結果
問題 | No.1421 国勢調査 (Hard) |
ユーザー |
![]() |
提出日時 | 2021-03-05 23:18:22 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 27 ms / 2,000 ms |
コード長 | 64,774 bytes |
コンパイル時間 | 3,389 ms |
コンパイル使用メモリ | 264,588 KB |
最終ジャッジ日時 | 2025-01-19 11:59:24 |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 30 |
ソースコード
#line 1 "other/par.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));elsereturn (__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));elsereturn (__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_EVALUATEDif (!__builtin_is_constant_evaluated()) {__glibcxx_assert(__shift_exponent != numeric_limits<_Tp>::digits);}#endifusing __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.#endiftemplate <class T, class Comp = less<T>>using priority_queue = std::priority_queue<T, vector<T>, Comp>;template <class T> using stack = std::stack<T, vector<T>>;template <class _T1, class _T2,typename = decltype(std::declval<const _T2 &>() <std::declval<const _T1 &>())>constexprtypename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,typename std::common_type<_T1, _T2>::type>::typemin(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 &>()))>constexprtypename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,typename std::common_type<_T1, _T2>::type>::typemin(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 &>())>constexprtypename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,typename std::common_type<_T1, _T2>::type>::typemax(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 &>()))>constexprtypename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,typename std::common_type<_T1, _T2>::type>::typemax(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 2 "Library/lib/cxx20"/** @file cxx20* @brief C++20 Features*/#line 9 "Library/lib/cxx20"#if __cplusplus <= 201703L#include <algorithm>#include <vector>namespace std {/** @fn erase_if* @brief Erase the elements of a container that do not satisfy the condition.* @param __cont Container.* @param __pred Predicate.* @return Number of the erased elements.*/template <typename _Tp, typename _Alloc, typename _Predicate>inline typename vector<_Tp, _Alloc>::size_type erase_if(vector<_Tp, _Alloc>& __cont, _Predicate __pred) {const auto __osz = __cont.size();__cont.erase(remove_if(__cont.begin(), __cont.end(), __pred), __cont.end());return __osz - __cont.size();}/** @fn erase* @brief Erase the elements of a container that are equal to the given value.* @param __cont Container.* @param __value Value.* @return Number of the erased elements.*/template <typename _Tp, typename _Alloc, typename _Up>inline typename vector<_Tp, _Alloc>::size_type erase(vector<_Tp, _Alloc>& __cont, const _Up& __value) {const auto __osz = __cont.size();__cont.erase(remove(__cont.begin(), __cont.end(), __value), __cont.end());return __osz - __cont.size();}} // namespace std#endif#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;}elsewhile (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;}elsefor (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>::typebinary_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>::typebinary_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>>::typeparallel_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>>::typeparallel_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>::typeexponential_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>::typeexponential_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>::typetrinary_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;elsefirst = 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>::typetrinary_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>::typetrinary_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;elsefirst = 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>::typetrinary_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-indexedunsigned 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;elsereturn __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;elsereturn __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 11 "Library/src/utils/sfinae.hpp"#ifndef __INT128_DEFINED__#ifdef __SIZEOF_INT128__#define __INT128_DEFINED__ 1#else#define __INT128_DEFINED__ 0#endif#endifnamespace 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 stdnamespace 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 >= 201402template <class _Tp>constexpr static bool is_integral_ext_v = is_integral_ext<_Tp>::value;#endiftemplate <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;};#endiftemplate <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> {};#if __cplusplus >= 201703Ltemplate <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);}};#endiftemplate <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);elsestatic_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 // INT128template <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;elseistream_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>>::typeoperator<<(_Os &__os, const _Tp (&__a)[_Nm]) {if constexpr (_Nm) {__os << *__a;for (auto __i = __a + 1, __e = __a + _Nm; __i != __e; ++__i)__os << ' ' << *__i;}return __os;}/*** @brief Stream insertion operator for std::pair.** @param __os Output stream* @param __p Pair* @return Reference to __os.*/template <class _Os, class _T1, class _T2>ostream_ref<_Os> operator<<(_Os &__os, const std::pair<_T1, _T2> &__p) {return __os << __p.first << ' ' << __p.second;}/*** @brief Stream insertion operator for std::tuple.** @param __os Output stream* @param __t Tuple* @return Reference to __os.*/template <class _Os, class _Tp, size_t _Nm = 0>typename std::enable_if<bool(std::tuple_size<_Tp>::value + 1),ostream_ref<_Os>>::typeoperator<<(_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>>::typeoperator<<(_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_checkatexit([] {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));elsereturn 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;elsereturn std::vector(sizes[I], make_vector<Tp, N, S, I + 1>(sizes, init));}/** @brief Make a multi-dimensional vector.* @param sizes The size of each dimension* @param init The initial value*/template <typename Tp, size_t N = SIZE_MAX, size_t I = 0, class... Args>constexpr auto make_vector([[maybe_unused]] std::tuple<Args...> const& sizes,Tp const& init = Tp()) {using tuple_type = std::tuple<Args...>;if constexpr (I == std::tuple_size_v<tuple_type> || I == N)return init;else {static_assert(std::is_convertible_v<std::tuple_element_t<I, tuple_type>, size_t>);return std::vector(std::get<I>(sizes),make_vector<Tp, N, I + 1>(sizes, init));}}/** @brief Make a multi-dimensional vector.* @param sizes The size of each dimension* @param init The initial value*/template <typename Tp, class Fst, class Snd>constexpr auto make_vector(std::pair<Fst, Snd> const& sizes,Tp const& init = Tp()) {static_assert(std::is_convertible_v<Fst, size_t>);static_assert(std::is_convertible_v<Snd, size_t>);return make_vector({(size_t)sizes.first, (size_t)sizes.second}, init);}} // namespace workspace#endif#line 2 "Library/src/utils/py-like/enumerate.hpp"/** @file enumerate.hpp* @brief Enumerate*/#line 2 "Library/src/utils/py-like/range.hpp"/*** @file range.hpp* @brief Range*/#line 9 "Library/src/utils/py-like/range.hpp"#line 2 "Library/src/utils/py-like/reversed.hpp"/*** @file reversed.hpp* @brief Reversed*/#include <initializer_list>#line 10 "Library/src/utils/py-like/reversed.hpp"namespace workspace {namespace internal {template <class Container> class reversed {Container cont;public:constexpr reversed(Container &&cont) : cont(cont) {}constexpr auto begin() { return std::rbegin(cont); }constexpr auto end() { return std::rend(cont); }};} // namespace internaltemplate <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 >= 201703Lnamespace workspace {template <class Index> class range {Index first, last;public:class iterator {Index current;public:using difference_type = std::ptrdiff_t;using value_type = Index;using reference = typename std::add_const<Index>::type &;using pointer = iterator;using iterator_category = std::bidirectional_iterator_tag;constexpr iterator(Index const &__i = Index()) noexcept : current(__i) {}constexpr bool operator==(iterator const &rhs) const noexcept {return current == rhs.current;}constexpr bool operator!