結果
問題 | No.1410 A lot of Bit Operations |
ユーザー | jell |
提出日時 | 2021-02-26 23:00:28 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 60,064 bytes |
コンパイル時間 | 4,095 ms |
コンパイル使用メモリ | 273,140 KB |
実行使用メモリ | 6,824 KB |
最終ジャッジ日時 | 2024-10-02 15:47:39 |
合計ジャッジ時間 | 5,182 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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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 |
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testcase_00 | AC | 2 ms
6,816 KB |
testcase_01 | AC | 2 ms
6,820 KB |
testcase_02 | AC | 2 ms
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testcase_03 | AC | 2 ms
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testcase_04 | AC | 1 ms
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testcase_05 | AC | 2 ms
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testcase_06 | AC | 2 ms
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testcase_07 | AC | 1 ms
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testcase_08 | AC | 1 ms
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testcase_09 | AC | 2 ms
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testcase_10 | AC | 2 ms
6,820 KB |
testcase_11 | AC | 1 ms
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testcase_12 | AC | 1 ms
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testcase_13 | AC | 2 ms
6,820 KB |
testcase_14 | AC | 2 ms
6,816 KB |
testcase_15 | AC | 2 ms
6,820 KB |
testcase_16 | AC | 1 ms
6,820 KB |
testcase_17 | AC | 1 ms
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testcase_18 | AC | 2 ms
6,820 KB |
testcase_19 | AC | 2 ms
6,816 KB |
testcase_20 | AC | 1 ms
6,820 KB |
testcase_21 | AC | 2 ms
6,820 KB |
testcase_22 | AC | 2 ms
6,820 KB |
testcase_23 | AC | 2 ms
6,820 KB |
testcase_24 | AC | 2 ms
6,820 KB |
testcase_25 | AC | 1 ms
6,820 KB |
testcase_26 | AC | 2 ms
6,820 KB |
testcase_27 | AC | 2 ms
6,820 KB |
testcase_28 | AC | 1 ms
6,820 KB |
testcase_29 | AC | 2 ms
6,816 KB |
testcase_30 | AC | 2 ms
6,816 KB |
testcase_31 | AC | 1 ms
6,824 KB |
testcase_32 | AC | 2 ms
6,820 KB |
testcase_33 | AC | 2 ms
6,816 KB |
testcase_34 | AC | 1 ms
6,820 KB |
testcase_35 | AC | 1 ms
6,820 KB |
testcase_36 | AC | 2 ms
6,820 KB |
testcase_37 | AC | 2 ms
6,820 KB |
testcase_38 | AC | 1 ms
6,816 KB |
testcase_39 | AC | 2 ms
6,816 KB |
testcase_40 | AC | 2 ms
6,820 KB |
testcase_41 | AC | 1 ms
6,816 KB |
testcase_42 | AC | 2 ms
6,820 KB |
testcase_43 | AC | 1 ms
6,820 KB |
testcase_44 | AC | 2 ms
6,816 KB |
testcase_45 | AC | 1 ms
6,820 KB |
ソースコード
#line 1 "other/y.cc" // #undef _GLIBCXX_DEBUG // #define NDEBUG #include <bits/extc++.h> #line 2 "Library/lib/alias" /** * @file alias * @brief Alias */ #line 13 "Library/lib/alias" #line 2 "Library/lib/bit" #if __cplusplus > 201703L #include <bit> #else #ifndef _GLIBCXX_BIT #define _GLIBCXX_BIT 1 #include <limits> #include <type_traits> namespace std { template <typename _Tp> constexpr _Tp __rotl(_Tp __x, int __s) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; const int __r = __s % _Nd; if (__r == 0) return __x; else if (__r > 0) return (__x << __r) | (__x >> ((_Nd - __r) % _Nd)); else return (__x >> -__r) | (__x << ((_Nd + __r) % _Nd)); // rotr(x, -r) } template <typename _Tp> constexpr _Tp __rotr(_Tp __x, int __s) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; const int __r = __s % _Nd; if (__r == 0) return __x; else if (__r > 0) return (__x >> __r) | (__x << ((_Nd - __r) % _Nd)); else return (__x << -__r) | (__x >> ((_Nd + __r) % _Nd)); // rotl(x, -r) } template <typename _Tp> constexpr int __countl_zero(_Tp __x) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; if (__x == 0) return _Nd; constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits; constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits; constexpr auto _Nd_u = numeric_limits<unsigned>::digits; if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u) { constexpr int __diff = _Nd_u - _Nd; return __builtin_clz(__x) - __diff; } else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul) { constexpr int __diff = _Nd_ul - _Nd; return __builtin_clzl(__x) - __diff; } else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull) { constexpr int __diff = _Nd_ull - _Nd; return __builtin_clzll(__x) - __diff; } else // (_Nd > _Nd_ull) { static_assert(_Nd <= (2 * _Nd_ull), "Maximum supported integer size is 128-bit"); unsigned long long __high = __x >> _Nd_ull; if (__high != 0) { constexpr int __diff = (2 * _Nd_ull) - _Nd; return __builtin_clzll(__high) - __diff; } constexpr auto __max_ull = numeric_limits<unsigned long long>::max(); unsigned long long __low = __x & __max_ull; return (_Nd - _Nd_ull) + __builtin_clzll(__low); } } template <typename _Tp> constexpr int __countl_one(_Tp __x) noexcept { if (__x == numeric_limits<_Tp>::max()) return numeric_limits<_Tp>::digits; return __countl_zero<_Tp>((_Tp)~__x); } template <typename _Tp> constexpr int __countr_zero(_Tp __x) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; if (__x == 0) return _Nd; constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits; constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits; constexpr auto _Nd_u = numeric_limits<unsigned>::digits; if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u) return __builtin_ctz(__x); else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul) return __builtin_ctzl(__x); else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull) return __builtin_ctzll(__x); else // (_Nd > _Nd_ull) { static_assert(_Nd <= (2 * _Nd_ull), "Maximum supported integer size is 128-bit"); constexpr auto __max_ull = numeric_limits<unsigned long long>::max(); unsigned long long __low = __x & __max_ull; if (__low != 0) return __builtin_ctzll(__low); unsigned long long __high = __x >> _Nd_ull; return __builtin_ctzll(__high) + _Nd_ull; } } template <typename _Tp> constexpr int __countr_one(_Tp __x) noexcept { if (__x == numeric_limits<_Tp>::max()) return numeric_limits<_Tp>::digits; return __countr_zero((_Tp)~__x); } template <typename _Tp> constexpr int __popcount(_Tp __x) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; if (__x == 0) return 0; constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits; constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits; constexpr auto _Nd_u = numeric_limits<unsigned>::digits; if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u) return __builtin_popcount(__x); else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul) return __builtin_popcountl(__x); else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull) return __builtin_popcountll(__x); else // (_Nd > _Nd_ull) { static_assert(_Nd <= (2 * _Nd_ull), "Maximum supported integer size is 128-bit"); constexpr auto __max_ull = numeric_limits<unsigned long long>::max(); unsigned long long __low = __x & __max_ull; unsigned long long __high = __x >> _Nd_ull; return __builtin_popcountll(__low) + __builtin_popcountll(__high); } } template <typename _Tp> constexpr bool __has_single_bit(_Tp __x) noexcept { return __popcount(__x) == 1; } template <typename _Tp> constexpr _Tp __bit_ceil(_Tp __x) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; if (__x == 0 || __x == 1) return 1; auto __shift_exponent = _Nd - __countl_zero((_Tp)(__x - 1u)); #ifdef _GLIBCXX_HAVE_BUILTIN_IS_CONSTANT_EVALUATED if (!