結果
| 問題 |
No.1441 MErGe
|
| コンテスト | |
| ユーザー |
 jell
|
| 提出日時 | 2021-03-26 22:27:57 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 300 ms / 1,000 ms |
| コード長 | 60,456 bytes |
| コンパイル時間 | 4,139 ms |
| コンパイル使用メモリ | 272,868 KB |
| 最終ジャッジ日時 | 2025-01-19 23:00:21 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 28 |
ソースコード
#line 1 "other/yu.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
namespace _alias_impl {
template <class> struct first_arg { using type = void; };
template <class _Tp, class = void> struct parse_comp : first_arg<_Tp> {};
template <class _Tp>
struct parse_comp<_Tp, std::__void_t<decltype(&_Tp::operator())>>
: first_arg<decltype(&_Tp::operator())> {};
template <class _R, class _Tp, class... _Args>
struct first_arg<_R(_Tp, _Args...)> {
using type = _Tp;
};
template <class _R, class _Tp, class... _Args>
struct first_arg<_R (*)(_Tp, _Args...)> {
using type = _Tp;
};
template <class _G, class _R, class _Tp, class... _Args>
struct first_arg<_R (_G::*)(_Tp, _Args...)> {
using type = _Tp;
};
template <class _G, class _R, class _Tp, class... _Args>
struct first_arg<_R (_G::*)(_Tp, _Args...) const> {
using type = _Tp;
};
} // namespace _alias_impl
template <class _Tp = void, class _Compare = std::less<_Tp>>
decltype(auto) make_priority_queue(_Compare __x = _Compare()) noexcept {
using type = std::conditional_t<
std::is_void<_Tp>::value,
std::decay_t<typename _alias_impl::parse_comp<_Compare>::type>, _Tp>;
return std::priority_queue<type, std::vector<type>, _Compare>(__x);
}
template <class _Tp = void, class _Compare = std::less<_Tp>>
decltype(auto) make_set(_Compare __x = _Compare()) noexcept {
using type = std::conditional_t<
std::is_void<_Tp>::value,
std::decay_t<typename _alias_impl::parse_comp<_Compare>::type>, _Tp>;
return std::set<type, _Compare>(__x);
}
template <class _Key, class _Mapped, class _Compare = std::less<_Key>>
decltype(auto) make_map(_Compare __x = _Compare()) noexcept {
return std::map<_Key, _Mapped, _Compare>(__x);
}
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 "other/yu.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 "other/yu.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::array.
*
* @param __os Output stream
* @param __a Array
* @return Reference to __os.
*/
template <class _Os, class _Tp, size_t _Nm>
ostream_ref<_Os> operator<<(_Os &__os, const std::array<_Tp, _Nm> &__a) {
if constexpr (_Nm) {
__os << __a[0];
for (size_t __i = 1; __i != _Nm; ++__i) __os << ' ' << __a[__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 15 "Library/lib/utils"
// #include "src/utils/py-like/enumerate.hpp"
#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 18 "Library/lib/utils"
// #include "src/utils/py-like/zip.hpp"
#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 11 "other/yu.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/data_structure/segment_tree/basic.hpp"
/**
* @file basic.hpp
* @brief Segment Tree
*/
#line 10 "Library/src/data_structure/segment_tree/basic.hpp"
#if __cplusplus >= 201703L
#include <optional>
#endif
#line 2 "Library/src/algebra/system/monoid.hpp"
/*
* @file monoid.hpp
* @brief Monoid
*/
#line 9 "Library/src/algebra/system/monoid.hpp"
namespace workspace {
template <class T, class E = T> struct min_monoid {
using value_type = T;
static T min, max;
T value;
min_monoid() : value(max) {}
min_monoid(const T &value) : value(value) {}
operator T() const { return value; }
min_monoid operator+(const min_monoid &rhs) const {
return value < rhs.value ? *this : rhs;
}
min_monoid operator*(const E &rhs) const;
};
template <class T, class E>
T min_monoid<T, E>::min = std::numeric_limits<T>::min() / 2;
template <class T, class E>
T min_monoid<T, E>::max = std::numeric_limits<T>::max() / 2;
