結果
| 問題 | No.1495 パンの仕入れ |
| ユーザー |
 jell
|
| 提出日時 | 2021-04-30 23:17:50 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 53,293 bytes |
| コンパイル時間 | 4,326 ms |
| コンパイル使用メモリ | 274,204 KB |
| 実行使用メモリ | 16,772 KB |
| 最終ジャッジ日時 | 2023-09-26 08:16:49 |
| 合計ジャッジ時間 | 9,871 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge12 |
（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 | 1 ms
4,380 KB |
| testcase_01 | AC | 1 ms
4,380 KB |
| testcase_02 | WA | - |
| testcase_03 | WA | - |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | WA | - |
| testcase_07 | WA | - |
| testcase_08 | WA | - |
| testcase_09 | WA | - |
| testcase_10 | WA | - |
| testcase_11 | WA | - |
| testcase_12 | WA | - |
| testcase_13 | WA | - |
| testcase_14 | WA | - |
| testcase_15 | WA | - |
| testcase_16 | WA | - |
| testcase_17 | WA | - |
| testcase_18 | WA | - |
| testcase_19 | WA | - |
| testcase_20 | WA | - |
| testcase_21 | WA | - |
| testcase_22 | WA | - |
| testcase_23 | WA | - |
| testcase_24 | WA | - |
| testcase_25 | WA | - |
| testcase_26 | WA | - |
| testcase_27 | WA | - |
| testcase_28 | WA | - |
| testcase_29 | WA | - |
| testcase_30 | WA | - |
| testcase_31 | WA | - |
| testcase_32 | WA | - |
| testcase_33 | WA | - |
| testcase_34 | WA | - |
| testcase_35 | WA | - |
| testcase_36 | WA | - |
| testcase_37 | WA | - |
| testcase_38 | WA | - |
| testcase_39 | WA | - |
| testcase_40 | WA | - |
| testcase_41 | WA | - |
| testcase_42 | WA | - |
| testcase_43 | WA | - |
| testcase_44 | WA | - |
| testcase_45 | AC | 2 ms
4,376 KB |
| testcase_46 | WA | - |
| testcase_47 | AC | 2 ms
4,380 KB |
ソースコード
#line 1 "other/b.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 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 __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 __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 _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/b.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 2 "Library/src/opt/binary_search.hpp"
/**
* @file binary_search.hpp
* @brief Binary Search
*/
#line 12 "Library/src/opt/binary_search.hpp"
namespace workspace {
namespace _impl {
template <class _Iter, class _Pred>
_Iter discrete_binary_search(_Iter __first, _Iter __last, _Pred &&__pred,
bool __crit) {
if (__first < __last)
while (1 < __last - __first) {
_Iter __mid = __first + ((__last - __first) >> 1);
(__pred(__mid) == __crit ? __first : __last) = __mid;
}
else
while (1 < __first - __last) {
_Iter __mid = __last + ((__first - __last) >> 1);
(__pred(__mid) == __crit ? __first : __last) = __mid;
}
return __first;
}
template <class _Real, class _Pred>
_Real continuous_binary_search(_Real __first, _Real __last, _Real __eps,
_Pred &&__pred, bool __crit) {
if (__first < __last)
for (auto __loop = std::numeric_limits<_Real>::digits;
__first + __eps < __last && __loop; --__loop) {
_Real __mid = (__first + __last) / 2;
(__pred(__mid) == __crit ? __first : __last) = __mid;
}
else
for (auto __loop = std::numeric_limits<_Real>::digits;
__last + __eps < __first && __loop; --__loop) {
_Real __mid = (__first + __last) / 2;
(__pred(__mid) == __crit ? __first : __last) = __mid;
}
return __first;
}
} // namespace _impl
/**
* @brief Binary search on a discrete range.
*
* @param __first Inclusive endpoint
* @param __last Exclusive endpoint
* @param __pred Predicate
* @return Return __x s.t. `__pred(__x) == __pred(__first)` and `__pred(__x) !=
* __pred(__x +/- 1)`. The sign is `+` iff `__first < __last`.
