結果
| 問題 | No.1431 東大文系数学2020第2問改 |
| ユーザー |
 jell
|
| 提出日時 | 2021-03-14 16:28:49 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 2,933 ms / 5,000 ms |
| コード長 | 63,458 bytes |
| コンパイル時間 | 4,377 ms |
| コンパイル使用メモリ | 272,944 KB |
| 実行使用メモリ | 77,524 KB |
| 最終ジャッジ日時 | 2024-11-06 06:13:56 |
| 合計ジャッジ時間 | 51,375 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,816 KB |
| testcase_01 | AC | 2 ms
6,820 KB |
| testcase_02 | AC | 2 ms
6,820 KB |
| testcase_03 | AC | 2,446 ms
70,512 KB |
| testcase_04 | AC | 2 ms
6,820 KB |
| testcase_05 | AC | 2,839 ms
76,676 KB |
| testcase_06 | AC | 2,628 ms
74,860 KB |
| testcase_07 | AC | 2,727 ms
74,172 KB |
| testcase_08 | AC | 2,679 ms
77,524 KB |
| testcase_09 | AC | 2,843 ms
76,344 KB |
| testcase_10 | AC | 1,985 ms
65,656 KB |
| testcase_11 | AC | 1,949 ms
66,784 KB |
| testcase_12 | AC | 1,998 ms
65,548 KB |
| testcase_13 | AC | 1,399 ms
57,628 KB |
| testcase_14 | AC | 1,397 ms
58,064 KB |
| testcase_15 | AC | 1,474 ms
59,416 KB |
| testcase_16 | AC | 1,675 ms
65,916 KB |
| testcase_17 | AC | 2,043 ms
75,068 KB |
| testcase_18 | AC | 2,043 ms
74,188 KB |
| testcase_19 | AC | 2,788 ms
74,016 KB |
| testcase_20 | AC | 1,944 ms
73,400 KB |
| testcase_21 | AC | 2,301 ms
69,624 KB |
| testcase_22 | AC | 1,124 ms
37,164 KB |
| testcase_23 | AC | 2,814 ms
75,968 KB |
| testcase_24 | AC | 2,933 ms
74,352 KB |
| testcase_25 | AC | 2 ms
6,820 KB |
| testcase_26 | AC | 11 ms
6,820 KB |
| testcase_27 | AC | 2 ms
6,820 KB |
ソースコード
#line 1 "atcoder-workspace/3.cc"
// #undef _GLIBCXX_DEBUG
// #define NDEBUG
#include <bits/extc++.h>
#line 2 "Library/lib/alias"
/**
* @file alias
* @brief Alias
*/
#line 13 "Library/lib/alias"
#line 2 "Library/lib/bit"
#if __cplusplus > 201703L
#include <bit>
#else
#ifndef _GLIBCXX_BIT
#define _GLIBCXX_BIT 1
#include <limits>
#include <type_traits>
namespace std {
template <typename _Tp> constexpr _Tp __rotl(_Tp __x, int __s) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
const int __r = __s % _Nd;
if (__r == 0)
return __x;
else if (__r > 0)
return (__x << __r) | (__x >> ((_Nd - __r) % _Nd));
else
return (__x >> -__r) | (__x << ((_Nd + __r) % _Nd)); // rotr(x, -r)
}
template <typename _Tp> constexpr _Tp __rotr(_Tp __x, int __s) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
const int __r = __s % _Nd;
if (__r == 0)
return __x;
else if (__r > 0)
return (__x >> __r) | (__x << ((_Nd - __r) % _Nd));
else
return (__x << -__r) | (__x >> ((_Nd + __r) % _Nd)); // rotl(x, -r)
}
template <typename _Tp> constexpr int __countl_zero(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return _Nd;
constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u) {
constexpr int __diff = _Nd_u - _Nd;
return __builtin_clz(__x) - __diff;
} else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul) {
constexpr int __diff = _Nd_ul - _Nd;
return __builtin_clzl(__x) - __diff;
} else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull) {
constexpr int __diff = _Nd_ull - _Nd;
return __builtin_clzll(__x) - __diff;
} else // (_Nd > _Nd_ull)
{
static_assert(_Nd <= (2 * _Nd_ull),
"Maximum supported integer size is 128-bit");
unsigned long long __high = __x >> _Nd_ull;
if (__high != 0) {
constexpr int __diff = (2 * _Nd_ull) - _Nd;
return __builtin_clzll(__high) - __diff;
}
constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
unsigned long long __low = __x & __max_ull;
return (_Nd - _Nd_ull) + __builtin_clzll(__low);
}
}
template <typename _Tp> constexpr int __countl_one(_Tp __x) noexcept {
if (__x == numeric_limits<_Tp>::max()) return numeric_limits<_Tp>::digits;
return __countl_zero<_Tp>((_Tp)~__x);
}
template <typename _Tp> constexpr int __countr_zero(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return _Nd;
constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
return __builtin_ctz(__x);
else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
return __builtin_ctzl(__x);
else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull)
return __builtin_ctzll(__x);
else // (_Nd > _Nd_ull)
{
static_assert(_Nd <= (2 * _Nd_ull),
"Maximum supported integer size is 128-bit");
constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
unsigned long long __low = __x & __max_ull;
if (__low != 0) return __builtin_ctzll(__low);
unsigned long long __high = __x >> _Nd_ull;
return __builtin_ctzll(__high) + _Nd_ull;
}
}
template <typename _Tp> constexpr int __countr_one(_Tp __x) noexcept {
if (__x == numeric_limits<_Tp>::max()) return numeric_limits<_Tp>::digits;
return __countr_zero((_Tp)~__x);
}
template <typename _Tp> constexpr int __popcount(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return 0;
constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
return __builtin_popcount(__x);
else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
return __builtin_popcountl(__x);
else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull)
return __builtin_popcountll(__x);
else // (_Nd > _Nd_ull)
{
static_assert(_Nd <= (2 * _Nd_ull),
"Maximum supported integer size is 128-bit");
constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
unsigned long long __low = __x & __max_ull;
unsigned long long __high = __x >> _Nd_ull;
return __builtin_popcountll(__low) + __builtin_popcountll(__high);
}
}
template <typename _Tp> constexpr bool __has_single_bit(_Tp __x) noexcept {
return __popcount(__x) == 1;
}
template <typename _Tp> constexpr _Tp __bit_ceil(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0 || __x == 1) return 1;
auto __shift_exponent = _Nd - __countl_zero((_Tp)(__x - 1u));
#ifdef _GLIBCXX_HAVE_BUILTIN_IS_CONSTANT_EVALUATED
if (!__builtin_is_constant_evaluated()) {
__glibcxx_assert(__shift_exponent != numeric_limits<_Tp>::digits);
}
#endif
using __promoted_type = decltype(__x << 1);
if _GLIBCXX17_CONSTEXPR (!is_same<__promoted_type, _Tp>::value) {
const int __extra_exp = sizeof(__promoted_type) / sizeof(_Tp) / 2;
__shift_exponent |= (__shift_exponent & _Nd) << __extra_exp;
}
return (_Tp)1u << __shift_exponent;
}
template <typename _Tp> constexpr _Tp __bit_floor(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return 0;
return (_Tp)1u << (_Nd - __countl_zero((_Tp)(__x >> 1)));
}
template <typename _Tp> constexpr _Tp __bit_width(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
return _Nd - __countl_zero(__x);
}
} // namespace std
#endif
#endif
#line 2 "Library/lib/limits"
#line 4 "Library/lib/limits"
namespace workspace {
template <class _Tp> struct numeric_limits : std::numeric_limits<_Tp> {};
#ifdef __SIZEOF_INT128__
template <> struct numeric_limits<__uint128_t> {
constexpr static __uint128_t max() { return ~__uint128_t(0); }
constexpr static __uint128_t min() { return 0; }
};
template <> struct numeric_limits<__int128_t> {
constexpr static __int128_t max() {
return numeric_limits<__uint128_t>::max() >> 1;
}
constexpr static __int128_t min() { return -max() - 1; }
};
#endif
} // namespace workspace
#line 16 "Library/lib/alias"
namespace workspace {
constexpr char eol = '\n';
using namespace std;
using i32 = int_least32_t;
using u32 = uint_least32_t;
using i64 = int_least64_t;
using u64 = uint_least64_t;
#ifdef __SIZEOF_INT128__
using i128 = __int128_t;
using u128 = __uint128_t;
#else
#warning 128bit integer is not available.