template <class T, class E = T> struct max_monoid : min_monoid<T, E> {
using base = min_monoid<T, E>;
using base::min_monoid;
max_monoid() : base(base::min) {}
max_monoid operator+(const max_monoid &rhs) const {
return !(base::value < rhs.value) ? *this : rhs;
}
max_monoid operator*(const E &rhs) const;
};
} // namespace workspace
#line 16 "Library/src/data_structure/segment_tree/basic.hpp"
namespace workspace {
/**
* @tparam Monoid `operator+`, `operator=`
* @tparam Container_tmpl `operator[]`, `size_type`
*/
template <class Monoid, class Endomorphism = void,
template <class...> class Container_tmpl = std::vector>
class segment_tree {
static_assert(
std::is_assignable<Monoid &, decltype(std::declval<Monoid>() +
std::declval<Monoid>())>::value,
"\'Monoid\' has no proper binary \'operator+\'.");
constexpr static bool __support_lazy = !std::is_void<Endomorphism>::value;
#if __cplusplus < 201703L
struct node_base {
node_base() = default;
node_base(Monoid const &__x) : __v(__x) {}
operator bool() const { return __f; }
void operator=(Monoid const &__x) {
__v = __x;
__f = true;
}
Monoid &operator*() { return __v; }
Monoid const &operator*() const { return __v; }
void reset() { __f = false; }
private:
Monoid __v{};
bool __f{true};
};
#else
struct node_base : std::optional<Monoid> {
using std::optional<Monoid>::operator=;
node_base() : std::optional<Monoid>(Monoid{}) {}
};
#endif
struct node_lazy : node_base {
using node_base::operator=;
std::optional<Endomorphism> __z;
};
using node =
typename std::conditional<__support_lazy, node_lazy, node_base>::type;
using container_type = Container_tmpl<node>;
public:
using size_type = typename container_type::size_type;
class iterator {
segment_tree *__p;
size_type __i;
public:
using difference_type = typename std::make_signed<size_type>::type;
using value_type = Monoid;
using reference = Monoid &;
using pointer = iterator;
using iterator_category = std::random_access_iterator_tag;
/**
* @brief Construct a new iterator object
*
*/
iterator() = default;
/**
* @brief Construct a new iterator object
*
* @param __p Pointer to a segment tree object
* @param __i Index
*/
iterator(segment_tree *__p, size_type __i) : __p(__p), __i(__i) {}
bool operator==(iterator const &rhs) const {
return __p == rhs.__p && __i == rhs.__i;
}
bool operator!=(iterator const &rhs) const { return !operator==(rhs); }
bool operator<(iterator const &rhs) const { return __i < rhs.__i; }
bool operator>(iterator const &rhs) const { return __i > rhs.__i; }
bool operator<=(iterator const &rhs) const { return __i <= rhs.__i; }
bool operator>=(iterator const &rhs) const { return __i >= rhs.__i; }
iterator &operator++() { return ++__i, *this; }
iterator &operator--() { return --__i, *this; }
difference_type operator-(iterator const &rhs) const {
return __i - rhs.__i;
}
/**
* @brief
*
* @return reference
*/
reference operator*() const { return __p->operator[](__i); }
};
using value_type = typename iterator::value_type;
using reference = typename iterator::reference;
iterator begin() { return {this, 0}; }
iterator end() { return {this, size_orig}; }
auto rbegin() { return std::make_reverse_iterator(end()); }
auto rend() { return std::make_reverse_iterator(begin()); }
protected:
public:
size_type size_orig, height, size_ext;
container_type data;
node &pull(size_type __i) noexcept {
if (!data[__i]) data[__i] = *pull(__i << 1) + *pull(__i << 1 | 1);
return data[__i];
}
void push(size_type __i) {
if (auto &__lz = data[__i].__z) {
apply(data[__i << 1], *__lz);
apply(data[__i << 1 | 1], *__lz);
__lz.reset();
}
}
void sync(size_type __i) {
if (!data[__i])
data[__i] = *pull(__i << 1) + *pull(__i << 1 | 1);
else if (data[__i].__z) {
