missing = 0;
}
return *this;
}
inline constexpr iterator& operator-=(const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
return *this += -diff;
}
inline constexpr decltype(auto) operator[](const difference_type diff) const noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
return *(*this + diff);
}
friend inline constexpr bool operator==(const iterator& lhs, std::default_sentinel_t) noexcept(NO_EXCEPT)
{
return lhs._current == lhs._end;
}
friend inline constexpr bool operator==(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires std::equality_comparable<std::ranges::iterator_t<Base>>
{
return lhs._current == rhs._current;
}
friend inline constexpr auto operator<=>(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base> && std::three_way_comparable<std::ranges::iterator_t<Base>>
{
return lhs._current <=> rhs._current;
}
friend inline constexpr iterator operator+(const iterator& itr, const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
auto res = itr; res += diff; return res;
}
friend inline constexpr iterator operator+(const difference_type diff, const iterator& itr) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
return itr + diff;
}
friend inline constexpr iterator operator-(const iterator& itr, const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<Base>
{
auto res = itr; res -= diff; return res;
}
friend inline constexpr const difference_type operator-(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires std::sized_sentinel_for<std::ranges::iterator_t<Base>, std::ranges::iterator_t<Base>>
{
const auto diff = lhs._current - rhs._current;
if constexpr(std::ranges::forward_range<Base>)
return (diff + lhs._missing - rhs._missing) / lhs._stride;
else if(diff < 0)
return -div_ceil(-diff, lhs._stride);
else
return div_ceil(diff, lhs._stride);
}
friend inline constexpr const difference_type operator-(std::default_sentinel_t, const iterator& rhs) noexcept(NO_EXCEPT)
requires std::sized_sentinel_for<std::ranges::sentinel_t<Base>, std::ranges::iterator_t<Base>>
{
return div_ceil(rhs._end - rhs._current, rhs._stride);
}
friend inline constexpr const difference_type operator-(const iterator& lhs, std::default_sentinel_t rhs) noexcept(NO_EXCEPT)
requires std::sized_sentinel_for<std::ranges::sentinel_t<Base>, std::ranges::iterator_t<Base>>
{
return -(rhs - lhs);
}
friend inline constexpr std::ranges::range_rvalue_reference_t<Base> iter_move(const iterator& itr) noexcept(NO_EXCEPT)
{
return std::ranges::iter_move(itr._current);
}
friend inline constexpr void iter_swap(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires std::indirectly_swappable<std::ranges::iterator_t<Base>>
{
std::ranges::iter_swap(lhs._current, rhs._current);
}
};
namespace views {
namespace internal {
template<class Range, class T>
concept can_stride_view = requires { stride_view(std::declval<Range>(), std::declval<T>()); };
}
struct Stride : adaptor::range_adaptor<Stride> {
template<std::ranges::viewable_range Range, class T = std::ranges::range_difference_t<Range>>
requires internal::can_stride_view<Range, T>
inline constexpr auto operator() [[nodiscard]] (Range&& res, std::type_identity_t<T> diff) const
{
return stride_view(std::forward<Range>(res), diff);
}
using adaptor::range_adaptor<Stride>::operator();
static constexpr int arity = 2;
static constexpr bool has_simple_call_op = true;
};
inline constexpr Stride stride;
} // namespace views
} // namespace uni
namespace std::ranges {
template<class View>
inline constexpr bool enable_borrowed_range<uni::stride_view<View>> = enable_borrowed_range<View>;
} // namespace std::ranges
#line 2 "view/zip.hpp"
#line 7 "view/zip.hpp"
#line 9 "view/zip.hpp"
#line 14 "view/zip.hpp"
namespace uni {
template<std::ranges::input_range... Views> requires(std::ranges::view<Views> && ...) && (sizeof...(Views) > 0)
struct zip_view : std::ranges::view_interface<zip_view<Views...>> {
private:
std::tuple<Views...> _views;
public:
template<bool> struct iterator;
template<bool> struct sentinel;
zip_view() = default;
constexpr explicit zip_view(Views... views) noexcept(NO_EXCEPT) : _views(std::move(views)...) {}
constexpr auto begin() noexcept(NO_EXCEPT) requires(!(internal::simple_view<Views> && ...))
{
return iterator<false>(tuple_transform(std::ranges::begin, this->_views));
}
constexpr auto begin() const noexcept(NO_EXCEPT) requires(std::ranges::range<const Views> && ...)