#endif
template <class T, class Comp = less<T>>
using priority_queue = std::priority_queue<T, vector<T>, Comp>;
template <class T> using stack = std::stack<T, vector<T>>;
template <class _T1, class _T2,
typename = decltype(std::declval<const _T2 &>() <
std::declval<const _T1 &>())>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
min(const _T1 &__x, const _T2 &__y) noexcept {
return __y < __x ? __y : __x;
}
template <class _T1, class _T2, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _T2 &>(), std::declval<const _T1 &>()))>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
min(const _T1 &__x, const _T2 &__y, _Compare __comp) noexcept {
return __comp(__y, __x) ? __y : __x;
}
template <class _Tp, typename = decltype(std::declval<const _Tp &>() <
std::declval<const _Tp &>())>
constexpr _Tp min(std::initializer_list<_Tp> __x) noexcept {
return *std::min_element(__x.begin(), __x.end());
}
template <class _Tp, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _Tp &>(), std::declval<const _Tp &>()))>
constexpr _Tp min(std::initializer_list<_Tp> __x, _Compare __comp) noexcept {
return *std::min_element(__x.begin(), __x.end(), __comp);
}
template <class _T1, class _T2,
typename = decltype(std::declval<const _T1 &>() <
std::declval<const _T2 &>())>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
max(const _T1 &__x, const _T2 &__y) noexcept {
return __x < __y ? __y : __x;
}
template <class _T1, class _T2, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _T1 &>(), std::declval<const _T2 &>()))>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
max(const _T1 &__x, const _T2 &__y, _Compare __comp) noexcept {
return __comp(__x, __y) ? __y : __x;
}
template <class _Tp, typename = decltype(std::declval<const _Tp &>() <
std::declval<const _Tp &>())>
constexpr _Tp max(std::initializer_list<_Tp> __x) noexcept {
return *std::max_element(__x.begin(), __x.end());
}
template <class _Tp, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _Tp &>(), std::declval<const _Tp &>()))>
constexpr _Tp max(std::initializer_list<_Tp> __x, _Compare __comp) noexcept {
return *std::max_element(__x.begin(), __x.end(), __comp);
}
template <typename _Tp> constexpr _Tp __bsf(_Tp __x) noexcept {
return std::__countr_zero(__x);
}
template <typename _Tp> constexpr _Tp __bsr(_Tp __x) noexcept {
return std::__bit_width(__x) - 1;
}
} // namespace workspace
#line 6 "atcoder-workspace/3.cc"
// #include "lib/cxx20"
#line 2 "Library/lib/direct"
/*
* @file direct
* @brief Pragma Directive
*/
#ifdef ONLINE_JUDGE
#pragma GCC optimize("O3")
#pragma GCC target("avx,avx2")
#pragma GCC optimize("unroll-loops")
#endif
#line 8 "atcoder-workspace/3.cc"
// #include "lib/opt"
#line 2 "Library/src/sys/clock.hpp"
/*
* @fn clock.hpp
* @brief Clock
*/
#line 9 "Library/src/sys/clock.hpp"
namespace workspace {
using namespace std::chrono;
namespace internal {
// The start time of the program.
const auto start_time{system_clock::now()};
} // namespace internal
/*
* @fn elapsed
* @return elapsed time of the program
*/
int64_t elapsed() {
const auto end_time{system_clock::now()};
return duration_cast<milliseconds>(end_time - internal::start_time).count();
}
} // namespace workspace
#line 2 "Library/src/sys/ejection.hpp"
/**
* @file ejection.hpp
* @brief Ejection
*/
#line 9 "Library/src/sys/ejection.hpp"
namespace workspace {
namespace internal {
struct ejection {
bool exit = 0;
};
} // namespace internal
/**
* @brief eject from a try block, throw nullptr
* @param arg output
*/
template <class Tp> void eject(Tp const &arg) {
std::cout << arg << "\n";
throw internal::ejection{};
}
void exit() { throw internal::ejection{true}; }
} // namespace workspace
#line 2 "Library/src/sys/iteration.hpp"
/**
* @file iteration.hpp
* @brief Case Iteration
*/
#line 9 "Library/src/sys/iteration.hpp"
#line 11 "Library/src/sys/iteration.hpp"
namespace workspace {
void main();
struct {
// 1-indexed
unsigned current{0};
unsigned total{1};
void read() { (std::cin >> total).ignore(); }
int iterate() {
static bool once = false;
assert(!once);
once = true;
while (current++ < total) {
try {
main();
} catch (internal::ejection const& status) {
if (status.exit) break;
}
}
return 0;
}
} case_info;
} // namespace workspace
#line 2 "Library/src/utils/cached.hpp"
/**
* @file cached.hpp
* @brief Cached
* @date 2021-02-25
*
*
*/
#line 13 "Library/src/utils/cached.hpp"
#line 2 "Library/src/utils/fixed_point.hpp"
/**
* @file fixed_point.hpp
* @brief Fixed Point Combinator
*/
#line 9 "Library/src/utils/fixed_point.hpp"
namespace workspace {
/**
* @brief Fixed Point Combinator
*/
template <class _F> class fixed_point {
_F __fn;
public:
/**
* @brief Construct a new fixed point object
*
* @param __fn 1st argument callable with the rest of its arguments.
* Return type specified.
*/
fixed_point(_F __fn) noexcept : __fn(std::forward<_F>(__fn)) {}
/**
* @brief Apply *this to 1st argument.
* @param __args Rest of arguments.
*/
template <class... _Args>
decltype(auto) operator()(_Args &&...__args) const noexcept {
return __fn(*this, std::forward<_Args>(__args)...);
}
};
} // namespace workspace
#line 15 "Library/src/utils/cached.hpp"
namespace workspace {
namespace cached_impl {
// Convert keys to tuple.
template <class... _Args> struct get_tuple {
using type = decltype(
std::tuple_cat(std::declval<std::tuple<std::conditional_t<
std::is_convertible<std::decay_t<_Args>, _Args>::value,
std::decay_t<_Args>, _Args>>>()...));
};
// Associative array.
template <class _Value, class... _Keys>
struct assoc
: std::integral_constant<int, !std::is_void<_Value>::value>,
std::conditional_t<std::is_void<_Value>::value,
std::set<typename get_tuple<_Keys...>::type>,
std::map<typename get_tuple<_Keys...>::type, _Value>> {
};
// Non-resursive lambda type.
template <class _F, class = void> struct is_recursive : std::false_type {};
// Resursive lambda type.
template <class _F>
struct is_recursive<
_F, std::__void_t<decltype(&_F::template operator()<fixed_point<_F> &>)>>
: std::true_type {};
// Recursive ver.
template <class _F> class _recursive {
template <class...> struct _cache;
template <class _G, class _R, class _H, class... _Args>
struct _cache<_R (_G::*)(_H, _Args...)> : assoc<_R, _Args...> {};
template <class _G, class _R, class _H, class... _Args>
struct _cache<_R (_G::*)(_H, _Args...) const> : assoc<_R, _Args...> {};
public:
using cache = _cache<decltype(&_F::template operator()<_recursive<_F> &>)>;
_recursive(_F __x) noexcept : __fn(__x), __cptr(new cache) {}
/**
* @brief Apply `*this` to 1st argument of the lambda.
* @param __args Rest of arguments.