apply(data[__i << 1], *data[__i].__z);
apply(data[__i << 1 | 1], *data[__i].__z);
data[__i].__z.reset();
}
}
template <class _End = Endomorphism>
void apply(node &__nd, _End const &endo) {
*__nd = *__nd * endo;
__nd.__z = __nd.__z ? *__nd.__z * endo : endo;
}
// template <class _End = Endomorphism>
// void apply_top(size_t __i, _End const &endo) {
// auto &__nd = pull(__i);
// *__nd = *__nd * endo;
// __nd.__z = __nd.__z ? *__nd.__z * endo : endo;
// }
template <class Pred>
constexpr decltype(std::declval<Pred>()(Monoid{})) pass_args(
Pred pred, Monoid const &_1, [[maybe_unused]] size_type _2) {
return pred(_1);
}
template <class Pred>
constexpr decltype(std::declval<Pred>()(Monoid{}, size_type{})) pass_args(
Pred pred, Monoid const &_1, size_type _2) {
return pred(_1, _2);
}
template <class Pred>
size_type left_partition_subtree(size_type __i, Monoid mono, size_type step,
Pred pred) {
assert(__i);
while (__i < size_ext) {
if constexpr (__support_lazy) push(__i);
const Monoid tmp = *pull((__i <<= 1) | 1) + mono;
if (pass_args(pred, tmp, ((__i | 1) << --step) ^ size_ext))
mono = tmp;
else
++__i;
}
return ++__i -= size_ext;
}
template <class Pred>
size_type right_partition_subtree(size_type __i, Monoid mono, size_type step,
Pred pred) {
assert(__i);
while (__i < size_ext) {
if constexpr (__support_lazy) push(__i);
const Monoid tmp = mono + *pull(__i <<= 1);
if (pass_args(pred, tmp, ((__i | 1) << --step) ^ size_ext))
++__i, mono = tmp;
}
return (__i -= size_ext) < size_orig ? __i : size_orig;
}
public:
/**
* @brief Construct a new segment tree object
*
* @param __n Number of elements.
*/
segment_tree(size_type __n = 0)
: size_orig{__n},
height(__n > 1 ? 64 - __builtin_clzll(__n - 1) : 0),
size_ext{size_type{1} << height} {
if constexpr (std::is_constructible<container_type, size_t>::value)
data = container_type(size_ext << 1);
data[0].reset();
}
/**
* @brief Construct a new segment tree object
*
* @param __n Number of elements.
* @param init
*/
segment_tree(size_type __n, Monoid const &init) : segment_tree(__n) {
for (auto i = begin(); i != end(); ++i) *i = init;
}
/**
* @brief Construct a new segment tree object
*
* @tparam Tp
* @param __n Number of elements.
* @param init
*/
template <class Tp, typename std::enable_if<std::is_convertible<
Tp, Monoid>::value>::type * = nullptr>
segment_tree(size_type __n, Tp &&init) : segment_tree(__n) {
for (auto i = begin(); i != end(); ++i) *i = init;
}
/**
* @brief Construct a new segment tree object
*
* @tparam Iterator
* @param __first
* @param __last
*/
template <class Iterator,
typename std::enable_if<std::is_convertible<
typename std::iterator_traits<Iterator>::value_type,
Monoid>::value> * = nullptr>
segment_tree(Iterator __first, Iterator __last)
: segment_tree(std::distance(__first, __last)) {
for (auto i = begin(); __first != __last; ++i, ++__first) *i = *__first;
}
operator Container_tmpl<value_type>() const {
Container_tmpl<value_type> __c(size());
for (size_type __i = 0; __i != size(); ++__i)
__c[__i] = *data[__i | size_ext];
return __c;
}
/**
* @return Number of elements.
*/
size_type size() const { return size_orig; }
/**
* @return Whether %segment_tree is empty.
*/
bool empty() const { return !size(); }
/**
* @param __i Index of the element
* @return Reference to the element.
*/
reference operator[](size_type __i) {
assert(__i < size_orig);
reference __ref = *data[__i |= size_ext];
if constexpr (__support_lazy) {
for (size_t __h{height}; __h; --__h) {
push(__i >> __h);
data[__i >> __h].reset();
}
} else {
while (data[__i >>= 1]) data[__i].reset();
}
return __ref;
}
/**
* @param first Left end, inclusive
* @param last Right end, exclusive
* @return Sum of elements in the interval.