{
return iterator<true>(tuple_transform(std::ranges::begin, this->_views));
}
constexpr auto end() noexcept(NO_EXCEPT) requires(!(internal::simple_view<Views> && ...))
{
if constexpr(!internal::zip_is_common<Views...>)
return sentinel<false>(tuple_transform(std::ranges::end, this->_views));
else if constexpr((std::ranges::random_access_range<Views> && ...))
return begin() + std::iter_difference_t<iterator<false>>(this->size());
else
return iterator<false>(tuple_transform(std::ranges::end, this->_views));
}
constexpr auto end() const noexcept(NO_EXCEPT) requires(std::ranges::range<const Views> && ...)
{
if constexpr(!internal::zip_is_common<const Views...>)
return sentinel<true>(tuple_transform(std::ranges::end, this->_views));
else if constexpr((std::ranges::random_access_range<const Views> && ...))
return this->begin() + std::iter_difference_t<iterator<true>>(this->size());
else
return iterator<true>(tuple_transform(std::ranges::end, _views));
}
constexpr auto size() noexcept(NO_EXCEPT) requires(std::ranges::sized_range<Views> && ...)
{
return std::apply(
[](auto... sizes)
{
using size_type = std::make_unsigned_t<std::common_type_t<decltype(sizes)...>>;
return uni::min(size_type(sizes)...);
},
tuple_transform(std::ranges::size, _views)
);
}
constexpr auto size() const noexcept(NO_EXCEPT) requires(std::ranges::sized_range<const Views> && ...)
{
return std::apply(
[](auto... sizes)
{
using size_type = std::make_unsigned_t<std::common_type_t<decltype(sizes)...>>;
return uni::min(size_type(sizes)...);
},
tuple_transform(std::ranges::size, _views)
);
}
};
template<class... Ranges> zip_view(Ranges &&...) -> zip_view<std::views::all_t<Ranges>...>;
namespace internal {
template<class iterator>
constexpr const typename iterator::iterator_collection& get_current(const iterator& itr) noexcept(NO_EXCEPT);
} // namespace internal
template<std::ranges::input_range... Views> requires(std::ranges::view<Views> && ...) && (sizeof...(Views) > 0)
template<bool Const>
struct zip_view<Views...>::iterator
: internal::zip_view_iterator_category<Const, Views...> {
using iterator_collection = internal::tuple_or_pair_t<
std::ranges::iterator_t<internal::maybe_const_t<Const, Views>>...
>;
private:
friend struct zip_view;
template<bool> friend struct zip_view::sentinel;
iterator_collection _current;
constexpr explicit iterator(decltype(_current) current) : _current(std::move(current)) {}
// template<std::copy_constructible F, std::ranges::input_range... Vs>
// requires
// (std::ranges::view<Vs> && ...) && (sizeof...(Vs) > 0) && std::is_object_v<F> &&
// std::regular_invocable<F&, std::ranges::range_reference_t<Vs>...> &&
// internal::can_reference<std::invoke_result_t<F&, std::ranges::range_reference_t<Vs>...>>
// friend struct zip_transform_view;
public:
using iterator_concept = internal::most_primitive_iterator_concept<Const, Views...>;
using value_type = internal::tuple_or_pair_t<std::ranges::range_value_t<internal::maybe_const_t<Const, Views>>...>;
using difference_type = std::common_type_t<std::ranges::range_difference_t<internal::maybe_const_t<Const, Views>>...>;
iterator() = default;
constexpr iterator(iterator<!Const> itr) noexcept(NO_EXCEPT)
requires Const &&
(
std::convertible_to<
std::ranges::iterator_t<Views>,
std::ranges::iterator_t<internal::maybe_const_t<Const, Views>>
> && ...