*/
template <class... _Args>
decltype(auto) operator()(_Args &&...__args) noexcept {
typename cache::key_type __key{__args...};
if constexpr (cache::value) {
if (auto __i = __cptr->lower_bound(__key);
__i != __cptr->end() && __i->first == __key)
return __i->second;
else
return __cptr
->emplace_hint(__i, std::move(__key),
__fn(*this, std::forward<_Args>(__args)...))
->second;
}
else if (auto __i = __cptr->lower_bound(__key);
__i == __cptr->end() || *__i != __key)
__cptr->emplace_hint(__i, std::move(__key)),
__fn(*this, std::forward<_Args>(__args)...);
}
private:
_F __fn;
std::shared_ptr<cache> __cptr;
};
// Non-recursive ver.
template <class _F> class _non_recursive {
template <class _T, class = void> struct _get_func { using type = _T; };
template <class _T>
struct _get_func<_T, std::__void_t<decltype(&_T::operator())>> {
using type = decltype(&_T::operator());
};
template <class...> struct _cache;
template <class _R, class... _Args>
struct _cache<_R(_Args...)> : assoc<_R, _Args...> {};
template <class _R, class... _Args>
struct _cache<_R (*)(_Args...)> : assoc<_R, _Args...> {};
template <class _G, class _R, class... _Args>
struct _cache<_R (_G::*)(_Args...)> : assoc<_R, _Args...> {};
template <class _G, class _R, class... _Args>
struct _cache<_R (_G::*)(_Args...) const> : assoc<_R, _Args...> {};
public:
using cache = _cache<typename _get_func<_F>::type>;
_non_recursive(_F __x) noexcept : __fn(__x), __cptr(new cache) {}
/**
* @param __args
*/
template <class... _Args>
decltype(auto) operator()(_Args &&...__args) noexcept {
typename cache::key_type __key{__args...};
if constexpr (cache::value) {
if (auto __i = __cptr->lower_bound(__key);
__i != __cptr->end() && __i->first == __key)
return __i->second;
else
return __cptr
->emplace_hint(__i, std::move(__key),
__fn(std::forward<_Args>(__args)...))
->second;
}
else if (auto __i = __cptr->lower_bound(__key);
__i == __cptr->end() || *__i != __key)
__cptr->emplace_hint(__i, std::move(__key)),
__fn(std::forward<_Args>(__args)...);
}
private:
_F __fn;
std::shared_ptr<cache> __cptr;
};
template <class _F>
using _cached = std::conditional_t<is_recursive<_F>::value, _recursive<_F>,
_non_recursive<_F>>;
} // namespace cached_impl
/**
* @brief Cached caller of function
*/
template <class _F> class cached : public cached_impl::_cached<_F> {
public:
/**
* @brief Construct a new cached object
*/
cached() noexcept : cached_impl::_cached<_F>(_F{}) {}
/**
* @brief Construct a new cached object
*
* @param __x Function
*/
cached(_F __x) noexcept : cached_impl::_cached<_F>(__x) {}
};
} // namespace workspace
#line 2 "Library/src/utils/cat.hpp"
/**
* @file cat.hpp
* @brief Cat
*/
#line 9 "Library/src/utils/cat.hpp"
namespace workspace {
/**
* @brief Concatenate two sequences.
*
* @param __c1
* @param __c2
* @return Concatenated sequence.
*/
template <class _C1, class _C2>
constexpr decltype(auto) cat(_C1 &&__c1, _C2 &&__c2) noexcept {
auto __c = std::forward<_C1>(__c1);
if constexpr (std::is_rvalue_reference<decltype(__c2)>::value)
__c.insert(std::end(__c), std::move_iterator(std::begin(__c2)),
std::move_iterator(std::end(__c2)));
else
__c.insert(std::end(__c), std::cbegin(__c2), std::cend(__c2));
return __c;
}
/**
* @return Concatenated sequence.
*/
template <class _C1, class _C2, class... _Args>
constexpr decltype(auto) cat(_C1 &&__c1, _C2 &&__c2,
_Args &&...__args) noexcept {
return cat(cat(std::forward<_C1>(__c1), std::forward<_C2>(__c2)),
std::forward<_Args>(__args)...);
}
} // namespace workspace
#line 2 "Library/src/utils/chval.hpp"
/**
* @file chval.hpp
* @brief Change Less/Greater
*/
#line 9 "Library/src/utils/chval.hpp"
namespace workspace {
/**
* @brief Substitute __y for __x if __y < __x.
* @param __x Reference
* @param __y Comparison target
* @return Whether or not __x is updated.
*/
template <class _T1, class _T2,
typename = decltype(std::declval<_T2>() < std::declval<_T1 &>())>
typename std::enable_if<std::is_assignable<_T1 &, _T2>::value, bool>::type chle(
_T1 &__x, _T2 &&__y) noexcept {
return __y < __x ? __x = std::forward<_T2>(__y), true : false;
}
/**
* @brief Substitute __y for __x if __x < __y.
* @param __x Reference
* @param __y Comparison target
* @return Whether or not __x is updated.
*/
template <class _T1, class _T2,
typename = decltype(std::declval<_T1 &>() < std::declval<_T2>())>
typename std::enable_if<std::is_assignable<_T1 &, _T2>::value, bool>::type chge(
_T1 &__x, _T2 &&__y) noexcept {
return __x < __y ? __x = std::forward<_T2>(__y), true : false;
}
/**
* @brief Substitute __y for __x if __comp(__y, __x) is true.
* @param __x Reference
* @param __y Comparison target
* @param __comp Compare function object
* @return Whether or not __x is updated.
*/
template <class _T1, class _T2, class _Compare,
typename = decltype(std::declval<_Compare>()(std::declval<_T2>(),
std::declval<_T1 &>()))>
typename std::enable_if<std::is_assignable<_T1 &, _T2>::value, bool>::type chle(
_T1 &__x, _T2 &&__y, _Compare __comp) noexcept {
return __comp(__y, __x) ? __x = std::forward<_T2>(__y), true : false;
}
/**
* @brief Substitute __y for __x if __comp(__x, __y) is true.
* @param __x Reference
* @param __y Comparison target
* @param __comp Compare function object
* @return Whether or not __x is updated.
*/
template <class _T1, class _T2, class _Compare,
typename = decltype(std::declval<_Compare>()(std::declval<_T1 &>(),
std::declval<_T2>()))>
typename std::enable_if<std::is_assignable<_T1 &, _T2>::value, bool>::type chge(
_T1 &__x, _T2 &&__y, _Compare __comp) noexcept {
return __comp(__x, __y) ? __x = std::forward<_T2>(__y), true : false;
}
} // namespace workspace
#line 6 "Library/lib/utils"
// #include "src/utils/grid.hpp"
#line 2 "Library/src/utils/hash.hpp"
#line 8 "Library/src/utils/hash.hpp"
#line 2 "Library/src/utils/sfinae.hpp"
/**
* @file sfinae.hpp
* @brief SFINAE
*/
#line 10 "Library/src/utils/sfinae.hpp"
#include <type_traits>
#ifndef __INT128_DEFINED__
#ifdef __SIZEOF_INT128__
#define __INT128_DEFINED__ 1
#else
#define __INT128_DEFINED__ 0
#endif
#endif
namespace std {
#if __INT128_DEFINED__
template <> struct make_signed<__uint128_t> { using type = __int128_t; };
template <> struct make_signed<__int128_t> { using type = __int128_t; };
template <> struct make_unsigned<__uint128_t> { using type = __uint128_t; };
template <> struct make_unsigned<__int128_t> { using type = __uint128_t; };
#endif
} // namespace std
namespace workspace {
template <class Tp, class... Args> struct variadic_front { using type = Tp; };
template <class... Args> struct variadic_back;
template <class Tp> struct variadic_back<Tp> { using type = Tp; };
template <class Tp, class... Args> struct variadic_back<Tp, Args...> {
using type = typename variadic_back<Args...>::type;
};
template <class type, template <class> class trait>
using enable_if_trait_type = typename std::enable_if<trait<type>::value>::type;
/**
* @brief Return type of subscripting ( @c [] ) access.
