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#include "template/in.hpp"
#pragma once #include <bits/stdc++.h> #include <unistd.h> #include "macros.hpp" #include "alias.hpp" #include "type_traits.hpp" template<std::size_t buf_size = IO_BUFFER_SIZE, std::size_t decimal_precision = 16> class Scanner { private: template<class, class = void> struct has_scan : std::false_type {}; template<class T> struct has_scan< T, decltype(std::declval<T>().scan(std::declval<Scanner&>()), (void)0)> : std::true_type {}; int fd; int idx, sz; bool state; std::array<char, IO_BUFFER_SIZE + 1> buffer; inline char cur() { if (idx == sz) load(); if (idx == sz) { state = false; return '\0'; } return buffer[idx]; } inline void next() { if (idx == sz) load(); if (idx == sz) return; ++idx; } public: inline void load() { int len = sz - idx; if (idx < len) return; std::memcpy(buffer.begin(), buffer.begin() + idx, len); sz = len + read(fd, buffer.data() + len, buf_size - len); buffer[sz] = 0; idx = 0; } Scanner(int fd) : fd(fd), idx(0), sz(0), state(true) {} Scanner(FILE* fp) : fd(fileno(fp)), idx(0), sz(0), state(true) {} inline char scan_char() { if (idx == sz) load(); return idx == sz ? '\0' : buffer[idx++]; } Scanner ignore(int n = 1) { if (idx + n > sz) load(); idx += n; return *this; } inline void discard_space() { if (idx == sz) load(); while (('\t' <= buffer[idx] && buffer[idx] <= '\r') || buffer[idx] == ' ') { if (++idx == sz) load(); } } void scan(char& a) { discard_space(); a = scan_char(); } void scan(bool& a) { discard_space(); a = scan_char() != '0'; } void scan(std::string& a) { discard_space(); a.clear(); while (cur() != '\0' && (buffer[idx] < '\t' || '\r' < buffer[idx]) && buffer[idx] != ' ') { a += scan_char(); } } template<std::size_t len> void scan(std::bitset<len>& a) { discard_space(); if (idx + len > sz) load(); rrep (i, len) a[i] = buffer[idx++] != '0'; } template<class T, typename std::enable_if<is_signed_int<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { discard_space(); if (buffer[idx] == '-') { ++idx; if (idx + 40 > sz && (idx == sz || ('0' <= buffer[sz - 1] && buffer[sz - 1] <= '9'))) load(); a = 0; while ('0' <= buffer[idx] && buffer[idx] <= '9') { a = a * 10 - (buffer[idx++] - '0'); } } else { if (idx + 40 > sz && '0' <= buffer[sz - 1] && buffer[sz - 1] <= '9') load(); a = 0; while ('0' <= buffer[idx] && buffer[idx] <= '9') { a = a * 10 + (buffer[idx++] - '0'); } } } template<class T, typename std::enable_if<is_unsigned_int<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { discard_space(); if (idx + 40 > sz && '0' <= buffer[sz - 1] && buffer[sz - 1] <= '9') load(); a = 0; while ('0' <= buffer[idx] && buffer[idx] <= '9') { a = a * 10 + (buffer[idx++] - '0'); } } template<class T, typename std::enable_if<std::is_floating_point<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { discard_space(); bool sgn = false; if (cur() == '-') { sgn = true; next(); } a = 0; while ('0' <= cur() && cur() <= '9') { a = a * 10 + cur() - '0'; next(); } if (cur() == '.') { next(); T n = 0, d = 1; for (int i = 0; '0' <= cur() && cur() <= '9' && i < (int)decimal_precision; ++i) { n = n * 10 + cur() - '0'; d *= 10; next(); } while ('0' <= cur() && cur() <= '9') next(); a += n / d; } if (sgn) a = -a; } private: template<std::size_t i, class... Args> void scan(std::tuple<Args...>& a) { if IF_CONSTEXPR (i < sizeof...(Args)) { scan(std::get<i>(a)); scan<i + 1, Args...>(a); } } public: template<class... Args> void scan(std::tuple<Args...>& a) { scan<0, Args...