)
: _current(std::move(itr._current))
{}
constexpr auto operator*() const noexcept(NO_EXCEPT) {
const auto f = [](auto &itr) -> decltype(auto) { return *itr; };
return tuple_transform(f, this->_current);
}
constexpr iterator& operator++() noexcept(NO_EXCEPT) {
tuple_for_each([](auto &itr) { ++itr; }, this->_current);
return *this;
}
constexpr void operator++(int) noexcept(NO_EXCEPT) { ++*this; }
constexpr iterator operator++(int) noexcept(NO_EXCEPT)
requires internal::all_forward<Const, Views...>
{
const auto res = *this; ++*this; return res;
}
constexpr iterator& operator--() noexcept(NO_EXCEPT)
requires internal::all_bidirectional<Const, Views...>
{
tuple_for_each([](auto &itr) { --itr; }, this->_current);
return *this;
}
constexpr iterator operator--(int) noexcept(NO_EXCEPT)
requires internal::all_bidirectional<Const, Views...>
{
const auto res = *this; --*this; return res;
}
constexpr iterator& operator+=(const difference_type diff) noexcept(NO_EXCEPT)
requires internal::all_random_access<Const, Views...>
{
const auto f = [&]<class Itr>(Itr& itr) constexpr noexcept(NO_EXCEPT) {
itr += std::iter_difference_t<Itr>(diff);
};
tuple_for_each(f, this->_current);
return *this;
}
constexpr iterator& operator-=(const difference_type diff) noexcept(NO_EXCEPT)
requires internal::all_random_access<Const, Views...>
{
const auto f = [&]<class Itr>(Itr& itr) constexpr noexcept(NO_EXCEPT) {
itr -= std::iter_difference_t<Itr>(diff);
};
tuple_for_each(f, this->_current);
return *this;
}
constexpr auto operator[](const difference_type diff) const noexcept(NO_EXCEPT)
requires internal::all_random_access<Const, Views...>
{
const auto f = [&]<class Itr>(Itr& itr) constexpr noexcept(NO_EXCEPT) -> decltype(auto) {
return itr[std::iter_difference_t<Itr>(diff)];
};
return tuple_transform(f, _current);
}
friend constexpr bool operator==(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires (
std::equality_comparable<
std::ranges::iterator_t<internal::maybe_const_t<Const, Views>>
> && ...
)
{
if constexpr(internal::all_bidirectional<Const, Views...>)
return lhs._current == rhs._current;
else
return [&]<std::size_t... Is>(std::index_sequence<Is...>) constexpr noexcept(NO_EXCEPT) {
return (
(std::get<Is>(lhs._current) == std::get<Is>(rhs._current)) || ...
);
}(std::make_index_sequence<sizeof...(Views)>{});
}
friend constexpr auto operator<=>(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires internal::all_random_access<Const, Views...>
{
return lhs._current <=> rhs._current;
}
friend constexpr iterator operator+(const iterator& itr, const difference_type diff) noexcept(NO_EXCEPT)
requires internal::all_random_access<Const, Views...>
{
auto res = itr; res += diff; return res;
}
friend constexpr iterator operator+(const difference_type diff, const iterator& itr) noexcept(NO_EXCEPT)
requires internal::all_random_access<Const, Views...>
{
auto res = itr; res += diff; return res;
}
friend constexpr iterator operator-(const iterator& itr, const difference_type diff) noexcept(NO_EXCEPT)
requires internal::all_random_access<Const, Views...>
{
auto res = itr; res -= diff; return res;
}
friend constexpr difference_type operator-(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires (
std::sized_sentinel_for<
std::ranges::iterator_t<internal::maybe_const_t<Const, Views>>,
std::ranges::iterator_t<internal::maybe_const_t<Const, Views>>
> && ...
)
{
return [&]<std::size_t... Is>(std::index_sequence<Is...>) constexpr noexcept(NO_EXCEPT) {
return std::ranges::min(
{
difference_type(std::get<Is>(lhs._current) - std::get<Is>(rhs._current)) ...
},
std::ranges::less{},
[](const difference_type diff) constexpr noexcept(NO_EXCEPT) {
return to_unsigned(diff < 0 ? -diff : diff);
}
);
}(std::make_index_sequence<sizeof...(Views)>{});
}
friend constexpr auto iter_move(const iterator& itr) noexcept(NO_EXCEPT) {
return tuple_transform(std::ranges::iter_move, itr._current);
}
friend constexpr void iter_swap(const iterator& lhs, const iterator& res) noexcept(NO_EXCEPT)
requires (
std::indirectly_swappable<
std::ranges::iterator_t<internal::maybe_const_t<Const, Views>>
> && ...
)
{
[&]<std::size_t... Is>(std::index_sequence<Is...>) constexpr noexcept(NO_EXCEPT) {
(
std::ranges::iter_swap(std::get<Is>(lhs._current), std::get<Is>(res._current)), ...
);
}(std::make_index_sequence<sizeof...(Views)>{});
}
template<class Itr> friend constexpr const typename Itr::iterator_collection& internal::get_current(const Itr&) noexcept(NO_EXCEPT);
};
template<class iterator>
constexpr const typename iterator::iterator_collection& internal::get_current(const iterator& itr) noexcept(NO_EXCEPT) { return itr._current; };
template<std::ranges::input_range... Views> requires(std::ranges::view<Views> && ...) && (sizeof...(Views) > 0)
template<bool Const>
struct zip_view<Views...>::sentinel {
friend struct zip_view;
template<bool> friend struct zip_view::iterator;
using sentinel_collection = internal::tuple_or_pair_t<
std::ranges::sentinel_t<internal::maybe_const_t<Const, Views>>...