__builtin_is_constant_evaluated()) { __glibcxx_assert(__shift_exponent != numeric_limits<_Tp>::digits); } #endif using __promoted_type = decltype(__x << 1); if _GLIBCXX17_CONSTEXPR (!is_same<__promoted_type, _Tp>::value) { const int __extra_exp = sizeof(__promoted_type) / sizeof(_Tp) / 2; __shift_exponent |= (__shift_exponent & _Nd) << __extra_exp; } return (_Tp)1u << __shift_exponent; } template <typename _Tp> constexpr _Tp __bit_floor(_Tp __x) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; if (__x == 0) return 0; return (_Tp)1u << (_Nd - __countl_zero((_Tp)(__x >> 1))); } template <typename _Tp> constexpr _Tp __bit_width(_Tp __x) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; return _Nd - __countl_zero(__x); } } // namespace std #endif #endif #line 2 "Library/lib/limits" #line 4 "Library/lib/limits" namespace std { #if defined(__STRICT_ANSI__) && defined(__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 std #line 16 "Library/lib/alias" namespace workspace { constexpr char eol = '\n'; using namespace std; using i32 = int_least32_t; using u32 = uint_least32_t; using i64 = int_least64_t; using u64 = uint_least64_t; #ifdef __SIZEOF_INT128__ using i128 = __int128_t; using u128 = __uint128_t; #else #warning 128bit integer is not available. #endif template <class T, class Comp = less<T>> using priority_queue = std::priority_queue<T, vector<T>, Comp>; template <class T> using stack = std::stack<T, vector<T>>; template <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/y.cc" // #include "lib/cxx20" #line 2 "Library/lib/direct" /* * @file direct * @brief Pragma Directive */ #ifdef ONLINE_JUDGE #pragma GCC optimize("O3") #pragma GCC target("avx,avx2") #pragma GCC optimize("unroll-loops") #endif #line 8 "other/y.cc" // #include "lib/opt" #line 2 "Library/src/sys/clock.hpp" /* * @fn clock.hpp * @brief Clock */ #line 9 "Library/src/sys/clock.hpp" namespace workspace { using namespace std::chrono; namespace internal { // The start time of the program. const auto start_time{system_clock::now()}; } // namespace internal /* * @fn elapsed * @return elapsed time of the program */ int64_t elapsed() { const auto end_time{system_clock::now()}; return duration_cast<milliseconds>(end_time - internal::start_time).count(); } } // namespace workspace #line 2 "Library/src/sys/ejection.hpp" /** * @file ejection.hpp * @brief Ejection */ #line 9 "Library/src/sys/ejection.hpp" namespace workspace { namespace internal { struct ejection { bool exit = 0; }; } // namespace internal /** * @brief eject from a try block, throw nullptr * @param arg output */ template <class Tp> void eject(Tp const &arg) { std::cout << arg << "\n"; throw internal::ejection{}; } void exit() { throw internal::ejection{true}; } } // namespace workspace #line 2 "Library/src/sys/iteration.hpp" /** * @file iteration.hpp * @brief Case Iteration */ #line 9 "Library/src/sys/iteration.hpp" #line 11 "Library/src/sys/iteration.hpp" namespace workspace { void main(); struct { // 1-indexed unsigned current{0}; unsigned total{1}; void read() { (std::cin >> total).ignore(); } int iterate() { static bool once = false; assert(!once); once = true; while (current++ < total) { try { main(); } catch (internal::ejection const& status) { if (status.exit) break; } } return 0; } } case_info; } // namespace workspace #line 2 "Library/src/utils/cached.hpp" /** * @file cached.hpp * @brief Cached * @date 2021-02-25 * * */ #line 12 "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: /** * @param __fn 1st argument callable with the rest of its arguments, and the * 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)...); } }; /** * @brief Cached version of Fixed Point Combinator */ template <class _F> class cached_fixed_point { template <class...> struct _cache; template <class _G, class _R, class _H, class... _Args> struct _cache<_R (_G::*)(_H, _Args...) const> : std::map<std::tuple<_Args...>, _R> {}; using cache = _cache<decltype(&_F::template operator()<cached_fixed_point<_F> &>)>; _F __fn; static cache __ca; public: /** * @param __fn 1st argument callable with the rest of its arguments, and the * return type specified. */ cached_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) noexcept { typename cache::key_type __key(__args...); if (auto __i = __ca.lower_bound(__key); __i != __ca.end() && __i->first == __key) return __i->second; else return __ca .emplace_hint(__i, std::move(__key), __fn(*this, std::forward<_Args>(__args)...)) ->second; } }; template <class _F> typename cached_fixed_point<_F>::cache cached_fixed_point<_F>::__ca; } // namespace workspace #line 14 "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_v<std::decay_t<_Args>, _Args>, std::decay_t<_Args>, _Args>>>()...)); }; // Associative array. template <class _Value, class... _Keys> struct assoc : std::bool_constant<!std::is_void_v<_Value>>, std::conditional_t<std::is_void_v<_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...> {}; using cache = _cache<decltype(&_F::template operator()<_recursive<_F> &>)>; _F __fn; static cache __ca; public: _recursive(_F __x) noexcept : __fn(__x) {} /** * @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 = __ca.lower_bound(__key); __i != __ca.end() && __i->first == __key) return __i->second; else return __ca .emplace_hint(__i, std::move(__key), __fn(*this, std::forward<_Args>(__args)...)) ->second; } else if (auto __i = __ca.lower_bound(__key); __i == __ca.end() || *__i != __key) __ca.emplace_hint(__i, std::move(__key)), __fn(*this, std::forward<_Args>(__args)...); } }; template <class _F> typename _recursive<_F>::cache _recursive<_F>::__ca; // 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...