*/
template <class _Iter, class _Pred>
typename std::enable_if<
std::is_convertible<decltype(std::declval<_Pred>()(std::declval<_Iter>())),
bool>::value,
_Iter>::type
binary_search(_Iter __first, _Iter __last, _Pred &&__pred) {
assert(__first != __last);
return _impl::discrete_binary_search(
__first, __last, std::forward<_Pred>(__pred), __pred(__first));
}
/**
* @brief Binary search on the real number line.
* @param __first __pred(__first) is true
* @param __last __pred(__last) is false
* @param eps the error tolerance
* @param __pred the predicate
* @return the boundary point
*/
template <class _Real, class _Pred>
typename std::enable_if<
std::is_convertible<decltype(std::declval<_Pred>()(std::declval<_Real>())),
bool>::value,
_Real>::type
binary_search(_Real __first, _Real __last, _Real __eps, _Pred &&__pred) {
assert(__first != __last);
return _impl::continuous_binary_search(
__first, __last, __eps, std::forward<_Pred>(__pred), __pred(__first));
}
/**
* @brief Parallel binary search on discrete ranges.
* @param ends a vector of pairs; __pred(first) is true, __pred(second) is false
* @param __pred the predicate
* @return the closest points to (second) where __pred is true
*/
template <class Array,
class _Iter = typename std::decay<
decltype(std::get<0>(std::declval<Array>()[0]))>::type,
class _Pred>
typename std::enable_if<
std::is_convertible<
decltype(std::declval<_Pred>()(std::declval<std::vector<_Iter>>())[0]),
bool>::value,
std::vector<_Iter>>::type
parallel_binary_search(Array ends, _Pred __pred) {
std::vector<_Iter> mids(std::size(ends));
for (;;) {
bool all_found = true;
for (size_t i{}; i != std::size(ends); ++i) {
const _Iter &__first = std::get<0>(ends[i]);
const _Iter &__last = std::get<1>(ends[i]);
const _Iter mid(
__first + typename std::make_signed<decltype(__last - __first)>::type(
__last - __first) /
2);
if (mids[i] != mid) {
all_found = false;
mids[i] = mid;
}
}
if (all_found) break;
const auto res = __pred(mids);
for (size_t i{}; i != std::size(ends); ++i) {
(res[i] ? std::get<0>(ends[i]) : std::get<1>(ends[i])) = mids[i];
}
}
return mids;
}
/**
* @brief Parallel binary search on the real number line.
* @param ends a vector of pairs; __pred(first) is true, __pred(second) is false
* @param eps the error tolerance
* @param __pred the predicate
* @return the boundary points
*/
template <class Array,
class _Real = typename std::decay<
decltype(std::get<0>(std::declval<Array>()[0]))>::type,
class _Pred>
typename std::enable_if<
std::is_convertible<
decltype(std::declval<_Pred>()(std::declval<std::vector<_Real>>())[0]),
bool>::value,
std::vector<_Real>>::type
parallel_binary_search(Array ends, const _Real eps, _Pred __pred) {
std::vector<_Real> mids(std::size(ends));
for (auto loops = 0; loops != std::numeric_limits<_Real>::digits; ++loops) {
bool all_found = true;
for (size_t i{}; i != std::size(ends); ++i) {
const _Real __first = std::get<0>(ends[i]);
const _Real __last = std::get<1>(ends[i]);
if (__first + eps < __last || __last + eps < __first) {
all_found = false;
mids[i] = (__first + __last) / 2;
}
}
if (all_found) break;
const auto res = __pred(mids);
for (size_t i{}; i != std::size(ends); ++i) {
(res[i] ? std::get<0>(ends[i]) : std::get<1>(ends[i])) = mids[i];
}
}
return mids;
}
} // namespace workspace
#line 2 "Library/src/opt/exponential_search.hpp"
/**
* @file exponential_search.hpp
* @brief Exponential Search
*/
#line 9 "Library/src/opt/exponential_search.hpp"
namespace workspace {
/**
* @brief Exponential search on a discrete range.
*
* @param __first Inclusive endpoint
* @param __last Exclusive endpoint
* @param __pred Predicate
* @return Return __x s.t. `__pred(__x) == __pred(__first)` and `__pred(__x) !=
* __pred(__x +/- 1)`. The sign is `+` iff `__first < __last`.