*/
template <class _Tp>
using subscripted_type =
typename std::decay<decltype(std::declval<_Tp&>()[0])>::type;
template <class Container>
using element_type = typename std::decay<decltype(
*std::begin(std::declval<Container&>()))>::type;
template <class _Tp, class = std::nullptr_t>
struct has_begin : std::false_type {};
template <class _Tp>
struct has_begin<_Tp, decltype(std::begin(std::declval<_Tp>()), nullptr)>
: std::true_type {};
template <class _Tp, class = std::nullptr_t>
struct has_mod : std::false_type {};
template <class _Tp>
struct has_mod<_Tp, decltype(_Tp::mod, nullptr)> : std::true_type {};
template <class _Tp, class = void> struct is_integral_ext : std::false_type {};
template <class _Tp>
struct is_integral_ext<
_Tp, typename std::enable_if<std::is_integral<_Tp>::value>::type>
: std::true_type {};
#if __INT128_DEFINED__
template <> struct is_integral_ext<__int128_t> : std::true_type {};
template <> struct is_integral_ext<__uint128_t> : std::true_type {};
#endif
#if __cplusplus >= 201402
template <class _Tp>
constexpr static bool is_integral_ext_v = is_integral_ext<_Tp>::value;
#endif
template <typename _Tp, typename = void> struct multiplicable_uint {
using type = uint_least32_t;
};
template <typename _Tp>
struct multiplicable_uint<
_Tp,
typename std::enable_if<(2 < sizeof(_Tp)) &&
(!__INT128_DEFINED__ || sizeof(_Tp) <= 4)>::type> {
using type = uint_least64_t;
};
#if __INT128_DEFINED__
template <typename _Tp>
struct multiplicable_uint<_Tp,
typename std::enable_if<(4 < sizeof(_Tp))>::type> {
using type = __uint128_t;
};
#endif
template <typename _Tp> struct multiplicable_int {
using type =
typename std::make_signed<typename multiplicable_uint<_Tp>::type>::type;
};
} // namespace workspace
#line 10 "Library/src/utils/hash.hpp"
namespace workspace {
template <class T, class = void> struct hash : std::hash<T> {};
template <class _Tp> struct hash<_Tp *> : std::hash<_Tp *> {};
#if __cplusplus >= 201703L
template <class Unique_bits_type>
struct hash<Unique_bits_type,
enable_if_trait_type<Unique_bits_type,
std::has_unique_object_representations>> {
size_t operator()(uint64_t x) const {
static const uint64_t m = std::random_device{}();
x ^= x >> 23;
x ^= m;
x ^= x >> 47;
return x - (x >> 32);
}
};
#endif
template <class Key> size_t hash_combine(const size_t &seed, const Key &key) {
return seed ^
(hash<Key>()(key) + 0x9e3779b9 /* + (seed << 6) + (seed >> 2) */);
}
template <class T1, class T2> struct hash<std::pair<T1, T2>> {
size_t operator()(const std::pair<T1, T2> &pair) const {
return hash_combine(hash<T1>()(pair.first), pair.second);
}
};
template <class... T> class hash<std::tuple<T...>> {
template <class Tuple, size_t index = std::tuple_size<Tuple>::value - 1>
struct tuple_hash {
static uint64_t apply(const Tuple &t) {
return hash_combine(tuple_hash<Tuple, index - 1>::apply(t),
std::get<index>(t));
}
};
template <class Tuple> struct tuple_hash<Tuple, size_t(-1)> {
static uint64_t apply(const Tuple &t) { return 0; }
};
public:
uint64_t operator()(const std::tuple<T...> &t) const {
return tuple_hash<std::tuple<T...>>::apply(t);
}
};
template <class hash_table> struct hash_table_wrapper : hash_table {
using key_type = typename hash_table::key_type;
size_t count(const key_type &key) const {
return hash_table::find(key) != hash_table::end();
}
template <class... Args> auto emplace(Args &&... args) {
return hash_table::insert(typename hash_table::value_type(args...));
}
};
template <class Key, class Mapped = __gnu_pbds::null_type>
using cc_hash_table =
hash_table_wrapper<__gnu_pbds::cc_hash_table<Key, Mapped, hash<Key>>>;
template <class Key, class Mapped = __gnu_pbds::null_type>
using gp_hash_table =
hash_table_wrapper<__gnu_pbds::gp_hash_table<Key, Mapped, hash<Key>>>;
template <class Key, class Mapped>
using unordered_map = std::unordered_map<Key, Mapped, hash<Key>>;
template <class Key> using unordered_set = std::unordered_set<Key, hash<Key>>;
} // namespace workspace
#line 2 "Library/src/utils/io/istream.hpp"
/**
* @file istream.hpp
* @brief Input Stream
*/
#include <cxxabi.h>
#line 13 "Library/src/utils/io/istream.hpp"
#line 15 "Library/src/utils/io/istream.hpp"
namespace workspace {
namespace internal {
template <class Tp, typename = std::nullptr_t> struct istream_helper {
istream_helper(std::istream &is, Tp &x) {
if constexpr (has_begin<Tp>::value)
for (auto &&e : x)
istream_helper<typename std::decay<decltype(e)>::type>(is, e);
else
static_assert(has_begin<Tp>::value, "istream unsupported type.");
}
};
template <class Tp>
struct istream_helper<
Tp,
decltype(std::declval<std::decay<decltype(std::declval<std::istream &>() >>
std::declval<Tp &>())>>(),
nullptr)> {
istream_helper(std::istream &is, Tp &x) { is >> x; }
};
#ifdef __SIZEOF_INT128__
template <> struct istream_helper<__uint128_t, std::nullptr_t> {
istream_helper(std::istream &__is, __uint128_t &__x) {
std::string __s;
__is >> __s;
bool __neg = false;
if (__s.front() == '-') __neg = true, __s.erase(__s.begin());
__x = 0;
for (char __d : __s) {
__x *= 10;
__d -= '0';
if (__neg)
__x -= __d;
else
__x += __d;
}
}
};
template <> struct istream_helper<__int128_t, std::nullptr_t> {
istream_helper(std::istream &__is, __int128_t &__x) {
std::string __s;
__is >> __s;
bool __neg = false;
if (__s.front() == '-') __neg = true, __s.erase(__s.begin());
__x = 0;
for (char __d : __s) {
__x *= 10;
__d -= '0';
if (__neg)
__x -= __d;
else
__x += __d;
}
}
};
#endif // INT128
template <class T1, class T2> struct istream_helper<std::pair<T1, T2>> {
istream_helper(std::istream &is, std::pair<T1, T2> &x) {
istream_helper<T1>(is, x.first), istream_helper<T2>(is, x.second);
}
};
template <class... Tps> struct istream_helper<std::tuple<Tps...>> {
istream_helper(std::istream &is, std::tuple<Tps...> &x) { iterate(is, x); }
private:
template <class Tp, size_t N = 0> void iterate(std::istream &is, Tp &x) {
if constexpr (N == std::tuple_size<Tp>::value)
return;
else
istream_helper<typename std::tuple_element<N, Tp>::type>(is,
std::get<N>(x)),
iterate<Tp, N + 1>(is, x);
}
};
} // namespace internal
/**
* @brief A wrapper class for std::istream.
*/
class istream : public std::istream {
public:
/**
* @brief Wrapped operator.
*/
template <typename Tp> istream &operator>>(Tp &x) {
internal::istream_helper<Tp>(*this, x);
if (std::istream::fail()) {
static auto once = atexit([] {
std::cerr << "\n\033[43m\033[30mwarning: failed to read \'"
<< abi::__cxa_demangle(typeid(Tp).name(), 0, 0, 0)
<< "\'.\033[0m\n\n";
});
assert(!once);
}
return *this;
}
};
decltype(auto) cin = static_cast<istream &>(std::cin);
} // namespace workspace
#line 2 "Library/src/utils/io/ostream.hpp"
/**
* @file ostream.hpp
* @brief Output Stream
*/
#line 9 "Library/src/utils/io/ostream.hpp"
namespace workspace {
template <class _Os> struct is_ostream {
template <typename... _Args>
static std::true_type __test(std::basic_ostream<_Args...> *);
static std::false_type __test(void *);
constexpr static bool value = decltype(__test(std::declval<_Os *>()))::value;
};
template <class _Os>
using ostream_ref =
typename std::enable_if<is_ostream<_Os>::value, _Os &>::type;
/**
* @brief Stream insertion operator for C-style array.
*
* @param __os Output stream
* @param __a Array
* @return Reference to __os.
*/
template <class _Os, class _Tp, size_t _Nm>
typename std::enable_if<bool(sizeof(_Tp) > 2), ostream_ref<_Os>>::type
operator<<(_Os &__os, const _Tp (&__a)[_Nm]) {
if constexpr (_Nm) {
__os << *__a;
for (auto __i = __a + 1, __e = __a + _Nm; __i != __e; ++__i)
__os << ' ' << *__i;
}
return __os;
}
/**
* @brief Stream insertion operator for std::pair.