> {}; using cache = _cache<typename _get_func<_F>::type>; _F __fn; cache __ca; public: _non_recursive(_F __fn) noexcept : __fn(__fn) {} /** * @param __args */ template <class... _Args> decltype(auto) operator()(_Args &&...__args) noexcept { typename cache::key_type __key(__args...); if constexpr (cache::value) { if (auto __i = __ca.lower_bound(__key); __i != __ca.end() && __i->first == __key) return __i->second; else return __ca .emplace_hint(__i, std::move(__key), __fn(std::forward<_Args>(__args)...)) ->second; } else if (auto __i = __ca.lower_bound(__key); __i == __ca.end() || *__i != __key) __ca.emplace_hint(__i, std::move(__key)), __fn(std::forward<_Args>(__args)...); } }; 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 * * @param __x Function */ cached(_F __x = _F()) 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 { /* * @fn chle * @brief Substitute y for x if comp(y, x) is true. * @param x Reference * @param y Const reference * @param comp Compare function * @return Whether or not x is updated */ template <class Tp, class Comp = std::less<Tp>> bool chle(Tp &x, const Tp &y, Comp comp = Comp()) { return comp(y, x) ? x = y, true : false; } /* * @fn chge * @brief Substitute y for x if comp(x, y) is true. * @param x Reference * @param y Const reference * @param comp Compare function * @return Whether or not x is updated */ template <class Tp, class Comp = std::less<Tp>> bool chge(Tp &x, const Tp &y, Comp comp = Comp()) { return comp(x, y) ? x = y, true : false; } } // namespace workspace #line 6 "Library/lib/utils" // #include "src/utils/grid.hpp" #line 2 "Library/src/utils/hash.hpp" #line 8 "Library/src/utils/hash.hpp" #line 2 "Library/src/utils/sfinae.hpp" /** * @file sfinae.hpp * @brief SFINAE */ #line 10 "Library/src/utils/sfinae.hpp" #include <type_traits> #ifndef __INT128_DEFINED__ #ifdef __SIZEOF_INT128__ #define __INT128_DEFINED__ 1 #else #define __INT128_DEFINED__ 0 #endif #endif namespace std { #if __INT128_DEFINED__ template <> struct make_signed<__uint128_t> { using type = __int128_t; }; template <> struct make_signed<__int128_t> { using type = __int128_t; }; template <> struct make_unsigned<__uint128_t> { using type = __uint128_t; }; template <> struct make_unsigned<__int128_t> { using type = __uint128_t; }; #endif } // namespace std namespace workspace { template <class Tp, class... Args> struct variadic_front { using type = Tp; }; template <class... Args> struct variadic_back; template <class Tp> struct variadic_back<Tp> { using type = Tp; }; template <class Tp, class... Args> struct variadic_back<Tp, Args...> { using type = typename variadic_back<Args...>::type; }; template <class type, template <class> class trait> using enable_if_trait_type = typename std::enable_if<trait<type>::value>::type; /** * @brief Return type of subscripting ( @c [] ) access. */ template <class _Tp> using subscripted_type = typename std::decay<decltype(std::declval<_Tp&>()[0])>::type; template <class Container> using element_type = typename std::decay<decltype( *std::begin(std::declval<Container&>()))>::type; template <class _Tp, class = std::nullptr_t> struct has_begin : std::false_type {}; template <class _Tp> struct has_begin<_Tp, decltype(std::begin(std::declval<_Tp>()), nullptr)> : std::true_type {}; template <class _Tp, class = std::nullptr_t> struct has_mod : std::false_type {}; template <class _Tp> struct has_mod<_Tp, decltype(_Tp::mod, nullptr)> : std::true_type {}; template <class _Tp, class = void> struct is_integral_ext : std::false_type {}; template <class _Tp> struct is_integral_ext< _Tp, typename std::enable_if<std::is_integral<_Tp>::value>::type> : std::true_type {}; #if __INT128_DEFINED__ template <> struct is_integral_ext<__int128_t> : std::true_type {}; template <> struct is_integral_ext<__uint128_t> : std::true_type {}; #endif #if __cplusplus >= 201402 template <class _Tp> constexpr static bool is_integral_ext_v = is_integral_ext<_Tp>::value; #endif template <typename _Tp, typename = void> struct multiplicable_uint { using type = uint_least32_t; }; template <typename _Tp> struct multiplicable_uint< _Tp, typename std::enable_if<(2 < sizeof(_Tp)) && (!__INT128_DEFINED__ || sizeof(_Tp) <= 4)>::type> { using type = uint_least64_t; }; #if __INT128_DEFINED__ template <typename _Tp> struct multiplicable_uint<_Tp, typename std::enable_if<(4 < sizeof(_Tp))>::type> { using type = __uint128_t; }; #endif template <typename _Tp> struct multiplicable_int { using type = typename std::make_signed<typename multiplicable_uint<_Tp>::type>::type; }; } // namespace workspace #line 10 "Library/src/utils/hash.hpp" namespace workspace { template <class T, class = void> struct hash : std::hash<T> {}; #if __cplusplus >= 201703L template <class Unique_bits_type> struct hash<Unique_bits_type, enable_if_trait_type<Unique_bits_type, std::has_unique_object_representations>> { size_t operator()(uint64_t x) const { static const uint64_t m = std::random_device{}(); x ^= x >> 23; x ^= m; x ^= x >> 47; return x - (x >> 32); } }; #endif template <class Key> size_t hash_combine(const size_t &seed, const Key &key) { return seed ^ (hash<Key>()(key) + 0x9e3779b9 /* + (seed << 6) + (seed >> 2) */); } template <class T1, class T2> struct hash<std::pair<T1, T2>> { size_t operator()(const std::pair<T1, T2> &pair) const { return hash_combine(hash<T1>()(pair.first), pair.second); } }; template <class... T> class hash<std::tuple<T...>> { template <class Tuple, size_t index = std::tuple_size<Tuple>::value - 1> struct tuple_hash { static uint64_t apply(const Tuple &t) { return hash_combine(tuple_hash<Tuple, index - 1>::apply(t), std::get<index>(t)); } }; template <class Tuple> struct tuple_hash<Tuple, size_t(-1)> { static uint64_t apply(const Tuple &t) { return 0; } }; public: uint64_t operator()(const std::tuple<T...> &t) const { return tuple_hash<std::tuple<T...