>;
sentinel_collection _end;
constexpr explicit sentinel(sentinel_collection end) noexcept(NO_EXCEPT) : _end(end) {}
public:
sentinel() = default;
constexpr sentinel(sentinel<!Const> itr) noexcept(NO_EXCEPT)
requires Const &&
(
std::convertible_to<
std::ranges::sentinel_t<Views>,
std::ranges::sentinel_t<internal::maybe_const_t<Const, Views>>
> && ...
)
: _end(std::move(itr._end))
{}
template<bool Const_>
requires (
std::sentinel_for<
std::ranges::sentinel_t<internal::maybe_const_t<Const, Views>>,
std::ranges::iterator_t<internal::maybe_const_t<Const_, Views>>
> && ...
)
friend constexpr bool operator==(const iterator<Const_>& lhs, const sentinel& rhs) noexcept(NO_EXCEPT)
{
return [&]<std::size_t... Is>(std::index_sequence<Is...>) constexpr noexcept(NO_EXCEPT) {
return (
(std::get<Is>(internal::get_current(lhs)) == std::get<Is>(rhs._end)) || ...);
}(std::make_index_sequence<sizeof...(Views)>{});
}
template<bool Const_>
requires (
std::sized_sentinel_for<
std::ranges::sentinel_t<internal::maybe_const_t<Const, Views>>,
std::ranges::iterator_t<internal::maybe_const_t<Const_, Views>>
> && ...
)
friend constexpr auto operator-(const iterator<Const_>& lhs, const sentinel& rhs) noexcept(NO_EXCEPT)
{
using return_type = std::common_type_t<std::ranges::range_difference_t<internal::maybe_const_t<Const_, Views>>...>;
return [&]<std::size_t... Is>(std::index_sequence<Is...>) constexpr noexcept(NO_EXCEPT) {
return std::ranges::min(
{ return_type(std::get<Is>(internal::get_current(lhs)) - std::get<Is>(rhs._end))... },
std::ranges::less{},
[](const return_type diff) {
return to_unsigned(diff < 0 ? -diff : diff);
}
);
}(std::make_index_sequence<sizeof...(Views)>{});
}
template<bool Const_>
requires (
std::sized_sentinel_for<
std::ranges::sentinel_t<internal::maybe_const_t<Const, Views>>,
std::ranges::iterator_t<internal::maybe_const_t<Const_, Views>>
> && ...
)
friend constexpr auto operator-(const sentinel &lhs, const iterator<Const_>& rhs) noexcept(NO_EXCEPT)
{
return -(rhs - lhs);
}
};
namespace views {
namespace internal {
template<class... Ts>
concept can_zip_view = requires { zip_view<std::views::all_t<Ts>...>(std::declval<Ts>()...); };
} // namespace internal
struct Zip {
template<class... Ts> requires(sizeof...(Ts) == 0 || internal::can_zip_view<Ts...>)
constexpr auto operator() [[nodiscard]] (Ts&&... vs) const {
if constexpr(sizeof...(Ts) == 0) return std::views::empty<std::tuple<>>;
else return zip_view<std::views::all_t<Ts>...>(std::forward<Ts>(vs)...);
}
};
inline constexpr Zip zip;
} // namespace views
} // namespace uni.