>(a); } template<class T, class U> void scan(std::pair<T, U>& a) { scan(a.first); scan(a.second); } template<class T, typename std::enable_if<is_range<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { for (auto&& i : a) scan(i); } template<class T, typename std::enable_if<has_scan<T>::value>::type* = nullptr> void scan(T& a) { a.scan(*this); } void operator()() {} template<class Head, class... Args> void operator()(Head& head, Args&... args) { scan(head); operator()(args...); } template<class T> Scanner& operator>>(T& a) { scan(a); return *this; } explicit operator bool() const { return state; } friend Scanner& getline(Scanner& scan, std::string& a) { a.erase(); char c; if ((c = scan.scan_char()) == '\n' || c == '\0') return scan; a += c; while ((c = scan.scan_char()) != '\n' && c != '\0') a += c; scan.state = true; return scan; } }; Scanner<> scan(0);
#line 2 "template/in.hpp" #include <bits/stdc++.h> #include <unistd.h> #line 2 "template/macros.hpp" #line 4 "template/macros.hpp" #ifndef __COUNTER__ #define __COUNTER__ __LINE__ #endif #define OVERLOAD5(a, b, c, d, e, ...) e #define REP1_0(b, c) REP1_1(b, c) #define REP1_1(b, c) \ for (ll REP_COUNTER_##c = 0; REP_COUNTER_##c < (ll)(b); ++REP_COUNTER_##c) #define REP1(b) REP1_0(b, __COUNTER__) #define REP2(i, b) for (ll i = 0; i < (ll)(b); ++i) #define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i) #define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c)) #define rep(...) OVERLOAD5(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__) #define RREP2(i, a) for (ll i = (ll)(a)-1; i >= 0; --i) #define RREP3(i, a, b) for (ll i = (ll)(a)-1; i >= (ll)(b); --i) #define RREP4(i, a, b, c) for (ll i = (ll)(a)-1; i >= (ll)(b); i -= (ll)(c)) #define rrep(...) OVERLOAD5(__VA_ARGS__, RREP4, RREP3, RREP2)(__VA_ARGS__) #define REPS2(i, b) for (ll i = 1; i <= (ll)(b); ++i) #define REPS3(i, a, b) for (ll i = (ll)(a) + 1; i <= (ll)(b); ++i) #define REPS4(i, a, b, c) for (ll i = (ll)(a) + 1; i <= (ll)(b); i += (ll)(c)) #define reps(...) OVERLOAD5(__VA_ARGS__, REPS4, REPS3, REPS2)(__VA_ARGS__) #define RREPS2(i, a) for (ll i = (ll)(a); i > 0; --i) #define RREPS3(i, a, b) for (ll i = (ll)(a); i > (ll)(b); --i) #define RREPS4(i, a, b, c) for (ll i = (ll)(a); i > (ll)(b); i -= (ll)(c)) #define rreps(...) OVERLOAD5(__VA_ARGS__, RREPS4, RREPS3, RREPS2)(__VA_ARGS__) #define each_for(...) for (auto&& __VA_ARGS__) #define each_const(...) for (const auto& __VA_ARGS__) #define all(v) std::begin(v), std::end(v) #define rall(v) std::rbegin(v), std::rend(v) #if __cpp_if_constexpr >= 201606L #define IF_CONSTEXPR constexpr #else #define IF_CONSTEXPR #endif #define IO_BUFFER_SIZE (1 << 17) #line 2 "template/alias.hpp" #line 4 "template/alias.hpp" using ll = long long; using uint = unsigned int; using ull = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; using ld = long double; using PLL = std::pair<ll, ll>; template<class T> using prique = std::priority_queue<T, std::vector<T>, std::greater<T>>; template<class T> struct infinity { static constexpr T value = std::numeric_limits<T>::max() / 2; static constexpr T mvalue = std::numeric_limits<T>::lowest() / 2; static constexpr T max = std::numeric_limits<T>::max(); static constexpr T min = std::numeric_limits<T>::lowest(); }; #if __cplusplus <= 201402L template<class T> constexpr T infinity<T>::value; template<class T> constexpr T infinity<T>::mvalue; template<class T> constexpr T infinity<T>::max; template<class T> constexpr T infinity<T>::min; #endif #if __cpp_variable_templates >= 201304L template<class T> constexpr T INF = infinity<T>::value; #endif constexpr ll inf = infinity<ll>::value; constexpr ld EPS = 1e-8; constexpr ld PI = 3.1415926535897932384626; #line 2 "template/type_traits.hpp" #line 5 "template/type_traits.hpp" template<class T, class... Args> struct function_traits_impl { using result_type = T; template<std::size_t idx> using argument_type = typename std::tuple_element<idx, std::tuple<Args...>>::type; using argument_tuple = std::tuple<Args...>; static constexpr std::size_t arg_size() { return sizeof...