>>::apply(t); } }; template <class hash_table> struct hash_table_wrapper : hash_table { using key_type = typename hash_table::key_type; size_t count(const key_type &key) const { return hash_table::find(key) != hash_table::end(); } template <class... Args> auto emplace(Args &&... args) { return hash_table::insert(typename hash_table::value_type(args...)); } }; template <class Key, class Mapped = __gnu_pbds::null_type> using cc_hash_table = hash_table_wrapper<__gnu_pbds::cc_hash_table<Key, Mapped, hash<Key>>>; template <class Key, class Mapped = __gnu_pbds::null_type> using gp_hash_table = hash_table_wrapper<__gnu_pbds::gp_hash_table<Key, Mapped, hash<Key>>>; template <class Key, class Mapped> using unordered_map = std::unordered_map<Key, Mapped, hash<Key>>; template <class Key> using unordered_set = std::unordered_set<Key, hash<Key>>; } // namespace workspace #line 2 "Library/src/utils/io/istream.hpp" /** * @file istream.hpp * @brief Input Stream */ #include <cxxabi.h> #line 13 "Library/src/utils/io/istream.hpp" #line 15 "Library/src/utils/io/istream.hpp" namespace workspace { namespace internal { template <class Tp, typename = std::nullptr_t> struct istream_helper { istream_helper(std::istream &is, Tp &x) { if constexpr (has_begin<Tp>::value) for (auto &&e : x) istream_helper<typename std::decay<decltype(e)>::type>(is, e); else static_assert(has_begin<Tp>::value, "istream unsupported type."); } }; template <class Tp> struct istream_helper< Tp, decltype(std::declval<std::decay<decltype(std::declval<std::istream &>() >> std::declval<Tp &>())>>(), nullptr)> { istream_helper(std::istream &is, Tp &x) { is >> x; } }; #ifdef __SIZEOF_INT128__ template <> struct istream_helper<__uint128_t, std::nullptr_t> { istream_helper(std::istream &__is, __uint128_t &__x) { std::string __s; __is >> __s; bool __neg = false; if (__s.front() == '-') __neg = true, __s.erase(__s.begin()); __x = 0; for (char __d : __s) { __x *= 10; __d -= '0'; if (__neg) __x -= __d; else __x += __d; } } }; template <> struct istream_helper<__int128_t, std::nullptr_t> { istream_helper(std::istream &__is, __int128_t &__x) { std::string __s; __is >> __s; bool __neg = false; if (__s.front() == '-') __neg = true, __s.erase(__s.begin()); __x = 0; for (char __d : __s) { __x *= 10; __d -= '0'; if (__neg) __x -= __d; else __x += __d; } } }; #endif // INT128 template <class T1, class T2> struct istream_helper<std::pair<T1, T2>> { istream_helper(std::istream &is, std::pair<T1, T2> &x) { istream_helper<T1>(is, x.first), istream_helper<T2>(is, x.second); } }; template <class... Tps> struct istream_helper<std::tuple<Tps...>> { istream_helper(std::istream &is, std::tuple<Tps...> &x) { iterate(is, x); } private: template <class Tp, size_t N = 0> void iterate(std::istream &is, Tp &x) { if constexpr (N == std::tuple_size<Tp>::value) return; else istream_helper<typename std::tuple_element<N, Tp>::type>(is, std::get<N>(x)), iterate<Tp, N + 1>(is, x); } }; } // namespace internal /** * @brief A wrapper class for std::istream. */ class istream : public std::istream { public: /** * @brief Wrapped operator. */ template <typename Tp> istream &operator>>(Tp &x) { internal::istream_helper<Tp>(*this, x); if (std::istream::fail()) { static auto once = atexit([] { std::cerr << "\n\033[43m\033[30mwarning: failed to read \'" << abi::__cxa_demangle(typeid(Tp).name(), 0, 0, 0) << "\'.\033[0m\n\n"; }); assert(!once); } return *this; } }; decltype(auto) cin = static_cast<istream &>(std::cin); } // namespace workspace #line 2 "Library/src/utils/io/ostream.hpp" /** * @file ostream.hpp * @brief Output Stream */ #line 9 "Library/src/utils/io/ostream.hpp" namespace workspace { template <class _Os> struct is_ostream { template <typename... _Args> static std::true_type __test(std::basic_ostream<_Args...> *); static std::false_type __test(void *); constexpr static bool value = decltype(__test(std::declval<_Os *>()))::value; }; template <class _Os> using ostream_ref = typename std::enable_if<is_ostream<_Os>::value, _Os &>::type; /** * @brief Stream insertion operator for C-style array. * * @param __os Output stream * @param __a Array * @return Reference to __os. */ template <class _Os, class _Tp, size_t _Nm> typename std::enable_if<bool(sizeof(_Tp) > 2), ostream_ref<_Os>>::type operator<<(_Os &__os, const _Tp (&__a)[_Nm]) { if constexpr (_Nm) { __os << *__a; for (auto __i = __a + 1, __e = __a + _Nm; __i != __e; ++__i) __os << ' ' << *__i; } return __os; } /** * @brief Stream insertion operator for std::pair. * * @param __os Output stream * @param __p Pair * @return Reference to __os. */ template <class _Os, class _T1, class _T2> ostream_ref<_Os> operator<<(_Os &__os, const std::pair<_T1, _T2> &__p) { return __os << __p.first << ' ' << __p.second; } /** * @brief Stream insertion operator for std::tuple. * * @param __os Output stream * @param __t Tuple * @return Reference to __os. */ template <class _Os, class _Tp, size_t _Nm = 0> typename std::enable_if<bool(std::tuple_size<_Tp>::value + 1), ostream_ref<_Os>>::type operator<<(_Os &__os, const _Tp &__t) { if constexpr (_Nm != std::tuple_size<_Tp>::value) { if constexpr (_Nm) __os << ' '; __os << std::get<_Nm>(__t); operator<<<_Os, _Tp, _Nm + 1>(__os, __t); } return __os; } template <class _Os, class _Container, typename = decltype(std::begin(std::declval<_Container>()))> typename std::enable_if< !std::is_same<typename std::decay<_Container>::type, std::string>::value && !std::is_same<typename std::decay<_Container>::type, char *>::value, ostream_ref<_Os>>::type operator<<(_Os &__os, const _Container &__cont) { bool __h = true; for (auto &&__e : __cont) __h ? __h = 0 : (__os << ' ', 0), __os << __e; return __os; } #ifdef __SIZEOF_INT128__ /** * @brief Stream insertion operator for __int128_t. * * @param __os Output Stream * @param __x 128-bit integer * @return Reference to __os. */ template <class _Os> ostream_ref<_Os> operator<<(_Os &__os, __int128_t __x) { if (!__x) return __os << '0'; if (__x < 0) __os << '-'; char __s[40], *__p = __s; while (__x) { auto __d = __x % 10; *__p++ = '0' + (__x < 0 ? -__d : __d); __x /= 10; } *__p = 0; for (char *__t = __s; __t < --__p; ++__t) *__t ^= *__p ^= *__t ^= *__p; return __os << __s; } /** * @brief Stream insertion operator for __uint128_t. * * @param __os Output Stream * @param __x 128-bit unsigned integer * @return Reference to __os. */ template <class _Os> ostream_ref<_Os> operator<<(_Os &__os, __uint128_t __x) { if (!