*/
value_type fold(size_type first, size_type last) {
assert(last <= size_orig);
if (!(first < last)) return {};
first += size_ext, last += size_ext;
value_type left{}, right{};
for (size_t l = first, r = last--; l != r; l >>= 1, r >>= 1) {
if (l & 1) left = left + *pull(l++);
if (r & 1) right = *pull(--r) + right;
if constexpr (__support_lazy) {
if (data[first >>= 1].__z) left = left * *data[first].__z;
if (data[last >>= 1].__z) right = right * *data[last].__z;
}
}
if constexpr (__support_lazy) {
while (first >>= 1, last >>= 1) {
if (data[first].__z) left = left * *data[first].__z;
if (data[last].__z) right = right * *data[last].__z;
}
}
// if (first >= last) return Monoid{};
// first += size_ext, last += size_ext - 1;
// Monoid left{}, right{};
// for (size_t l = first, r = last + 1; last; l >>= 1, r >>= 1) {
// if (l < r) {
// if (l & 1) left = left + data[l++];
// if (r & 1) right = data[--r] + right;
// }
// if (first >>= 1, last >>= 1) {
// left = left * lazy[first];
// right = right * lazy[last];
// }
// }
// return left + right;
return left + right;
}
/**
* @return The whole sum.
*/
value_type fold() { return fold(0, size_orig); }
template <class _End = Endomorphism>
void update(size_type first, size_type last, _End const &endo) {
static_assert(__support_lazy);
assert(last <= size_orig);
if (!(first < last)) return;
first += size_ext, last += size_ext;
--last;
for (auto i = height; i; --i) push(first >> i), push(last >> i);
++last;
for (auto l = first, r = last; l < r; l >>= 1, r >>= 1) {
if (l & 1) apply(pull(l++), endo);
if (r & 1) apply(pull(--r), endo);
}
for (first >>= __builtin_ffs(first); data[first]; first >>= 1)
data[first].reset();
for (last >>= __builtin_ffs(last); data[last]; last >>= 1)
data[last].reset();
}
/**
* @brief Binary search for the partition point.
* @param right Right fixed end of the interval, exclusive
* @param pred Predicate in the form of either 'bool(Monoid)' or 'bool(Monoid,
* size_type)'
* @return Left end of the extremal interval satisfying the condition,
* inclusive.
*/
template <class Pred> size_type left_partition(size_type right, Pred pred) {
assert(right <= size_orig);
right += size_ext;
if constexpr (__support_lazy)
for (size_t i{height}; i; --i) push(right >> i);
Monoid mono{};
for (size_type left{size_ext}, step{}; left != right;
left >>= 1, right >>= 1, ++step) {
if ((left & 1) != (right & 1)) {
Monoid tmp = *pull(--right) + mono;
if (!pass_args(pred, tmp, (right << step) ^ size_ext))
return left_partition_subtree(right, mono, step, pred);
mono = tmp;
}
}
return 0;
}
/**
* @brief Binary search for the partition point.
* @param left Left fixed end of the interval, inclusive
* @param pred Predicate in the form of either 'bool(Monoid)' or 'bool(Monoid,
* size_type)'
* @return Right end of the extremal interval satisfying the condition,
* exclusive.
*/
template <class Pred> size_type right_partition(size_type left, Pred pred) {
assert(left <= size_orig);
left += size_ext;
if constexpr (__support_lazy)
for (size_t i{height}; i; --i) push(left >> i);
Monoid mono{};
for (size_type right{size_ext << 1}, step{}; left != right;
left >>= 1, right >>= 1, ++step) {
if ((left & 1) != (right & 1)) {
Monoid tmp = mono + *pull(left);
if (!pass_args(pred, tmp, ((left + 1) << step) ^ size_ext))
return right_partition_subtree(left, mono, step, pred);
mono = tmp;
++left;
}
}
return size_orig;
}
};
} // namespace workspace
#line 27 "other/yu.cc"
namespace workspace {
void main() {
// start here!
int n, q;
cin >> n >> q;
struct endo {
bool flag = false;
endo operator*(endo r) { return {flag or r.flag}; }
};
struct data {
i64 v = 0, c = 0;
data() {}
data(i64 a) : v(a), c(1) {}
data(i64 v, i64 c) : v(v), c(c) {}
data operator+(data r) const { return {v + r.v, c + r.c}; }
data operator*(endo r) { return !r.flag ? *this : data(); }
};
segment_tree<data, endo> sgt(n);
for (auto &x : sgt) {
int a;
cin >> a;
x = a;
}
while (q--) {
int tp;
cin >> tp;
int l, r;
cin >> l >> r;
++r;
l = sgt.right_partition(0, [&](auto x) { return x.c < l; });
r = sgt.right_partition(0, [&](auto x) { return x.c < r; });
switch (tp) {
case 1: {
auto f = sgt.fold(l, r);
sgt.update(l, r, {1});
sgt[l] = f.v;
} break;
case 2: {
cout << sgt.fold(l, r).v << "\n";
} break;
}
}
}
} // namespace workspace