=(iterator const &rhs) const noexcept {return current != rhs.current;}constexpr iterator &operator++() noexcept {++current;return *this;}constexpr iterator &operator--() noexcept {--current;return *this;}constexpr reference operator*() const noexcept { return current; }};constexpr range(Index first, Index last) noexcept: first(first), last(last) {}constexpr range(Index last) noexcept : first(), last(last) {}constexpr iterator begin() const noexcept { return iterator{first}; }constexpr iterator end() const noexcept { return iterator{last}; }constexpr reverse_iterator<iterator> rbegin() const noexcept {return reverse_iterator<iterator>(end());}constexpr reverse_iterator<iterator> rend() const noexcept {return reverse_iterator<iterator>(begin());}};template <class... Args> constexpr auto rrange(Args &&... args) noexcept {return internal::reversed(range(std::forward<Args>(args)...));}} // namespace workspace#endif#line 2 "Library/src/utils/py-like/zip.hpp"/*** @file zip.hpp* @brief Zip*/#line 11 "Library/src/utils/py-like/zip.hpp"#line 14 "Library/src/utils/py-like/zip.hpp"#if __cplusplus >= 201703Lnamespace workspace {namespace internal {template <class> struct zipped_iterator;template <class...> struct zipped_iterator_tuple;template <class... Args> class zipped {using ref_tuple = std::tuple<Args...>;ref_tuple args;template <size_t N = 0> constexpr auto begin_cat() const noexcept {if constexpr (N != std::tuple_size<ref_tuple>::value) {return std::tuple_cat(std::tuple(std::begin(std::get<N>(args))),begin_cat<N + 1>());} elsereturn std::tuple<>();}template <size_t N = 0> constexpr auto end_cat() const noexcept {if constexpr (N != std::tuple_size<ref_tuple>::value) {return std::tuple_cat(std::tuple(std::end(std::get<N>(args))),end_cat<N + 1>());} elsereturn std::tuple<>();}public:constexpr zipped(Args &&... args) noexcept : args(args...) {}class iterator {using base_tuple = typename zipped_iterator_tuple<Args...>::type;public:using iterator_category =typename common_iterator_category<base_tuple>::type;using difference_type = std::ptrdiff_t;using value_type = zipped_iterator<base_tuple>;using reference = zipped_iterator<base_tuple> &;using pointer = iterator;protected:value_type current;template <size_t N = 0>constexpr bool equal(const iterator &rhs) const noexcept {if constexpr (N != std::tuple_size<base_tuple>::value) {return std::get<N>(current) == std::get<N>(rhs.current) ||equal<N + 1>(rhs);} elsereturn false;}template <size_t N = 0> constexpr void increment() noexcept {if constexpr (N != std::tuple_size<base_tuple>::value) {++std::get<N>(current);increment<N + 1>();}}template <size_t N = 0> constexpr void decrement() noexcept {if constexpr (N != std::tuple_size<base_tuple>::value) {--std::get<N>(current);decrement<N + 1>();}}template <size_t N = 0>constexpr void advance(difference_type __d) noexcept {if constexpr (N != std::tuple_size<base_tuple>::value) {std::get<N>(current) += __d;advance<N + 1>(__d);}}public:constexpr iterator() noexcept = default;constexpr iterator(base_tuple const ¤t) noexcept : current(current) {}constexpr bool operator==(const iterator &rhs) const noexcept {return equal(rhs);}constexpr bool operator!=(const iterator &rhs) const noexcept {return !equal(rhs);}constexpr iterator &operator++() noexcept {increment();return *this;}constexpr iterator &operator--() noexcept {decrement();return *this;}constexpr bool operator<(const iterator &rhs) const noexcept {return std::get<0>(current) < std::get<0>(rhs.current);}constexpr bool operator<=(const iterator &rhs) const noexcept {return std::get<0>(current) <= std::get<0>(rhs.current);}constexpr iterator &operator+=(difference_type __d) noexcept {advance(__d);return *this;}constexpr iterator &operator-=(difference_type __d) noexcept {advance(-__d);return *this;}constexpr iterator operator+(difference_type __d) const noexcept {return iterator{*this} += __d;}constexpr iterator operator-(difference_type __d) const noexcept {return iterator{*this} -= __d;}constexpr difference_type operator-(const iterator &rhs) const noexcept {return std::get<0>(current) - std::get<0>(rhs.current);}constexpr reference operator*() noexcept { return current; }};constexpr iterator begin() const noexcept { return iterator{begin_cat()}; }constexpr iterator end() const noexcept { return iterator{end_cat()}; }constexpr reverse_iterator<iterator> rbegin() const noexcept {return reverse_iterator<iterator>{end()};}constexpr reverse_iterator<iterator> rend() const noexcept {return reverse_iterator<iterator>{begin()};}};template <class Tp, class... Args> struct zipped_iterator_tuple<Tp, Args...