__x) return __os << '0'; char __s[40], *__p = __s; while (__x) *__p++ = '0' + __x % 10, __x /= 10; *__p = 0; for (char *__t = __s; __t < --__p; ++__t) *__t ^= *__p ^= *__t ^= *__p; return __os << __s; } #endif } // namespace workspace #line 10 "Library/lib/utils" // #include "src/utils/io/read.hpp" #line 2 "Library/src/utils/io/setup.hpp" /* * @file setup.hpp * @brief I/O Setup */ #line 10 "Library/src/utils/io/setup.hpp" namespace workspace { /* * @fn io_setup * @brief Setup I/O. * @param precision Standard output precision */ void io_setup(int precision) { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(precision); #ifdef _buffer_check atexit([] { char bufc; if (std::cin >> bufc) std::cerr << "\n\033[43m\033[30mwarning: buffer not empty.\033[0m\n\n"; }); #endif } } // namespace workspace #line 2 "Library/src/utils/iterator/category.hpp" /* * @file category.hpp * @brief Iterator Category */ #line 10 "Library/src/utils/iterator/category.hpp" namespace workspace { /* * @tparam Tuple Tuple of iterator types */ template <class Tuple, size_t N = std::tuple_size<Tuple>::value - 1> struct common_iterator_category { using type = typename std::common_type< typename common_iterator_category<Tuple, N - 1>::type, typename std::iterator_traits<typename std::tuple_element< N, Tuple>::type>::iterator_category>::type; }; template <class Tuple> struct common_iterator_category<Tuple, 0> { using type = typename std::iterator_traits< typename std::tuple_element<0, Tuple>::type>::iterator_category; }; } // namespace workspace #line 2 "Library/src/utils/iterator/reverse.hpp" /* * @file reverse_iterator.hpp * @brief Reverse Iterator */ #if __cplusplus >= 201703L #include <iterator> #include <optional> namespace workspace { /* * @class reverse_iterator * @brief Wrapper class for `std::reverse_iterator`. * @see http://gcc.gnu.org/PR51823 */ template <class Iterator> class reverse_iterator : public std::reverse_iterator<Iterator> { using base_std = std::reverse_iterator<Iterator>; std::optional<typename base_std::value_type> deref; public: using base_std::reverse_iterator; constexpr typename base_std::reference operator*() noexcept { if (!deref) { Iterator tmp = base_std::current; deref = *--tmp; } return deref.value(); } constexpr reverse_iterator &operator++() noexcept { base_std::operator++(); deref.reset(); return *this; } constexpr reverse_iterator &operator--() noexcept { base_std::operator++(); deref.reset(); return *this; } constexpr reverse_iterator operator++(int) noexcept { base_std::operator++(); deref.reset(); return *this; } constexpr reverse_iterator operator--(int) noexcept { base_std::operator++(); deref.reset(); return *this; } }; } // namespace workspace #endif #line 2 "Library/src/utils/make_vector.hpp" /* * @file make_vector.hpp * @brief Multi-dimensional Vector */ #if __cplusplus >= 201703L #include <tuple> #include <vector> namespace workspace { /* * @brief Make a multi-dimensional vector. * @tparam Tp type of the elements * @tparam N dimension * @tparam S integer type * @param sizes The size of each dimension * @param init The initial value */ template <typename Tp, size_t N, typename S> constexpr auto make_vector([[maybe_unused]] S* sizes, Tp const& init = Tp()) { static_assert(std::is_convertible_v<S, size_t>); if constexpr (N) return std::vector(*sizes, make_vector<Tp, N - 1, S>(std::next(sizes), init)); else return init; } /* * @brief Make a multi-dimensional vector. * @param sizes The size of each dimension * @param init The initial value */ template <typename Tp, size_t N, typename S> constexpr auto make_vector(const S (&sizes)[N], Tp const& init = Tp()) { return make_vector<Tp, N, S>((S*)sizes, init); } /* * @brief Make a multi-dimensional vector. * @param sizes The size of each dimension * @param init The initial value */ template <typename Tp, size_t N, typename S, size_t I = 0> constexpr auto make_vector([[maybe_unused]] std::array<S, N> const& sizes, Tp const& init = Tp()) { static_assert(std::is_convertible_v<S, size_t>); if constexpr (I == N) return init; else return std::vector(sizes[I], make_vector<Tp, N, S, I + 1>(sizes, init)); } /* * @brief Make a multi-dimensional vector. * @param sizes The size of each dimension * @param init The initial value */ template <typename Tp, size_t N = SIZE_MAX, size_t I = 0, class... Args> constexpr auto make_vector([[maybe_unused]] std::tuple<Args...> const& sizes, Tp const& init = Tp()) { using tuple_type = std::tuple<Args...>; if constexpr (I == std::tuple_size_v<tuple_type> || I == N) return init; else { static_assert( std::is_convertible_v<std::tuple_element_t<I, tuple_type>, size_t>); return std::vector(std::get<I>(sizes), make_vector<Tp, N, I + 1>(sizes, init)); } } /* * @brief Make a multi-dimensional vector. * @param sizes The size of each dimension * @param init The initial value */ template <typename Tp, class Fst, class Snd> constexpr auto make_vector(std::pair<Fst, Snd> const& sizes, Tp const& init = Tp()) { static_assert(std::is_convertible_v<Fst, size_t>); static_assert(std::is_convertible_v<Snd, size_t>); return make_vector({(size_t)sizes.first, (size_t)sizes.second}, init); } } // namespace workspace #endif #line 2 "Library/src/utils/py-like/enumerate.hpp" /* * @file enumerate.hpp * @brief Enumerate */ #line 2 "Library/src/utils/py-like/range.hpp" /** * @file range.hpp * @brief Range */ #line 9 "Library/src/utils/py-like/range.hpp" #line 2 "Library/src/utils/py-like/reversed.hpp" /** * @file reversed.hpp * @brief Reversed */ #include <initializer_list> #line 10 "Library/src/utils/py-like/reversed.hpp" namespace workspace { namespace internal { template <class Container> class reversed { Container cont; public: constexpr reversed(Container &&cont) : cont(cont) {} constexpr auto begin() { return std::rbegin(cont); } constexpr auto end() { return std::rend(cont); } }; } // namespace internal template <class Container> constexpr auto reversed(Container &&cont) noexcept { return internal::reversed<Container>{std::forward<Container>(cont)}; } template <class Tp> constexpr auto reversed(std::initializer_list<Tp> &&cont) noexcept { return internal::reversed<std::initializer_list<Tp>>{ std::forward<std::initializer_list<Tp>>(cont)}; } } // namespace workspace #line 12 "Library/src/utils/py-like/range.hpp" #if __cplusplus >= 201703L namespace workspace { template <class Index> class range { Index first, last; public: class iterator { Index current; public: using difference_type = std::ptrdiff_t; using value_type = Index; using reference = typename std::add_const<Index>::type &; using pointer = iterator; using iterator_category = std::bidirectional_iterator_tag; constexpr iterator(Index const &__i = Index()) noexcept : current(__i) {} constexpr bool operator==(iterator const &rhs) const noexcept { return current == rhs.current; } constexpr bool operator!