namespace std::ranges {
template<class... Views>
inline constexpr bool enable_borrowed_range<uni::zip_view<Views...>> = (enable_borrowed_range<Views> && ...);
}
#line 15 "include/all.hpp"
#line 2 "random/adaptor.hpp"
#line 6 "random/adaptor.hpp"
#line 8 "random/adaptor.hpp"
namespace uni {
template<class Engine>
struct random_adaptor {
using result_type = typename Engine::result_type;
using signed_result_type = typename std::make_signed_t<result_type>;
private:
Engine engine;
public:
static constexpr result_type MIN = Engine::min();
static constexpr result_type MAX = Engine::max();
static constexpr result_type min() noexcept(NO_EXCEPT) { return MIN; }
static constexpr result_type max() noexcept(NO_EXCEPT) { return MAX; }
constexpr random_adaptor(unsigned long seed = 3141592653UL) noexcept(NO_EXCEPT) { this->engine.seed(seed); };
inline constexpr result_type operator()() noexcept(NO_EXCEPT) {
return this->engine();
}
inline constexpr result_type operator()(const result_type sup) noexcept(NO_EXCEPT) {
assert(0 < sup);
return this->engine() % sup;
}
inline constexpr signed_result_type operator()(const signed_result_type min, const signed_result_type sup) noexcept(NO_EXCEPT) {
assert(min < sup);
return min + (*this)(sup - min);
};
template<class T = double>
inline constexpr auto real() noexcept(NO_EXCEPT) {
const auto v = static_cast<T>((this->engine() + 0.5) / (1.0 + this->max()));
return static_cast<T>((this->operator()() + v) / (1.0 + this->max()));
}
};
} // namespace uni
#line 18 "include/all.hpp"
#line 2 "utility/restrictor.hpp"
#line 4 "utility/restrictor.hpp"
#line 6 "utility/restrictor.hpp"
namespace uni {
template<class T, T INF, T SUP>
struct static_restrictor {
using restrictor = static_restrictor;
protected:
T _v = INF;
inline void _clamp() noexcept(NO_EXCEPT) { this->_v = std::clamp(this->_v, INF, SUP); }
inline restrictor& _assign(const T& v) noexcept(NO_EXCEPT) {
this->_v = std::clamp(v, INF, SUP);
return *this;
}
inline restrictor& _assign_raw(const T& v) noexcept(NO_EXCEPT) {
this->_v = v;
return *this;
}
public:
static_restrictor() noexcept(NO_EXCEPT) = default;
static_restrictor(T v) noexcept(NO_EXCEPT) : _v(v) { this->_clamp(); }
inline T val() const noexcept(NO_EXCEPT) { return this->_v; }
static inline static_restrictor raw(const T& v) noexcept(NO_EXCEPT) {
static_restrictor res;
res._assign_raw(v);
return res;
}
restrictor& operator++() noexcept(NO_EXCEPT) { return this->_assign(this->_v + 1); }
restrictor& operator--() noexcept(NO_EXCEPT) { return this->_assign(this->_v - 1); }
restrictor operator++(int) noexcept(NO_EXCEPT) { auto res = *this; return ++(*this), res; }
restrictor operator--(int) noexcept(NO_EXCEPT) { auto res = *this; return --(*this), res; }
restrictor& operator+=(const restrictor& rhs) noexcept(NO_EXCEPT) {
return this->_assign_raw(add_clamp(this->_v, rhs._v, INF, SUP));
}
restrictor& operator-=(const restrictor& rhs) noexcept(NO_EXCEPT) {
return this->_assign_raw(sub_clamp(this->_v, rhs._v, INF, SUP));
}
restrictor& operator*=(const restrictor& rhs) noexcept(NO_EXCEPT) {
return this->_assign_raw(mul_clamp(this->_v, rhs._v, INF, SUP));
}
restrictor& operator/=(const restrictor& rhs) noexcept(NO_EXCEPT) {
return this->_assign(this->_v / rhs.val());
}
restrictor operator+() const noexcept(NO_EXCEPT) { return *this; }
restrictor operator-() const noexcept(NO_EXCEPT) { return restrictor(-this->_v); }
friend restrictor operator+(restrictor lhs, const restrictor& rhs) noexcept(NO_EXCEPT) {
return lhs += rhs;
}
friend restrictor operator-(restrictor lhs, const restrictor& rhs) noexcept(NO_EXCEPT) {
return lhs -= rhs;
}
friend restrictor operator*(restrictor lhs, const restrictor& rhs) noexcept(NO_EXCEPT) {
return lhs *= rhs;
}
friend restrictor operator/(restrictor lhs, const restrictor& rhs) noexcept(NO_EXCEPT) {
return lhs /= rhs;
}
friend bool operator==(const restrictor& lhs, const restrictor& rhs) noexcept(NO_EXCEPT) {
return lhs._v == rhs._v;
}
friend bool operator!=(const restrictor& lhs, const restrictor& rhs) noexcept(NO_EXCEPT) {
return lhs._v != rhs._v;
}