*
* @param __os Output stream
* @param __p Pair
* @return Reference to __os.
*/
template <class _Os, class _T1, class _T2>
ostream_ref<_Os> operator<<(_Os &__os, const std::pair<_T1, _T2> &__p) {
return __os << __p.first << ' ' << __p.second;
}
/**
* @brief Stream insertion operator for std::tuple.
*
* @param __os Output stream
* @param __t Tuple
* @return Reference to __os.
*/
template <class _Os, class _Tp, size_t _Nm = 0>
typename std::enable_if<bool(std::tuple_size<_Tp>::value + 1),
ostream_ref<_Os>>::type
operator<<(_Os &__os, const _Tp &__t) {
if constexpr (_Nm != std::tuple_size<_Tp>::value) {
if constexpr (_Nm) __os << ' ';
__os << std::get<_Nm>(__t);
operator<<<_Os, _Tp, _Nm + 1>(__os, __t);
}
return __os;
}
template <class _Os, class _Container,
typename = decltype(std::begin(std::declval<_Container>()))>
typename std::enable_if<
!std::is_same<typename std::decay<_Container>::type, std::string>::value &&
!std::is_same<typename std::decay<_Container>::type, char *>::value,
ostream_ref<_Os>>::type
operator<<(_Os &__os, const _Container &__cont) {
bool __h = true;
for (auto &&__e : __cont) __h ? __h = 0 : (__os << ' ', 0), __os << __e;
return __os;
}
#ifdef __SIZEOF_INT128__
/**
* @brief Stream insertion operator for __int128_t.
*
* @param __os Output Stream
* @param __x 128-bit integer
* @return Reference to __os.
*/
template <class _Os> ostream_ref<_Os> operator<<(_Os &__os, __int128_t __x) {
if (!__x) return __os << '0';
if (__x < 0) __os << '-';
char __s[40], *__p = __s;
while (__x) {
auto __d = __x % 10;
*__p++ = '0' + (__x < 0 ? -__d : __d);
__x /= 10;
}
*__p = 0;
for (char *__t = __s; __t < --__p; ++__t) *__t ^= *__p ^= *__t ^= *__p;
return __os << __s;
}
/**
* @brief Stream insertion operator for __uint128_t.
*
* @param __os Output Stream
* @param __x 128-bit unsigned integer
* @return Reference to __os.
*/
template <class _Os> ostream_ref<_Os> operator<<(_Os &__os, __uint128_t __x) {
if (!__x) return __os << '0';
char __s[40], *__p = __s;
while (__x) *__p++ = '0' + __x % 10, __x /= 10;
*__p = 0;
for (char *__t = __s; __t < --__p; ++__t) *__t ^= *__p ^= *__t ^= *__p;
return __os << __s;
}
#endif
} // namespace workspace
#line 10 "Library/lib/utils"
// #include "src/utils/io/read.hpp"
#line 2 "Library/src/utils/io/setup.hpp"
/**
* @file setup.hpp
* @brief I/O Setup
*/
#line 10 "Library/src/utils/io/setup.hpp"
namespace workspace {
/**
* @brief Setup I/O.
* @param __n Standard output precision
*/
void io_setup(int __n) {
std::cin.tie(0)->sync_with_stdio(0);
std::cout << std::fixed << std::setprecision(__n);
#ifdef _buffer_check
atexit([] {
char bufc;
if (std::cin >> bufc)
std::cerr << "\n\033[43m\033[30mwarning: buffer not empty.\033[0m\n\n";
});
#endif
}
} // namespace workspace
#line 2 "Library/src/utils/iterator/category.hpp"
/*
* @file category.hpp
* @brief Iterator Category
*/
#line 10 "Library/src/utils/iterator/category.hpp"
namespace workspace {
/*
* @tparam Tuple Tuple of iterator types
*/
template <class Tuple, size_t N = std::tuple_size<Tuple>::value - 1>
struct common_iterator_category {
using type = typename std::common_type<
typename common_iterator_category<Tuple, N - 1>::type,
typename std::iterator_traits<typename std::tuple_element<
N, Tuple>::type>::iterator_category>::type;
};
template <class Tuple> struct common_iterator_category<Tuple, 0> {
using type = typename std::iterator_traits<
typename std::tuple_element<0, Tuple>::type>::iterator_category;
};
} // namespace workspace
#line 2 "Library/src/utils/iterator/reverse.hpp"
/*
* @file reverse_iterator.hpp
* @brief Reverse Iterator
*/
#if __cplusplus >= 201703L
#include <iterator>
#include <optional>
namespace workspace {
/*
* @class reverse_iterator
* @brief Wrapper class for `std::reverse_iterator`.
* @see http://gcc.gnu.org/PR51823
*/
template <class Iterator>
class reverse_iterator : public std::reverse_iterator<Iterator> {
using base_std = std::reverse_iterator<Iterator>;
std::optional<typename base_std::value_type> deref;
public:
using base_std::reverse_iterator;
constexpr typename base_std::reference operator*() noexcept {
if (!deref) {
Iterator tmp = base_std::current;
deref = *--tmp;
}
return deref.value();
}
constexpr reverse_iterator &operator++() noexcept {
base_std::operator++();
deref.reset();
return *this;
}
constexpr reverse_iterator &operator--() noexcept {
base_std::operator++();
deref.reset();
return *this;
}
constexpr reverse_iterator operator++(int) noexcept {
base_std::operator++();
deref.reset();
return *this;
}
constexpr reverse_iterator operator--(int) noexcept {
base_std::operator++();
deref.reset();
return *this;
}
};
} // namespace workspace
#endif
#line 2 "Library/src/utils/make_vector.hpp"
/*
* @file make_vector.hpp
* @brief Multi-dimensional Vector
*/
#if __cplusplus >= 201703L
#include <tuple>
#include <vector>
namespace workspace {
/*
* @brief Make a multi-dimensional vector.