=(iterator const &rhs) const noexcept { return current != rhs.current; } constexpr iterator &operator++() noexcept { ++current; return *this; } constexpr iterator &operator--() noexcept { --current; return *this; } constexpr reference operator*() const noexcept { return current; } }; constexpr range(Index first, Index last) noexcept : first(first), last(last) {} constexpr range(Index last) noexcept : first(), last(last) {} constexpr iterator begin() const noexcept { return iterator{first}; } constexpr iterator end() const noexcept { return iterator{last}; } constexpr reverse_iterator<iterator> rbegin() const noexcept { return reverse_iterator<iterator>(end()); } constexpr reverse_iterator<iterator> rend() const noexcept { return reverse_iterator<iterator>(begin()); } }; template <class... Args> constexpr auto rrange(Args &&... args) noexcept { return internal::reversed(range(std::forward<Args>(args)...)); } } // namespace workspace #endif #line 2 "Library/src/utils/py-like/zip.hpp" /** * @file zip.hpp * @brief Zip */ #line 11 "Library/src/utils/py-like/zip.hpp" #line 14 "Library/src/utils/py-like/zip.hpp" #if __cplusplus >= 201703L namespace workspace { namespace internal { template <class> struct zipped_iterator; template <class...> struct zipped_iterator_tuple; template <class... Args> class zipped { using ref_tuple = std::tuple<Args...>; ref_tuple args; template <size_t N = 0> constexpr auto begin_cat() const noexcept { if constexpr (N != std::tuple_size<ref_tuple>::value) { return std::tuple_cat(std::tuple(std::begin(std::get<N>(args))), begin_cat<N + 1>()); } else return std::tuple<>(); } template <size_t N = 0> constexpr auto end_cat() const noexcept { if constexpr (N != std::tuple_size<ref_tuple>::value) { return std::tuple_cat(std::tuple(std::end(std::get<N>(args))), end_cat<N + 1>()); } else return std::tuple<>(); } public: constexpr zipped(Args &&... args) noexcept : args(args...) {} class iterator { using base_tuple = typename zipped_iterator_tuple<Args...>::type; public: using iterator_category = typename common_iterator_category<base_tuple>::type; using difference_type = std::ptrdiff_t; using value_type = zipped_iterator<base_tuple>; using reference = zipped_iterator<base_tuple> &; using pointer = iterator; protected: value_type current; template <size_t N = 0> constexpr bool equal(const iterator &rhs) const noexcept { if constexpr (N != std::tuple_size<base_tuple>::value) { return std::get<N>(current) == std::get<N>(rhs.current) || equal<N + 1>(rhs); } else return false; } template <size_t N = 0> constexpr void increment() noexcept { if constexpr (N != std::tuple_size<base_tuple>::value) { ++std::get<N>(current); increment<N + 1>(); } } template <size_t N = 0> constexpr void decrement() noexcept { if constexpr (N != std::tuple_size<base_tuple>::value) { --std::get<N>(current); decrement<N + 1>(); } } template <size_t N = 0> constexpr void advance(difference_type __d) noexcept { if constexpr (N != std::tuple_size<base_tuple>::value) { std::get<N>(current) += __d; advance<N + 1>(__d); } } public: constexpr iterator() noexcept = default; constexpr iterator(base_tuple const ¤t) noexcept : current(current) {} constexpr bool operator==(const iterator &rhs) const noexcept { return equal(rhs); } constexpr bool operator!=(const iterator &rhs) const noexcept { return !equal(rhs); } constexpr iterator &operator++() noexcept { increment(); return *this; } constexpr iterator &operator--() noexcept { decrement(); return *this; } constexpr bool operator<(const iterator &rhs) const noexcept { return std::get<0>(current) < std::get<0>(rhs.current); } constexpr bool operator<=(const iterator &rhs) const noexcept { return std::get<0>(current) <= std::get<0>(rhs.current); } constexpr iterator &operator+=(difference_type __d) noexcept { advance(__d); return *this; } constexpr iterator &operator-=(difference_type __d) noexcept { advance(-__d); return *this; } constexpr iterator operator+(difference_type __d) const noexcept { return iterator{*this} += __d; } constexpr iterator operator-(difference_type __d) const noexcept { return iterator{*this} -= __d; } constexpr difference_type operator-(const iterator &rhs) const noexcept { return std::get<0>(current) - std::get<0>(rhs.current); } constexpr reference operator*() noexcept { return current; } }; constexpr iterator begin() const noexcept { return iterator{begin_cat()}; } constexpr iterator end() const noexcept { return iterator{end_cat()}; } constexpr reverse_iterator<iterator> rbegin() const noexcept { return reverse_iterator<iterator>{end()}; } constexpr reverse_iterator<iterator> rend() const noexcept { return reverse_iterator<iterator>{begin()}; } }; template <class Tp, class... Args> struct zipped_iterator_tuple<Tp, Args...> { using type = decltype(std::tuple_cat( std::declval<std::tuple<decltype(std::begin(std::declval<Tp>()))>>(), std::declval<typename zipped_iterator_tuple<Args...>::type>())); }; template <> struct zipped_iterator_tuple<> { using type = std::tuple<>; }; template <class Iter_tuple> struct zipped_iterator : Iter_tuple { constexpr zipped_iterator(Iter_tuple const &__t) noexcept : Iter_tuple::tuple(__t) {} constexpr zipped_iterator(zipped_iterator const &__t) = default; constexpr zipped_iterator &operator=(zipped_iterator const &__t) = default; // Avoid move initialization. constexpr zipped_iterator(zipped_iterator &&__t) : zipped_iterator(static_cast<zipped_iterator const &>(__t)) {} // Avoid move assignment. zipped_iterator &operator=(zipped_iterator &&__t) { return operator=(static_cast<zipped_iterator const &>(__t)); } template <size_t N> friend constexpr auto &get(zipped_iterator<Iter_tuple> const &__z) noexcept { return *std::get<N>(__z); } template <size_t N> friend constexpr auto get(zipped_iterator<Iter_tuple> &&__z) noexcept { return *std::get<N>(__z); } }; } // namespace internal } // namespace workspace namespace std { template <size_t N, class Iter_tuple> struct tuple_element<N, workspace::internal::zipped_iterator<Iter_tuple>> { using type = typename remove_reference<typename iterator_traits< typename tuple_element<N, Iter_tuple>::type>::reference>::type; }; template <class Iter_tuple> struct tuple_size<workspace::internal::zipped_iterator<Iter_tuple>> : tuple_size<Iter_tuple> {}; } // namespace std namespace workspace { template <class... Args> constexpr auto zip(Args &&... args) noexcept { return internal::zipped<Args...