friend bool operator<(const restrictor& lhs, const restrictor& rhs) noexcept(NO_EXCEPT) {
return lhs._v < rhs._v;
}
friend bool operator>(const restrictor& lhs, const restrictor& rhs) noexcept(NO_EXCEPT) {
return lhs._v > rhs._v;
}
friend bool operator<=(const restrictor& lhs, const restrictor& rhs) noexcept(NO_EXCEPT) {
return lhs._v <= rhs._v;
}
friend bool operator>=(const restrictor& lhs, const restrictor& rhs) noexcept(NO_EXCEPT) {
return lhs._v >= rhs._v;
}
friend bool operator<=>(const restrictor& lhs, const restrictor& rhs) noexcept(NO_EXCEPT) {
return lhs._v <=> rhs._v;
}
};
} // namespace uni
namespace std {
template<class T, T INF, T SUP>
T abs(const uni::static_restrictor<T,INF,SUP>& v) noexcept(NO_EXCEPT) { return std::abs(v.val()); }
}
#line 2 "utility/string.hpp"
#line 7 "utility/string.hpp"
#line 10 "utility/string.hpp"
namespace uni {
template<std::input_iterator I, std::sentinel_for<I> S, class Res = std::string>
Res to_lower(I first, S last) noexcept(NO_EXCEPT) {
Res res;
res.reserve(std::ranges::distance(first, last));
std::ranges::transform(first, last, std::back_inserter(res), ::tolower);
return res;
}
template<std::input_iterator I, std::sentinel_for<I> S, class Res = std::string>
Res to_uppwer(I first, S last) noexcept(NO_EXCEPT) {
Res res;
res.reserve(std::ranges::distance(first, last));
std::ranges::transform(first, last, std::back_inserter(res), ::toupper);
return res;
}
template<class Res = std::string>
Res to_lower(const std::string str) noexcept(NO_EXCEPT) {
return to_lower<std::string::const_iterator, std::string::const_iterator, Res>(std::begin(str), std::end(str));
}
template<class Res = std::string>
Res to_uppwer(const std::string str) noexcept(NO_EXCEPT) {
return to_uppwer<std::string::const_iterator, std::string::const_iterator, Res>(std::begin(str), std::end(str));
}
} // namespace uni
#line 2 "utility/timer.hpp"
#line 7 "utility/timer.hpp"
#line 10 "utility/timer.hpp"
namespace uni {
struct timer {
using time_point = std::chrono::milliseconds::rep;
using progress_type = long double;
private:
time_point _time_limit = 0;
progress_type progress_duration = 0;
std::chrono::system_clock::time_point clock_start, clock_end;
public:
timer() noexcept = default;
explicit timer(const time_point time_limit) noexcept(NO_EXCEPT) { this->reset(time_limit); }
inline time_point limit() noexcept(NO_EXCEPT) { return this->_time_limit; }
inline timer& reset() noexcept(NO_EXCEPT) {
this->clock_start = std::chrono::system_clock::now();
this->clock_end = clock_start + std::chrono::milliseconds(this->_time_limit);
return *this;
}
inline timer& reset(const time_point time_limit) noexcept(NO_EXCEPT) {
this->_time_limit = time_limit;
this->progress_duration =
static_cast<progress_type>(
std::chrono::duration_cast<std::chrono::system_clock::duration>(
std::chrono::milliseconds(time_limit)
).count()
);
return this->reset();
}
inline time_point elapsed() const noexcept(NO_EXCEPT) {
return std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now() - this->clock_start).count();
}
inline time_point remaining() const noexcept(NO_EXCEPT) {
return _time_limit - this->elapsed();
}
inline bool expired() const noexcept(NO_EXCEPT) { return this->elapsed() >= _time_limit; }
inline progress_type progress() const noexcept(NO_EXCEPT) {
return std::clamp<progress_type>((std::chrono::system_clock::now() - this->clock_start).count() / this->progress_duration, 0, 1);
}
};
} // namespace uni
#line 23 "include/all.hpp"
#line 25 "include/all.hpp"
#line 28 "include/all.hpp"
#line 12 "verify/aizu-online-judge/itp1_1_a/0001.test.cpp"
static_assert(std::same_as<uni::algebraic::make_opposite_t<uni::algebraic::affine<std::nullptr_t>>, uni::algebraic::opposite<uni::algebraic::affine<std::nullptr_t>>>);
static_assert(std::same_as<uni::algebraic::make_opposite_t<uni::algebraic::make_opposite_t<uni::algebraic::affine<std::nullptr_t>>>, uni::algebraic::affine<std::nullptr_t>>);
static_assert(std::same_as<uni::algebraic::make_opposite_t<uni::algebraic::addition<std::nullptr_t>>, uni::algebraic::addition<std::nullptr_t>>);
signed main() {
print("Hello World");
}
verify/aizu-online-judge/itp1_1_a/0001.test.cpp