*/
template <class _Iter, class _Pred>
typename std::enable_if<
std::is_convertible<decltype(std::declval<_Pred>()(std::declval<_Iter>())),
bool>::value,
_Iter>::type
exponential_search(_Iter __first, _Iter __last, _Pred&& __pred) {
assert(__first != __last);
bool __crit = __pred(__first);
if (__first < __last) {
for (decltype(__last - __first) __step = 1; __step < __last - __first;
__step <<= 1)
if (__pred(__first += __step) != __crit)
return _impl::discrete_binary_search(
__first - __step, __first, std::forward<_Pred>(__pred), __crit);
}
else {
for (decltype(__first - __last) __step = 1; __step < __first - __last;
__step <<= 1)
if (__pred(__first -= __step) != __crit)
return _impl::discrete_binary_search(
__first + __step, __first, std::forward<_Pred>(__pred), __crit);
}
return _impl::discrete_binary_search(__first, __last,
std::forward<_Pred>(__pred), __crit);
}
/**
* @brief Exponential search on the real number line.
*
* @param __first Endpoint
* @param __last Endpoint
* @param __eps Error tolerance
* @param __pred Predicate
* @return A boundary point `__x` s.t. `__pred(__x) == __pred(__first)`.
*/
template <class _Real, class _Pred>
typename std::enable_if<
std::is_convertible<decltype(std::declval<_Pred>()(std::declval<_Real>())),
bool>::value,
_Real>::type
exponential_search(_Real __first, _Real __last, _Real __eps, _Pred&& __pred) {
bool __crit = __pred(__first);
if (__first < __last) {
for (_Real __step = __eps; __step < __last - __first; __step += __step)
if (__pred(__first += __step) != __crit)
return _impl::continuous_binary_search(__first - __step, __first, __eps,
std::forward<_Pred>(__pred),
__crit);
}
else {
for (_Real __step = __eps; __step < __first - __last; __step += __step)
if (__pred(__first -= __step) != __crit)
return _impl::continuous_binary_search(__first + __step, __first, __eps,
std::forward<_Pred>(__pred),
__crit);
}
return _impl::continuous_binary_search(__first, __last, __eps,
std::forward<_Pred>(__pred), __crit);
}
} // namespace workspace
#line 2 "Library/src/opt/trinary_search.hpp"
/*
* @file trinary_search.hpp
* @brief Trinary Search
*/
#line 9 "Library/src/opt/trinary_search.hpp"
#include <type_traits>
namespace workspace {
/*
* @brief Trinary search on discrete range.
* @param first Left end, inclusive
* @param last Right end, exclusive
* @param comp Compare function
* @return Local minimal point.
*/
template <class Iter, class Comp>
typename std::enable_if<
std::is_convertible<decltype(std::declval<Comp>()(std::declval<Iter>(),
std::declval<Iter>())),
bool>::value,
Iter>::type
trinary_search(Iter first, Iter last, Comp comp) {
assert(first < last);
typename std::make_signed<decltype(last - first)>::type dist(last - first);
while (2 < dist) {
Iter left(first + dist / 3), right(first + dist * 2 / 3);
if (comp(left, right))
last = right, dist = (dist + dist) / 3;
else
first = left, dist -= dist / 3;
}
if (1 < dist && comp(first + 1, first)) ++first;
return first;
}
/*
* @brief Trinary search on discrete range.
* @param first Left end, inclusive
* @param last Right end, exclusive
* @param func Function
* @return Local minimal point.
*/
template <class Iter, class Func>
typename std::enable_if<
std::is_same<decltype(std::declval<Func>()(std::declval<Iter>()), nullptr),
std::nullptr_t>::value,
Iter>::type
trinary_search(Iter const &first, Iter const &last, Func func) {
return trinary_search(first, last, [&](Iter const &__i, Iter const &__j) {
return func(__i) < func(__j);
});
}
/*
* @brief Trinary search on the real number line.
* @param first Left end
* @param last Right end
* @param eps Error tolerance
* @param comp Compare function
* @return Local minimal point.