>(std::forward<Args>(args)...); } template <class... Args> constexpr auto zip(std::initializer_list<Args> const &... args) noexcept { return internal::zipped<const std::initializer_list<Args>...>(args...); } } // namespace workspace #endif #line 10 "Library/src/utils/py-like/enumerate.hpp" #if __cplusplus >= 201703L namespace workspace { constexpr size_t min_size() noexcept { return SIZE_MAX; } template <class Container, class... Args> constexpr size_t min_size(Container const &cont, Args &&... args) noexcept { return std::min(std::size(cont), min_size(std::forward<Args>(args)...)); } template <class... Args> constexpr auto enumerate(Args &&... args) noexcept { return zip(range(min_size(args...)), std::forward<Args>(args)...); } template <class... Args> constexpr auto enumerate(std::initializer_list<Args> const &... args) noexcept { return zip(range(min_size(args...)), std::vector(args)...); } } // namespace workspace #endif #line 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> void shuffle(RAIter const& __first, RAIter const& __last) { static std::mt19937 engine(std::random_device{}()); std::shuffle(__first, __last, engine); } } // namespace workspace #line 2 "Library/src/utils/round_div.hpp" /* * @file round_div.hpp * @brief Round Integer Division */ #line 9 "Library/src/utils/round_div.hpp" #line 11 "Library/src/utils/round_div.hpp" namespace workspace { /* * @fn floor_div * @brief floor of fraction. * @param x the numerator * @param y the denominator * @return maximum integer z s.t. z <= x / y * @note y must be nonzero. */ template <typename T1, typename T2> constexpr typename std::enable_if<(is_integral_ext<T1>::value && is_integral_ext<T2>::value), typename std::common_type<T1, T2>::type>::type floor_div(T1 x, T2 y) { assert(y != 0); if (y < 0) x = -x, y = -y; return x < 0 ? (x - y + 1) / y : x / y; } /* * @fn ceil_div * @brief ceil of fraction. * @param x the numerator * @param y the denominator * @return minimum integer z s.t. z >= x / y * @note y must be nonzero. */ template <typename T1, typename T2> constexpr typename std::enable_if<(is_integral_ext<T1>::value && is_integral_ext<T2>::value), typename std::common_type<T1, T2>::type>::type ceil_div(T1 x, T2 y) { assert(y != 0); if (y < 0) x = -x, y = -y; return x < 0 ? x / y : (x + y - 1) / y; } } // namespace workspace #line 22 "Library/lib/utils" // #include "src/utils/sfinae.hpp" #line 11 "other/y.cc" signed main() { using namespace workspace; io_setup(15); /* given case_info.read(); //*/ /* unspecified case_info.total = -1; //*/ return case_info.iterate(); } #line 2 "Library/src/modular/inverse.hpp" /* * @file inverse.hpp * @brief Inverse Table */ #line 9 "Library/src/modular/inverse.hpp" #line 2 "Library/src/modular/modint.hpp" /** * @file modint.hpp * * @brief Modular Arithmetic */ #line 12 "Library/src/modular/modint.hpp" #line 14 "Library/src/modular/modint.hpp" namespace workspace { namespace internal { /** * @brief Base of modular arithmetic. * * @tparam Mod identifier, which represents modulus if positive * @tparam Storage Reserved size for inverse calculation */ template <auto Mod, unsigned Storage> struct modint_base { static_assert(is_integral_ext<decltype(Mod)>::value, "Mod must be integral type."); using mod_type = typename std::make_signed<typename std::conditional< 0 < Mod, typename std::add_const<decltype(Mod)>::type, decltype(Mod)>::type>::type; using value_type = typename std::decay<mod_type>::type; using mul_type = typename multiplicable_uint<value_type>::type; static mod_type mod; static value_type storage; constexpr static void reserve(unsigned __n) noexcept { storage = __n; } value_type value = 0; public: constexpr modint_base() noexcept = default; template <class int_type, typename std::enable_if<is_integral_ext<int_type>::value>::type * = nullptr> constexpr modint_base(int_type n) noexcept : value((n %= mod) < 0 ? n += mod : n) {} constexpr modint_base(bool n) noexcept : value(n) {} constexpr operator value_type() const noexcept { return value; } constexpr static modint_base one() noexcept { return 1; } // unary operators {{ constexpr modint_base operator++(int) noexcept { modint_base __t{*this}; operator++(); return __t; } constexpr modint_base operator--(int) noexcept { modint_base __t{*this}; operator--(); return __t; } constexpr modint_base &operator++() noexcept { if (++value == mod) value = 0; return *this; } constexpr modint_base &operator--() noexcept { if (!value) value = mod; --value; return *this; } constexpr modint_base operator-() const noexcept { modint_base __t; __t.value = value ? mod - value : 0; return __t; } // }} unary operators // operator+= {{ constexpr modint_base &operator+=(const modint_base &rhs) noexcept { if ((value += rhs.value) >= mod) value -= mod; return *this; } template <class int_type> constexpr typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type & operator+=(int_type const &rhs) noexcept { if (((value += rhs) %= mod) < 0) value += mod; return *this; } // }} operator+= // operator+ {{ template <class int_type> constexpr typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type operator+(int_type const &rhs) const noexcept { return modint_base{*this} += rhs; } constexpr modint_base operator+(modint_base rhs) const noexcept { return rhs += *this; } template <class int_type> constexpr friend typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type operator+(int_type const &lhs, modint_base rhs) noexcept { return rhs += lhs; } // }} operator+ // operator-= {{ constexpr modint_base &operator-=(const modint_base &rhs) noexcept { if ((value -= rhs.value) < 0) value += mod; return *this; } template <class int_type> constexpr typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type & operator-=(int_type rhs) noexcept { if (((value -= rhs) %= mod) < 0) value += mod; return *this; } // }} operator-= // operator- {{ template <class int_type> constexpr typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type operator-(int_type const &rhs) const noexcept { return modint_base{*this} -= rhs; } constexpr modint_base operator-(const modint_base &rhs) const noexcept { modint_base __t; if (((__t.value = value) -= rhs.value) < 0) __t.value += mod; return __t; } template <class int_type> constexpr friend typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type