(Args); } }; template<class> struct function_traits_helper; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...)> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...)&> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...) const> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...) const&> { using type = function_traits_impl<Res, Args...>; }; #if __cpp_noexcept_function_type >= 201510L template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...) noexcept> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...)& noexcept> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...) const noexcept> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...) const& noexcept> { using type = function_traits_impl<Res, Args...>; }; #endif template<class F> using function_traits = typename function_traits_helper< decltype(&std::remove_reference<F>::type::operator())>::type; template<class F> using function_result_type = typename function_traits<F>::result_type; template<class F, std::size_t idx> using function_argument_type = typename function_traits<F>::template argument_type<idx>; template<class F> using function_argument_tuple = typename function_traits<F>::argument_tuple; template<class T> using is_signed_int = std::integral_constant<bool, (std::is_integral<T>::value && std::is_signed<T>::value) || std::is_same<T, i128>::value>; template<class T> using is_unsigned_int = std::integral_constant<bool, (std::is_integral<T>::value && std::is_unsigned<T>::value) || std::is_same<T, u128>::value>; template<class T> using is_int = std::integral_constant<bool, is_signed_int<T>::value || is_unsigned_int<T>::value>; template<class T> using make_signed_int = typename std::conditional< std::is_same<T, i128>::value || std::is_same<T, u128>::value, std::common_type<i128>, std::make_signed<T>>::type; template<class T> using make_unsigned_int = typename std::conditional< std::is_same<T, i128>::value || std::is_same<T, u128>::value, std::common_type<u128>, std::make_unsigned<T>>::type; template<class T, class = void> struct is_range : std::false_type {}; template<class T> struct is_range< T, decltype(all(std::declval<typename std::add_lvalue_reference<T>::type>()), (void)0)> : std::true_type {}; template<class T, bool = is_range<T>::value> struct range_rank : std::integral_constant<std::size_t, 0> {}; template<class T> struct range_rank<T, true> : std::integral_constant<std::size_t, range_rank<typename T::value_type>::value + 1> {}; template<std::size_t size> struct int_least { static_assert(size <= 128, "size must be less than or equal to 128"); using type = typename std::conditional< size <= 8, std::int_least8_t, typename std::conditional< size <= 16, std::int_least16_t, typename std::conditional< size <= 32, std::int_least32_t, typename std::conditional<size <= 64, std::int_least64_t, i128>::type>::type>::type>::type; }; template<std::size_t size> using int_least_t = typename int_least<size>::type; template<std::size_t size> struct uint_least { static_assert(size <= 128, "size must be less than or equal to 128"); using type = typename std::conditional< size <= 8, std::uint_least8_t, typename std::conditional< size <= 16, std::uint_least16_t, typename std::conditional< size <= 32, std::uint_least32_t, typename std::conditional<size <= 64, std::uint_least64_t, u128>::type>::type>::type>::type; }; template<std::size_t size> using uint_least_t = typename uint_least<size>::type; template<class T> using double_size_int = int_least<std::numeric_limits<T>::digits * 2 + 1>; template<class T> using double_size_int_t = typename double_size_int<T>::type; template<class T> using double_size_uint = uint_least<std::numeric_limits<T>::digits * 2>; template<class T> using double_size_uint_t = typename double_size_uint<T>::type; template<class T> using