*/
template <class Real, class Comp>
typename std::enable_if<
std::is_convertible<decltype(std::declval<Comp>()(std::declval<Real>(),
std::declval<Real>())),
bool>::value,
Real>::type
trinary_search(Real first, Real last, Real const &eps, Comp comp) {
assert(first < last);
while (eps < last - first) {
Real left{(first * 2 + last) / 3}, right{(first + last * 2) / 3};
if (comp(left, right))
last = right;
else
first = left;
}
return first;
}
/*
* @brief Trinary search on the real number line.
* @param first Left end
* @param last Right end
* @param eps Error tolerance
* @param func Function
* @return Local minimal point.
*/
template <class Real, class Func>
typename std::enable_if<
std::is_same<decltype(std::declval<Func>()(std::declval<Real>()), nullptr),
std::nullptr_t>::value,
Real>::type
trinary_search(Real const &first, Real const &last, Real const &eps,
Func func) {
return trinary_search(
first, last, eps,
[&](Real const &__i, Real const &__j) { return func(__i) < func(__j); });
}
} // namespace workspace
#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/lib/utils"
// #include "src/utils/cached.hpp"
#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 chgr(
_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 chgr(
_T1 &__x, _T2 &&__y, _Compare __comp) noexcept {
return __comp(__x, __y) ? __x = std::forward<_T2>(__y), true : false;
}
} // namespace workspace
#line 5 "Library/lib/utils"
// #include "src/utils/fixed_point.hpp"
// #include "src/utils/hash.hpp"
#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 2 "Library/src/utils/sfinae.hpp"
/**
* @file sfinae.hpp
* @brief SFINAE
*/
#line 11 "Library/src/utils/sfinae.hpp"
#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; };
template <> struct is_signed<__uint128_t> : std::false_type {};
template <> struct is_signed<__int128_t> : std::true_type {};
template <> struct is_unsigned<__uint128_t> : std::true_type {};
template <> struct is_unsigned<__int128_t> : std::false_type {};
#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;
};
template <typename _Tp> struct multiplicable {
using type = std::conditional_t<
is_integral_ext<_Tp>::value,
std::conditional_t<std::is_signed<_Tp>::value,
typename multiplicable_int<_Tp>::type,
typename multiplicable_uint<_Tp>::type>,
_Tp>;
};
} // namespace workspace
#line 15 "Library/src/utils/io/istream.hpp"
namespace workspace {
namespace _istream_impl {
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<std::decay_t<decltype(__e)>>(__is, __e);
else
static_assert(has_begin<_Tp>::value, "istream unsupported type.");
}
};
template <class _Tp>
struct istream_helper<
_Tp,
decltype(std::declval<std::decay_t<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 _istream_impl
/**
* @brief A wrapper class for std::istream.
*/
class istream : public std::istream {
public:
/**
* @brief Wrapped operator.
*/
template <typename _Tp> istream &operator>>(_Tp &__x) {
_istream_impl::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<std::decay_t<_Container>, std::string>::value &&
!std::is_same<std::decay_t<_Container>, 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 9 "Library/lib/utils"
// #include "src/utils/io/read.hpp"
#line 2 "Library/src/utils/grid/motion.hpp"
/**
* @file motion.hpp
* @brief Motion
*/
#line 9 "Library/src/utils/grid/motion.hpp"
namespace workspace {
/**
* @brief Transpose.
*
* @param __grid
*/
template <class _Grid,
typename = decltype(std::declval<std::decay_t<_Grid>>()[0].resize(0))>
constexpr decltype(auto) transpose(_Grid &&__grid) noexcept {
auto __h = std::size(__grid), __w = std::size(__grid[0]);
std::decay_t<_Grid> __t(__w);
for (auto &&__r : __t) __r.resize(__h);
for (size_t __i = 0; __i != __h; ++__i)
for (size_t __j = 0; __j != __w; ++__j)
if constexpr (std::is_rvalue_reference<decltype(__grid)>::value)
__t[__j][__i] = std::move(__grid[__i][__j]);
else
__t[__j][__i] = __grid[__i][__j];
return __t;
}
/**
* @brief Transpose.