operator-(int_type lhs, const modint_base &rhs) noexcept { if (((lhs -= rhs.value) %= mod) < 0) lhs += mod; modint_base __t; __t.value = lhs; return __t; } // }} operator- // operator*= {{ constexpr modint_base &operator*=(const modint_base &rhs) noexcept { value = static_cast<mul_type>(value) * rhs.value % mod; return *this; } template <class int_type> constexpr typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type & operator*=(int_type rhs) noexcept { if (!rhs) value = 0; else if (value) { if ((rhs %= mod) < 0) rhs += mod; mul_type __r(value); value = static_cast<value_type &&>((__r *= rhs) %= mod); } return *this; } // }} operator*= // operator* {{ constexpr modint_base operator*(const modint_base &rhs) const noexcept { modint_base __t; __t.value = static_cast<mul_type>(value) * rhs.value % mod; return __t; } template <class int_type> constexpr typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type operator*(int_type rhs) const noexcept { if (!value or !rhs) return {}; if ((rhs %= mod) < 0) rhs += mod; mul_type __r(value); modint_base __t; __t.value = static_cast<value_type &&>((__r *= rhs) %= mod); return __t; } template <class int_type> constexpr friend typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type operator*(int_type lhs, const modint_base &rhs) noexcept { if (!lhs or !rhs.value) return {}; if ((lhs %= mod) < 0) lhs += mod; mul_type __r(lhs); modint_base __t; __t.value = static_cast<value_type &&>((__r *= rhs.value) %= mod); return __t; } // }} operator* protected: static value_type _mem(value_type __x) { static std::vector<value_type> __m{0, 1}; static value_type __i = (__m.reserve(Storage), 1); while (__i < __x) { ++__i; __m.emplace_back(mod - mul_type(mod / __i) * __m[mod % __i] % mod); } return __m[__x]; } template <class int_type> constexpr static typename std::enable_if<is_integral_ext<int_type>::value, value_type>::type _div(mul_type __r, int_type __x) noexcept { assert(__x); if (!__r) return 0; int_type __v{}; bool __neg = __x < 0 ? __x = -__x, true : false; if (__x < storage) __v = _mem(__x); else { int_type __y{mod}, __u{1}, __t; while (__x) __t = __y / __x, __y ^= __x ^= (__y -= __t * __x) ^= __x, __v ^= __u ^= (__v -= __t * __u) ^= __u; if (__y < 0) __neg ^= 1; } if (__neg) __v = 0 < __v ? mod - __v : -__v; else if (__v < 0) __v += mod; if (__r == 1) return static_cast<value_type>(__v); return static_cast<value_type>((__r *= __v) %= mod); } public: // operator/= {{ constexpr modint_base &operator/=(const modint_base &rhs) noexcept { if (value) value = _div(value, rhs.value); return *this; } template <class int_type> constexpr typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type & operator/=(int_type rhs) noexcept { if (value) value = _div(value, rhs %= mod); return *this; } // }} operator/= // operator/ {{ constexpr modint_base operator/(const modint_base &rhs) const noexcept { if (!value) return {}; modint_base __t; __t.value = _div(value, rhs.value); return __t; } template <class int_type> constexpr typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type operator/(int_type rhs) const noexcept { if (!value) return {}; modint_base __t; __t.value = _div(value, rhs %= mod); return __t; } template <class int_type> constexpr friend typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type operator/(int_type lhs, const modint_base &rhs) noexcept { if (!lhs) return {}; if ((lhs %= mod) < 0) lhs += mod; modint_base __t; __t.value = _div(lhs, rhs.value); return __t; } // }} operator/ constexpr modint_base inv() const noexcept { return _div(1, value); } template <class int_type> friend constexpr typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type pow(modint_base b, int_type e) noexcept { if (e < 0) { e = -e; b.value = _div(1, b.value); } modint_base __r; for (__r.value = 1; e; e >>= 1, b *= b) if (e & 1) __r *= b; return __r; } template <class int_type> constexpr typename std::enable_if<is_integral_ext<int_type>::value, modint_base>::type pow(int_type e) const noexcept { modint_base __r, b; __r.value = 1; for (b.value = e < 0 ? e = -e, _div(1, value) : value; e; e >>= 1, b *= b) if (e & 1) __r *= b; return __r; } friend std::ostream &operator<<(std::ostream &os, const modint_base &rhs) noexcept { return os << rhs.value; } friend std::istream &operator>>(std::istream &is, modint_base &rhs) noexcept { intmax_t value; rhs = (is >> value, value); return is; } }; template <auto Mod, unsigned Storage> typename modint_base<Mod, Storage>::mod_type modint_base<Mod, Storage>::mod = Mod > 0 ? Mod : 0; template <auto Mod, unsigned Storage> typename modint_base<Mod, Storage>::value_type modint_base<Mod, Storage>::storage = Storage; } // namespace internal /** * @brief Modular arithmetic. * * @tparam Mod modulus * @tparam Storage Reserved size for inverse calculation */ template <auto Mod, unsigned Storage = 0, typename std::enable_if<(Mod > 0)>::type * = nullptr> using modint = internal::modint_base<Mod, Storage>; /** * @brief Runtime modular arithmetic. * * @tparam type_id uniquely assigned * @tparam Storage Reserved size for inverse calculation */ template <unsigned type_id = 0, unsigned Storage = 0> using modint_runtime = internal::modint_base<-(signed)type_id, Storage>; // #define modint_newtype modint_runtime<__COUNTER__> } // namespace workspace #line 11 "Library/src/modular/inverse.hpp" namespace workspace { // Modulus must be prime. template <class Modint> struct inverse_table { static_assert(std::is_same<std::nullptr_t, decltype((void *)Modint::mod, nullptr)>::value); using value_type = Modint; constexpr value_type operator()(int n) const { constexpr int_fast64_t mod = value_type::mod; assert(n %= mod); if (n < 0) n += mod; if (inv.empty()) inv = {1, mod != 1}; for (int m(inv.size()); m <= n; ++m) inv.emplace_back(mod / m * -inv[mod % m]); return inv[n]; } private: static std::vector<value_type> inv; }; template <class Modint> std::vector<Modint> inverse_table<Modint>::inv; } // namespace workspace #line 27 "other/y.cc" namespace workspace { using mint = modint<(int)1e9 + 7>; void main() { // start here! i64 n; string k; cin >> n >> k; if (!n) { cout << count(begin(k), end(k), 'o') << "\n"; return; } mint ans, p2 = mint(2).pow(n - 1); for (auto i : range(8)) { if (k[i] == 'o') { ans += p2 * 8 - (p2 - 1) * __popcount(i) * (4 - __popcount(i)); } } ans *= mint(4).pow(n - 1); cout << ans << "\n"; } } // namespace workspace