* @tparam Tp type of the elements
* @tparam N dimension
* @tparam S integer type
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N, typename S>
constexpr auto make_vector([[maybe_unused]] S* sizes, Tp const& init = Tp()) {
static_assert(std::is_convertible_v<S, size_t>);
if constexpr (N)
return std::vector(*sizes,
make_vector<Tp, N - 1, S>(std::next(sizes), init));
else
return init;
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N, typename S>
constexpr auto make_vector(const S (&sizes)[N], Tp const& init = Tp()) {
return make_vector<Tp, N, S>((S*)sizes, init);
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N, typename S, size_t I = 0>
constexpr auto make_vector([[maybe_unused]] std::array<S, N> const& sizes,
Tp const& init = Tp()) {
static_assert(std::is_convertible_v<S, size_t>);
if constexpr (I == N)
return init;
else
return std::vector(sizes[I], make_vector<Tp, N, S, I + 1>(sizes, init));
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N = SIZE_MAX, size_t I = 0, class... Args>
constexpr auto make_vector([[maybe_unused]] std::tuple<Args...> const& sizes,
Tp const& init = Tp()) {
using tuple_type = std::tuple<Args...>;
if constexpr (I == std::tuple_size_v<tuple_type> || I == N)
return init;
else {
static_assert(
std::is_convertible_v<std::tuple_element_t<I, tuple_type>, size_t>);
return std::vector(std::get<I>(sizes),
make_vector<Tp, N, I + 1>(sizes, init));
}
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, class Fst, class Snd>
constexpr auto make_vector(std::pair<Fst, Snd> const& sizes,
Tp const& init = Tp()) {
static_assert(std::is_convertible_v<Fst, size_t>);
static_assert(std::is_convertible_v<Snd, size_t>);
return make_vector({(size_t)sizes.first, (size_t)sizes.second}, init);
}
} // namespace workspace
#endif
#line 2 "Library/src/utils/py-like/enumerate.hpp"
/*
* @file enumerate.hpp
* @brief Enumerate
*/
#line 2 "Library/src/utils/py-like/range.hpp"
/**
* @file range.hpp
* @brief Range
*/
#line 9 "Library/src/utils/py-like/range.hpp"
#line 2 "Library/src/utils/py-like/reversed.hpp"
/**
* @file reversed.hpp
* @brief Reversed
*/
#include <initializer_list>
#line 10 "Library/src/utils/py-like/reversed.hpp"
namespace workspace {
namespace internal {
template <class Container> class reversed {
Container cont;
public:
constexpr reversed(Container &&cont) : cont(cont) {}
constexpr auto begin() { return std::rbegin(cont); }
constexpr auto end() { return std::rend(cont); }
};
} // namespace internal
template <class Container> constexpr auto reversed(Container &&cont) noexcept {
return internal::reversed<Container>{std::forward<Container>(cont)};
}
template <class Tp>
constexpr auto reversed(std::initializer_list<Tp> &&cont) noexcept {
return internal::reversed<std::initializer_list<Tp>>{
std::forward<std::initializer_list<Tp>>(cont)};
}
} // namespace workspace
#line 12 "Library/src/utils/py-like/range.hpp"
#if __cplusplus >= 201703L
namespace workspace {
template <class Index> class range {
Index first, last;
public:
class iterator {
Index current;
public:
using difference_type = std::ptrdiff_t;
using value_type = Index;
using reference = typename std::add_const<Index>::type &;
using pointer = iterator;
using iterator_category = std::bidirectional_iterator_tag;
constexpr iterator(Index const &__i = Index()) noexcept : current(__i) {}
constexpr bool operator==(iterator const &rhs) const noexcept {
return current == rhs.current;
}
constexpr bool operator!=(iterator const &rhs) const noexcept {
return current != rhs.current;
}
constexpr iterator &operator++() noexcept {
++current;
return *this;
}
constexpr iterator &operator--() noexcept {
--current;
return *this;
}
constexpr reference operator*() const noexcept { return current; }
};
constexpr range(Index first, Index last) noexcept
: first(first), last(last) {}
constexpr range(Index last) noexcept : first(), last(last) {}
constexpr iterator begin() const noexcept { return iterator{first}; }
constexpr iterator end() const noexcept { return iterator{last}; }
constexpr reverse_iterator<iterator> rbegin() const noexcept {
return reverse_iterator<iterator>(end());
}
constexpr reverse_iterator<iterator> rend() const noexcept {
return reverse_iterator<iterator>(begin());
}
};
template <class... Args> constexpr auto rrange(Args &&... args) noexcept {
return internal::reversed(range(std::forward<Args>(args)...));
}
} // namespace workspace
#endif
#line 2 "Library/src/utils/py-like/zip.hpp"
/**
* @file zip.hpp
* @brief Zip
*/
#line 11 "Library/src/utils/py-like/zip.hpp"
#line 14 "Library/src/utils/py-like/zip.hpp"
#if __cplusplus >= 201703L
namespace workspace {
namespace internal {
template <class> struct zipped_iterator;
template <class...> struct zipped_iterator_tuple;
template <class... Args> class zipped {
using ref_tuple = std::tuple<Args...>;
ref_tuple args;
template <size_t N = 0> constexpr auto begin_cat() const noexcept {
if constexpr (N != std::tuple_size<ref_tuple>::value) {
return std::tuple_cat(std::tuple(std::begin(std::get<N>(args))),
begin_cat<N + 1>());
} else
return std::tuple<>();
}
template <size_t N = 0> constexpr auto end_cat() const noexcept {
if constexpr (N != std::tuple_size<ref_tuple>::value) {
return std::tuple_cat(std::tuple(std::end(std::get<N>(args))),
end_cat<N + 1>());
} else
return std::tuple<>();
}
public:
constexpr zipped(Args &&... args) noexcept : args(args...) {}
class iterator {
using base_tuple = typename zipped_iterator_tuple<Args...>::type;
public:
using iterator_category =
typename common_iterator_category<base_tuple>::type;
using difference_type = std::ptrdiff_t;
using value_type = zipped_iterator<base_tuple>;
using reference = zipped_iterator<base_tuple> &;
using pointer = iterator;
protected:
value_type current;
template <size_t N = 0>
constexpr bool equal(const iterator &rhs) const noexcept {
if constexpr (N != std::tuple_size<base_tuple>::value) {
return std::get<N>(current) == std::get<N>(rhs.current) ||
equal<N + 1>(rhs);
} else
return false;
}
template <size_t N = 0> constexpr void increment() noexcept {
if constexpr (N != std::tuple_size<base_tuple>::value) {
++std::get<N>(current);
increment<N + 1>();
}
}
template <size_t N = 0> constexpr void decrement() noexcept {
if constexpr (N != std::tuple_size<base_tuple>::value) {
--std::get<N>(current);
decrement<N + 1>();
}
}
template <size_t N = 0>
constexpr void advance(difference_type __d) noexcept {
if constexpr (N != std::tuple_size<base_tuple>::value) {
std::get<N>(current) += __d;
advance<N + 1>(__d);
}
}
public:
constexpr iterator() noexcept = default;
constexpr iterator(base_tuple const ¤t) noexcept : current(current) {}
constexpr bool operator==(const iterator &rhs) const noexcept {
return equal(rhs);
}
constexpr bool operator!=(const iterator &rhs) const noexcept {
return !equal(rhs);
}
constexpr iterator &operator++() noexcept {
increment();
return *this;
}
constexpr iterator &operator--() noexcept {
decrement();
return *this;
}
constexpr bool operator<(const iterator &rhs) const noexcept {
return std::get<0>(current) < std::get<0>(rhs.current);
}
constexpr bool operator<=(const iterator &rhs) const noexcept {
return std::get<0>(current) <= std::get<0>(rhs.current);
}
constexpr iterator &operator+=(difference_type __d) noexcept {
advance(__d);
return *this;
}
constexpr iterator &operator-=(difference_type __d) noexcept {
advance(-__d);
return *this;
}
constexpr iterator operator+(difference_type __d) const noexcept {
return iterator{*this} += __d;
}
constexpr iterator operator-(difference_type __d) const noexcept {
return iterator{*this} -= __d;
}
constexpr difference_type operator-(const iterator &rhs) const noexcept {
return std::get<0>(current) - std::get<0>(rhs.current);
}
constexpr reference operator*() noexcept { return current; }
};
constexpr iterator begin() const noexcept { return iterator{begin_cat()}; }
constexpr iterator end() const noexcept { return iterator{end_cat()}; }
constexpr reverse_iterator<iterator> rbegin() const noexcept {
return reverse_iterator<iterator>{end()};
}
constexpr reverse_iterator<iterator> rend() const noexcept {
return reverse_iterator<iterator>{begin()};
}
};
template <class Tp, class... Args> struct zipped_iterator_tuple<Tp, Args...> {
using type = decltype(std::tuple_cat(
std::declval<std::tuple<decltype(std::begin(std::declval<Tp>()))>>(),
std::declval<typename zipped_iterator_tuple<Args...>::type>()));
};
template <> struct zipped_iterator_tuple<> { using type = std::tuple<>; };
template <class Iter_tuple> struct zipped_iterator : Iter_tuple {
constexpr zipped_iterator(Iter_tuple const &__t) noexcept
: Iter_tuple::tuple(__t) {}
constexpr zipped_iterator(zipped_iterator const &__t) = default;
constexpr zipped_iterator &operator=(zipped_iterator const &__t) = default;
// Avoid move initialization.
constexpr zipped_iterator(zipped_iterator &&__t)
: zipped_iterator(static_cast<zipped_iterator const &>(__t)) {}
// Avoid move assignment.