*
* @param __grid
*/
template <class _Tp, size_t _Rows, size_t _Cols>
constexpr decltype(auto) transpose(const _Tp (&__grid)[_Rows][_Cols]) noexcept {
std::array<std::array<_Tp, _Rows>, _Cols> __t;
for (size_t __i = 0; __i != _Rows; ++__i)
for (size_t __j = 0; __j != _Cols; ++__j) __t[__j][__i] = __grid[__i][__j];
return __t;
}
/**
* @brief Transpose.
*
* @param __grid
*/
template <class _Tp, size_t _Rows, size_t _Cols>
constexpr decltype(auto) transpose(_Tp(&&__grid)[_Rows][_Cols]) noexcept {
std::array<std::array<_Tp, _Rows>, _Cols> __t;
for (size_t __i = 0; __i != _Rows; ++__i)
for (size_t __j = 0; __j != _Cols; ++__j)
__t[__j][__i] = std::move(__grid[__i][__j]);
return __t;
}
/**
* @brief Transpose.
*
* @param __grid
*/
template <class _Tp, size_t _Rows, size_t _Cols>
constexpr decltype(auto) transpose(
const std::array<std::array<_Tp, _Cols>, _Rows> &__grid) noexcept {
std::array<std::array<_Tp, _Rows>, _Cols> __t;
for (size_t __i = 0; __i != _Rows; ++__i)
for (size_t __j = 0; __j != _Cols; ++__j) __t[__j][__i] = __grid[__i][__j];
return __t;
}
/**
* @brief Transpose.
*
* @param __grid
*/
template <class _Tp, size_t _Rows, size_t _Cols>
constexpr decltype(auto) transpose(
std::array<std::array<_Tp, _Cols>, _Rows> &&__grid) noexcept {
std::array<std::array<_Tp, _Rows>, _Cols> __t;
for (size_t __i = 0; __i != _Rows; ++__i)
for (size_t __j = 0; __j != _Cols; ++__j)
__t[__j][__i] = std::move(__grid[__i][__j]);
return __t;
}
/**
* @brief Roll the grid counter-clockwise.
*
* @param __grid
* @return
*/
template <class _Grid> decltype(auto) roll_ccw(_Grid &&__grid) noexcept {
if constexpr (std::is_rvalue_reference<decltype(__grid)>::value) {
auto __t = transpose(std::move(__grid));
std::reverse(std::begin(__t), std::end(__t));
return __t;
}
else {
auto __t = transpose(__grid);
std::reverse(std::begin(__t), std::end(__t));
return __t;
}
}
/**
* @brief Roll the grid clockwise.
*
* @param __grid
* @return
*/
template <class _Grid> decltype(auto) roll_cw(_Grid &&__grid) noexcept {
if constexpr (std::is_rvalue_reference<decltype(__grid)>::value) {
std::reverse(std::begin(__grid), std::end(__grid));
return transpose(std::move(__grid));
}
else {
auto __t = transpose(__grid);
for (auto &&__r : __t) std::reverse(std::begin(__r), std::end(__r));
return __t;
}
}
} // namespace workspace
#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.
*
* @param __dim Dimension
* @param __x Initial value
*/
template <typename _Tp, class _Dim, size_t _Nm>
constexpr decltype(auto) make_vector([[maybe_unused]] _Dim* __dim,
const _Tp& __x = _Tp()) {
static_assert(std::is_convertible<_Dim, size_t>::value);
if constexpr (_Nm)
return std::vector(*__dim,
make_vector<_Tp, _Dim, _Nm - 1>(std::next(__dim), __x));
else
return __x;
}
/**
* @brief Make a multi-dimensional vector.
*
* @param __dim Dimension
* @param __x Initial value
*/
template <typename _Tp, class _Dim, size_t _Nm>
constexpr decltype(auto) make_vector(const _Dim (&__dim)[_Nm],
const _Tp& __x = _Tp()) {
return make_vector<_Tp, _Dim, _Nm>((_Dim*)__dim, __x);
}
/**
* @brief Make a multi-dimensional vector.