> {using type = decltype(std::tuple_cat(std::declval<std::tuple<decltype(std::begin(std::declval<Tp>()))>>(),std::declval<typename zipped_iterator_tuple<Args...>::type>()));};template <> struct zipped_iterator_tuple<> { using type = std::tuple<>; };template <class Iter_tuple> struct zipped_iterator : Iter_tuple {constexpr zipped_iterator(Iter_tuple const &__t) noexcept: Iter_tuple::tuple(__t) {}constexpr zipped_iterator(zipped_iterator const &__t) = default;constexpr zipped_iterator &operator=(zipped_iterator const &__t) = default;// Avoid move initialization.constexpr zipped_iterator(zipped_iterator &&__t): zipped_iterator(static_cast<zipped_iterator const &>(__t)) {}// Avoid move assignment.zipped_iterator &operator=(zipped_iterator &&__t) {return operator=(static_cast<zipped_iterator const &>(__t));}template <size_t N>friend constexpr auto &get(zipped_iterator<Iter_tuple> const &__z) noexcept {return *std::get<N>(__z);}template <size_t N>friend constexpr auto get(zipped_iterator<Iter_tuple> &&__z) noexcept {return *std::get<N>(__z);}};} // namespace internal} // namespace workspacenamespace std {template <size_t N, class Iter_tuple>struct tuple_element<N, workspace::internal::zipped_iterator<Iter_tuple>> {using type = typename remove_reference<typename iterator_traits<typename tuple_element<N, Iter_tuple>::type>::reference>::type;};template <class Iter_tuple>struct tuple_size<workspace::internal::zipped_iterator<Iter_tuple>>: tuple_size<Iter_tuple> {};} // namespace stdnamespace workspace {template <class... Args> constexpr auto zip(Args &&... args) noexcept {return internal::zipped<Args...>(std::forward<Args>(args)...);}template <class... Args>constexpr auto zip(std::initializer_list<Args> const &... args) noexcept {return internal::zipped<const std::initializer_list<Args>...>(args...);}} // namespace workspace#endif#line 10 "Library/src/utils/py-like/enumerate.hpp"#if __cplusplus >= 201703Lnamespace workspace {constexpr size_t min_size() noexcept { return SIZE_MAX; }template <class Container, class... Args>constexpr size_t min_size(Container const &cont, Args &&... args) noexcept {return std::min(std::size(cont), min_size(std::forward<Args>(args)...));}template <class... Args> constexpr auto enumerate(Args &&... args) noexcept {return zip(range(min_size(args...)), std::forward<Args>(args)...);}template <class... Args>constexpr auto enumerate(std::initializer_list<Args> const &... args) noexcept {return zip(range(min_size(args...)), std::vector(args)...);}} // namespace workspace#endif#line 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>::typefloor_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>::typeceil_div(T1 x, T2 y) {assert(y != 0);if (y < 0) x = -x, y = -y;return x < 0 ? x / y : (x + y - 1) / y;}} // namespace workspace#line 22 "Library/lib/utils"// #include "src/utils/sfinae.hpp"#line 11 "other/par.cc"signed main() {using namespace workspace;io_setup(15);/* givencase_info.read(); //*//* unspecifiedcase_info.total = -1; //*/return case_info.iterate();}namespace workspace {void main() {// start here!int n, m;cin >> n >> m;vector<pair<i64, int>> b;for (auto i : range(m)) {cin >> i;i64 x{};for (auto j : range(i)) {cin >> j;--j;x |= 1ll << j;}int y;cin >> y;for (auto &&[s, t] : b) {if (chle(x, s ^ x)) {y ^= t;}}if (x) {b.emplace_back(x, y);} else {if (y) {eject(-1);}}}sort(begin(b), end(b));vector<int> ans(n);for (auto [s, t] : b) {for (auto i : range(n)) {if (s & 1) {if (s > 1) {t ^= ans[i];} else {ans[i] = t;}}s >>= 1;}}for (auto &&x : ans) {cout << x << "\n";}}} // namespace workspace