zipped_iterator &operator=(zipped_iterator &&__t) {
return operator=(static_cast<zipped_iterator const &>(__t));
}
template <size_t N>
friend constexpr auto &get(zipped_iterator<Iter_tuple> const &__z) noexcept {
return *std::get<N>(__z);
}
template <size_t N>
friend constexpr auto get(zipped_iterator<Iter_tuple> &&__z) noexcept {
return *std::get<N>(__z);
}
};
} // namespace internal
} // namespace workspace
namespace std {
template <size_t N, class Iter_tuple>
struct tuple_element<N, workspace::internal::zipped_iterator<Iter_tuple>> {
using type = typename remove_reference<typename iterator_traits<
typename tuple_element<N, Iter_tuple>::type>::reference>::type;
};
template <class Iter_tuple>
struct tuple_size<workspace::internal::zipped_iterator<Iter_tuple>>
: tuple_size<Iter_tuple> {};
} // namespace std
namespace workspace {
template <class... Args> constexpr auto zip(Args &&... args) noexcept {
return internal::zipped<Args...>(std::forward<Args>(args)...);
}
template <class... Args>
constexpr auto zip(std::initializer_list<Args> const &... args) noexcept {
return internal::zipped<const std::initializer_list<Args>...>(args...);
}
} // namespace workspace
#endif
#line 10 "Library/src/utils/py-like/enumerate.hpp"
#if __cplusplus >= 201703L
namespace workspace {
constexpr size_t min_size() noexcept { return SIZE_MAX; }
template <class Container, class... Args>
constexpr size_t min_size(Container const &cont, Args &&... args) noexcept {
return std::min(std::size(cont), min_size(std::forward<Args>(args)...));
}
template <class... Args> constexpr auto enumerate(Args &&... args) noexcept {
return zip(range(min_size(args...)), std::forward<Args>(args)...);
}
template <class... Args>
constexpr auto enumerate(std::initializer_list<Args> const &... args) noexcept {
return zip(range(min_size(args...)), std::vector(args)...);
}
} // namespace workspace
#endif
#line 2 "Library/src/utils/rand/rng.hpp"
/**
* @file rng.hpp
* @brief Random Number Generator
*/
#line 9 "Library/src/utils/rand/rng.hpp"
namespace workspace {
template <typename _Arithmetic>
using uniform_distribution = typename std::conditional<
std::is_integral<_Arithmetic>::value,
std::uniform_int_distribution<_Arithmetic>,
std::uniform_real_distribution<_Arithmetic>>::type;
template <typename _Arithmetic, class _Engine = std::mt19937>
class random_number_generator : uniform_distribution<_Arithmetic> {
using base = uniform_distribution<_Arithmetic>;
_Engine __engine;
public:
random_number_generator(_Arithmetic __min, _Arithmetic __max)
: base(__min, __max), __engine(std::random_device{}()) {}
random_number_generator(_Arithmetic __max = 1)
: random_number_generator(0, __max) {}
random_number_generator(typename base::param_type const& __param)
: base(__param), __engine(std::random_device{}()) {}
decltype(auto) operator()() noexcept { return base::operator()(__engine); }
};
} // namespace workspace
#line 2 "Library/src/utils/rand/shuffle.hpp"
/**
* @file shuffle.hpp
* @brief Shuffle
*/
#line 10 "Library/src/utils/rand/shuffle.hpp"
namespace workspace {
template <class _RAIter, class _Engine = std::mt19937>
void shuffle(_RAIter __first, _RAIter __last) {
static _Engine __engine(std::random_device{}());
std::shuffle(__first, __last, __engine);
}
} // namespace workspace
#line 2 "Library/src/utils/round_div.hpp"
/*
* @file round_div.hpp
* @brief Round Integer Division
*/
#line 9 "Library/src/utils/round_div.hpp"
#line 11 "Library/src/utils/round_div.hpp"
namespace workspace {
/*
* @fn floor_div
* @brief floor of fraction.
* @param x the numerator
* @param y the denominator
* @return maximum integer z s.t. z <= x / y
* @note y must be nonzero.
*/
template <typename T1, typename T2>
constexpr typename std::enable_if<(is_integral_ext<T1>::value &&
is_integral_ext<T2>::value),
typename std::common_type<T1, T2>::type>::type
floor_div(T1 x, T2 y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x < 0 ? (x - y + 1) / y : x / y;
}
/*
* @fn ceil_div
* @brief ceil of fraction.
* @param x the numerator
* @param y the denominator
* @return minimum integer z s.t. z >= x / y
* @note y must be nonzero.
*/
template <typename T1, typename T2>
constexpr typename std::enable_if<(is_integral_ext<T1>::value &&
is_integral_ext<T2>::value),
typename std::common_type<T1, T2>::type>::type
ceil_div(T1 x, T2 y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x < 0 ? x / y : (x + y - 1) / y;
}
} // namespace workspace
#line 22 "Library/lib/utils"
// #include "src/utils/sfinae.hpp"
#line 11 "atcoder-workspace/3.cc"
signed main() {
using namespace workspace;
io_setup(15);
/* given
case_info.read(); //*/
/* unspecified
case_info.total = -1; //*/
return case_info.iterate();
}
#line 2 "Library/src/combinatorics/binomial.hpp"
/**
* @file binomial.hpp
* @brief Binomial Coefficient
* @date 2021-01-15
*
*
*/
#line 2 "Library/src/modular/modint.hpp"
/**
* @file modint.hpp
*
* @brief Modular Arithmetic
*/
#line 12 "Library/src/modular/modint.hpp"
#line 14 "Library/src/modular/modint.hpp"
namespace workspace {
namespace internal {
/**
* @brief Base of modular arithmetic.
*
* @tparam Mod identifier, which represents modulus if positive
* @tparam Storage Reserved size for inverse calculation
*/
template <auto Mod, unsigned Storage> struct modint_base {
static_assert(is_integral_ext<decltype(Mod)>::value,
"Mod must be integral type.");
using mod_type = typename std::make_signed<typename std::conditional<
0 < Mod, typename std::add_const<decltype(Mod)>::type,
decltype(Mod)>::type>::type;
using value_type = typename std::decay<mod_type>::type;
using mul_type = typename multiplicable_uint<value_type>::type;
// Modulus
static mod_type mod;
static unsigned storage;
constexpr static void reserve(unsigned __n) noexcept { storage = __n; }
value_type value = 0;
struct direct_ctor_t {};
constexpr static direct_ctor_t direct_ctor_tag{};
// Direct constructor
template <class _Tp>
constexpr modint_base(_Tp __n, direct_ctor_t) : value(__n) {}
public:
constexpr modint_base() noexcept = default;
template <class _Tp, typename std::enable_if<
is_integral_ext<_Tp>::value>::type * = nullptr>
constexpr modint_base(_Tp __n) noexcept
: value((__n %= mod) < 0 ? __n += mod : __n) {}
constexpr modint_base(bool __n) noexcept : value(__n) {}
constexpr operator value_type() const noexcept { return value; }
constexpr static modint_base one() noexcept { return 1; }
// unary operators {{
constexpr modint_base operator++(int) noexcept {
modint_base __t{*this};
operator++();
return __t;
}
constexpr modint_base operator--(int) noexcept {
modint_base __t{*this};
operator--();
return __t;
}
constexpr modint_base &operator++() noexcept {
if (++value == mod) value = 0;
return *this;
}
constexpr modint_base &operator--() noexcept {
if (!value)
value = mod - 1;
else
--value;
return *this;
}
constexpr modint_base operator+() const noexcept { return *this; }
constexpr modint_base operator-() const noexcept {
return {value ? mod - value : 0, direct_ctor_tag};
}
// }} unary operators
// operator+= {{
constexpr modint_base &operator+=(const modint_base &__x) noexcept {
if ((value += __x.value) >= mod) value -= mod;
return *this;
}
template <class _Tp>
constexpr
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type &
operator+=(_Tp const &__x) noexcept {
if (((value += __x) %= mod) < 0) value += mod;
return *this;
}
// }} operator+=
// operator+ {{
template <class _Tp>
constexpr
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type
operator+(_Tp const &__x) const noexcept {
return modint_base{*this} += __x;
}
constexpr modint_base operator+(modint_base __x) const noexcept {
return __x += *this;
}
template <class _Tp>
constexpr friend