*
* @param __dim Dimension
* @param __x Initial value
*/
template <typename _Tp, class _Dim, size_t _Nm = 0>
constexpr decltype(auto) make_vector([[maybe_unused]] const _Dim& __dim,
const _Tp& __x = _Tp()) {
if constexpr (_Nm == std::tuple_size<_Dim>::value)
return __x;
else {
static_assert(
std::is_convertible<std::tuple_element_t<_Nm, _Dim>, size_t>::value);
return std::vector(std::get<_Nm>(__dim),
make_vector<_Tp, _Dim, _Nm + 1>(__dim, __x));
}
}
} // 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 _reversed_impl {
template <class _Container> class reversed {
_Container __cont;
public:
constexpr reversed(_Container &&__cont) noexcept : __cont(__cont) {}
constexpr decltype(auto) begin() noexcept { return std::rbegin(__cont); }
constexpr decltype(auto) begin() const noexcept {
return std::rbegin(__cont);
}
constexpr decltype(auto) end() noexcept { return std::rend(__cont); }
constexpr decltype(auto) end() const noexcept { return std::rend(__cont); }
constexpr decltype(auto) size() const noexcept { return std::size(__cont); }
};
} // namespace _reversed_impl
template <class _Container>
constexpr decltype(auto) reversed(_Container &&__cont) noexcept {
return _reversed_impl::reversed<_Container>{std::forward<_Container>(__cont)};
}
template <class _Tp>
constexpr decltype(auto) reversed(
std::initializer_list<_Tp> &&__cont) noexcept {
return _reversed_impl::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(const _Index &__i = _Index()) noexcept : current(__i) {}
constexpr bool operator==(const iterator &__x) const noexcept {
return current == __x.current;
}
constexpr bool operator!=(const iterator &__x) const noexcept {
return current != __x.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());
}
constexpr size_t size() const noexcept {
return std::distance(__first, __last);
}
};
template <class... _Args>
constexpr decltype(auto) rrange(_Args &&...__args) noexcept {
return reversed(range(std::forward<_Args>(__args)...));
}
template <class _Container>
constexpr decltype(auto) iterate(_Container &&__cont) noexcept {
return range(std::begin(__cont), std::end(__cont));
}
template <class _Container>
constexpr decltype(auto) riterate(_Container &&__cont) noexcept {
return range(std::rbegin(__cont), std::rend(__cont));
}
} // namespace workspace
#endif
#line 17 "Library/lib/utils"
// #include "src/utils/py-like/reversed.hpp"
// #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/b.cc"
signed main() {
using namespace workspace;
io_setup(15);
//* given
case_info.read(); //*/
/* unspecified
case_info.total = -1; //*/
return case_info.iterate();
}
namespace workspace {
void main() {
// start here!
int n, m, k;
cin >> n >> m >> k;
vector<vector<i64>> needs(n);
for (auto _ : range(m)) {
int x, y;
cin >> x >> y;
needs[x - 1].emplace_back(y);
}
bool any = 0;
vector<tuple<i64, i64, i64>> curves;
for (auto &&v : needs) {
if (v.empty()) {
any = true;
continue;
}
i64 s = 0, ss = 0;
for (auto &&x : v) {
s += x;
ss += x * x;
}
curves.emplace_back(v.size(), -2 * s, ss);
}
auto siml = [&](i64 g) -> pair<i64, i64> {
i64 xs = 0, cost{};
for (auto [a, b, c] : curves) {
auto x = max(0, floor_div(g - a - b, a * 2));
xs += x;
cost += (a * x + b) * x + c;
}
return {xs, cost};
};
auto pred = [&](i64 g) -> bool { return siml(g).first <= k; };
const i64 inf = roundl(sqrt((1ll << 62) / m));
auto g = binary_search(-inf, inf, pred);
auto [xs, cost] = siml(g);
auto ans = g * (k - xs) + cost;
if (any) {
cost = 0;
xs = 0;
for (auto [a, b, c] : curves) {
auto x = max(0, floor_div(-a - b, a * 2) + 1);
xs += x;
cost += (a * x + b) * x + c;
}
if (xs <= k) chle(ans, cost);
}
cout << ans << "\n";
}
} // namespace workspace