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type
operator+(_Tp const &__x, modint_base __y) noexcept {
return __y += __x;
}
// }} operator+
// operator-= {{
constexpr modint_base &operator-=(const modint_base &__x) noexcept {
if ((value -= __x.value) < 0) value += mod;
return *this;
}
template <class _Tp>
constexpr
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type &
operator-=(_Tp __x) noexcept {
if (((value -= __x) %= mod) < 0) value += mod;
return *this;
}
// }} operator-=
// operator- {{
template <class _Tp>
constexpr
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type
operator-(_Tp const &__x) const noexcept {
return modint_base{*this} -= __x;
}
constexpr modint_base operator-(const modint_base &__x) const noexcept {
modint_base __t;
if (((__t.value = value) -= __x.value) < 0) __t.value += mod;
return __t;
}
template <class _Tp>
constexpr friend
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type
operator-(_Tp __x, const modint_base &__y) noexcept {
if (((__x -= __y.value) %= mod) < 0) __x += mod;
modint_base __t;
__t.value = __x;
return __t;
}
// }} operator-
// operator*= {{
constexpr modint_base &operator*=(const modint_base &__x) noexcept {
value =
static_cast<value_type>(value * static_cast<mul_type>(__x.value) % mod);
return *this;
}
template <class _Tp>
constexpr
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type &
operator*=(_Tp __x) noexcept {
value = static_cast<value_type>(
value * mul_type((__x %= mod) < 0 ? __x + mod : __x) % mod);
return *this;
}
// }} operator*=
// operator* {{
constexpr modint_base operator*(const modint_base &__x) const noexcept {
return {static_cast<mul_type>(value) * __x.value % mod, direct_ctor_tag};
}
template <class _Tp>
constexpr
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type
operator*(_Tp __x) const noexcept {
__x %= mod;
if (__x < 0) __x += mod;
return {static_cast<mul_type>(value) * __x % mod, direct_ctor_tag};
}
template <class _Tp>
constexpr friend
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type
operator*(_Tp __x, const modint_base &__y) noexcept {
__x %= mod;
if (__x < 0) __x += mod;
return {static_cast<mul_type>(__x) * __y.value % mod, direct_ctor_tag};
}
// }} operator*
protected:
static value_type _mem(value_type __x) {
static std::vector<value_type> __m{0, 1};
static value_type __i = (__m.reserve(Storage), 1);
while (__i < __x) {
++__i;
__m.emplace_back(mod - mul_type(mod / __i) * __m[mod % __i] % mod);
}
return __m[__x];
}
template <class _Tp>
constexpr static
typename std::enable_if<is_integral_ext<_Tp>::value, value_type>::type
_div(mul_type __r, _Tp __x) noexcept {
assert(__x != _Tp(0));
if (!__r) return 0;
std::make_signed_t<_Tp> __v{};
bool __neg = __x < 0 ? __x = -__x, true : false;
if (static_cast<decltype(storage)>(__x) < storage)
__v = _mem(__x);
else {
decltype(__v) __y{mod}, __u{1}, __t;
while (__x)
__t = __y / __x, __y ^= __x ^= (__y -= __t * __x) ^= __x,
__v ^= __u ^= (__v -= __t * __u) ^= __u;
if (__y < 0) __neg ^= 1;
}
if (__neg)
__v = 0 < __v ? mod - __v : -__v;
else if (__v < 0)
__v += mod;
return __r == mul_type(1) ? static_cast<value_type>(__v)
: static_cast<value_type>(__r * __v % mod);
}
public:
// operator/= {{
constexpr modint_base &operator/=(const modint_base &__x) noexcept {
if (value) value = _div(value, __x.value);
return *this;
}
template <class _Tp>
constexpr
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type &
operator/=(_Tp __x) noexcept {
if (value) value = _div(value, __x %= mod);
return *this;
}
// }} operator/=
// operator/ {{
constexpr modint_base operator/(const modint_base &__x) const noexcept {
if (!value) return {};
return {_div(value, __x.value), direct_ctor_tag};
}
template <class _Tp>
constexpr
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type
operator/(_Tp __x) const noexcept {
if (!value) return {};
return {_div(value, __x %= mod), direct_ctor_tag};
}
template <class _Tp>
constexpr friend
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type
operator/(_Tp __x, const modint_base &__y) noexcept {
if (!__x) return {};
if ((__x %= mod) < 0) __x += mod;
return {_div(__x, __y.value), direct_ctor_tag};
}
// }} operator/
constexpr modint_base inv() const noexcept { return _div(1, value); }
template <class _Tp>
friend constexpr
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type
pow(modint_base b, _Tp e) noexcept {
if (e < 0) {
e = -e;
b.value = _div(1, b.value);
}
modint_base __r;
for (__r.value = 1; e; e >>= 1, b *= b)
if (e & 1) __r *= b;
return __r;
}
template <class _Tp>
constexpr
typename std::enable_if<is_integral_ext<_Tp>::value, modint_base>::type
pow(_Tp __e) const noexcept {
modint_base __r, b;
__r.value = 1;
for (b.value = __e < 0 ? __e = -__e, _div(1, value) : value; __e;
__e >>= 1, b *= b)
if (__e & 1) __r *= b;
return __r;
}
template <class _Os>
friend _Os &operator<<(_Os &__os, const modint_base &__x) noexcept {
return __os << __x.value;
}
friend std::istream &operator>>(std::istream &__is,
modint_base &__x) noexcept {
intmax_t value;
__x = (__is >> value, value);
return __is;
}
};
template <auto Mod, unsigned Storage>
typename modint_base<Mod, Storage>::mod_type modint_base<Mod, Storage>::mod =
Mod > 0 ? Mod : 0;
template <auto Mod, unsigned Storage>
unsigned modint_base<Mod, Storage>::storage = Storage;
} // namespace internal
/**
* @brief Modular arithmetic.
*
* @tparam Mod modulus
* @tparam Storage Reserved size for inverse calculation
*/
template <auto Mod, unsigned Storage = 0,
typename std::enable_if<(Mod > 0)>::type * = nullptr>
using modint = internal::modint_base<Mod, Storage>;
/**
* @brief Runtime modular arithmetic.
*
* @tparam type_id uniquely assigned
* @tparam Storage Reserved size for inverse calculation
*/
template <unsigned type_id = 0, unsigned Storage = 0>
using modint_runtime = internal::modint_base<-(signed)type_id, Storage>;
// #define modint_newtype modint_runtime<__COUNTER__>
} // namespace workspace
#line 2 "Library/src/combinatorics/factorial.hpp"
/**
* @file factorial.hpp
* @brief Factorial
* @date 2021-01-15
*
*
*/
#line 12 "Library/src/combinatorics/factorial.hpp"
namespace workspace {
template <class _Tp> _Tp factorial(int32_t __x) noexcept {
if (__x < 0) return 0;
static std::vector<_Tp> __t{1};
static int32_t __i = (__t.reserve(0x1000000), 0);
while (__i < __x) {
++__i;
__t.emplace_back(__t.back() * _Tp(__i));
}
return __t[__x];
}
template <class _Tp> _Tp factorial_inverse(int32_t __x) noexcept {
if (__x < 0) return 0;
static std::vector<_Tp> __t{1};
static int32_t __i = (__t.reserve(0x1000000), 0);
while (__i < __x) {
++__i;
__t.emplace_back(__t.back() / _Tp(__i));
}
return __t[__x];
}
} // namespace workspace
#line 13 "Library/src/combinatorics/binomial.hpp"
namespace workspace {
/**
* @brief Binomial coefficient for integer args.
*/
template <class _Tp> _Tp binomial(int_fast32_t __x, int_fast32_t __y) {
// if (!__y) return 1;
if (__y < 0 || __x < __y) return 0;
return factorial<_Tp>(__x) * factorial_inverse<_Tp>(__y) *
factorial_inverse<_Tp>(__x - __y);
}
} // namespace workspace
#line 27 "atcoder-workspace/3.cc"
namespace workspace {
using mint = modint<998244353>;
auto bi = binomial<mint>;
struct aaa {
int inv[1 << 17];
constexpr aaa() : inv{} {
for (int i = 0; i < 1 << 17; ++i) inv[i] = i;
}
};
struct aaaa {
aaaa() {}
aaaa(std::nullptr_t) {}
};
void main() {
// start here!
auto _a = aaaa(), _a2 = aaaa(nullptr);
// constexpr aaa _a{};
int n, m, k;
cin >> n >> m >> k;
mint ans;
for (auto i : range(n + 1)) {
for (auto j : range(n + 1)) {
mint add = bi(n, i) * bi(n, j) * bi((n - i) * (n - j), m) * bi(i + j, k);
if ((i + j) % 2) add = -add;
ans += add;
}
}
if (k & 1) ans = -ans;
cout << ans << "\n";
}
} // namespace workspace