double_size = typename std::conditional<is_signed_int<T>::value, double_size_int<T>, double_size_uint<T>>::type; template<class T> using double_size_t = typename double_size<T>::type; #line 8 "template/in.hpp" template<std::size_t buf_size = IO_BUFFER_SIZE, std::size_t decimal_precision = 16> class Scanner { private: template<class, class = void> struct has_scan : std::false_type {}; template<class T> struct has_scan< T, decltype(std::declval<T>().scan(std::declval<Scanner&>()), (void)0)> : std::true_type {}; int fd; int idx, sz; bool state; std::array<char, IO_BUFFER_SIZE + 1> buffer; inline char cur() { if (idx == sz) load(); if (idx == sz) { state = false; return '\0'; } return buffer[idx]; } inline void next() { if (idx == sz) load(); if (idx == sz) return; ++idx; } public: inline void load() { int len = sz - idx; if (idx < len) return; std::memcpy(buffer.begin(), buffer.begin() + idx, len); sz = len + read(fd, buffer.data() + len, buf_size - len); buffer[sz] = 0; idx = 0; } Scanner(int fd) : fd(fd), idx(0), sz(0), state(true) {} Scanner(FILE* fp) : fd(fileno(fp)), idx(0), sz(0), state(true) {} inline char scan_char() { if (idx == sz) load(); return idx == sz ? '\0' : buffer[idx++]; } Scanner ignore(int n = 1) { if (idx + n > sz) load(); idx += n; return *this; } inline void discard_space() { if (idx == sz) load(); while (('\t' <= buffer[idx] && buffer[idx] <= '\r') || buffer[idx] == ' ') { if (++idx == sz) load(); } } void scan(char& a) { discard_space(); a = scan_char(); } void scan(bool& a) { discard_space(); a = scan_char() != '0'; } void scan(std::string& a) { discard_space(); a.clear(); while (cur() != '\0' && (buffer[idx] < '\t' || '\r' < buffer[idx]) && buffer[idx] != ' ') { a += scan_char(); } } template<std::size_t len> void scan(std::bitset<len>& a) { discard_space(); if (idx + len > sz) load(); rrep (i, len) a[i] = buffer[idx++] != '0'; } template<class T, typename std::enable_if<is_signed_int<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { discard_space(); if (buffer[idx] == '-') { ++idx; if (idx + 40 > sz && (idx == sz || ('0' <= buffer[sz - 1] && buffer[sz - 1] <= '9'))) load(); a = 0; while ('0' <= buffer[idx] && buffer[idx] <= '9') { a = a * 10 - (buffer[idx++] - '0'); } } else { if (idx + 40 > sz && '0' <= buffer[sz - 1] && buffer[sz - 1] <= '9') load(); a = 0; while ('0' <= buffer[idx] && buffer[idx] <= '9') { a = a * 10 + (buffer[idx++] - '0'); } } } template<class T, typename std::enable_if<is_unsigned_int<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { discard_space(); if (idx + 40 > sz && '0' <= buffer[sz - 1] && buffer[sz - 1] <= '9') load(); a = 0; while ('0' <= buffer[idx] && buffer[idx] <= '9') { a = a * 10 + (buffer[idx++] - '0'); } } template<class T, typename std::enable_if<std::is_floating_point<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { discard_space(); bool sgn = false; if (cur() == '-') { sgn = true; next(); } a = 0; while ('0' <= cur() && cur() <= '9') { a = a * 10 + cur() - '0'; next(); } if (cur() == '.') { next(); T n = 0, d = 1; for (int i = 0; '0' <= cur() && cur() <= '9' && i < (int)decimal_precision; ++i) { n = n * 10 + cur() - '0'; d *= 10; next(); } while ('0' <= cur() && cur() <= '9') next(); a += n / d; } if (sgn) a = -a; } private: template<std::size_t i, class... Args> void scan(std::tuple<Args...>& a) { if IF_CONSTEXPR (i < sizeof...(Args)) { scan(std::get<i>(a)); scan<i + 1, Args...>(a); } } public: template<class... Args> void scan(std::tuple<Args...>& a) { scan<0, Args...>(a); } template<class T, class U> void scan(std::pair<T, U>& a) { scan(a.first); scan(a.second); } template<class T, typename std::enable_if<is_range<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { for (auto&& i : a) scan(i); } template<class T, typename std::enable_if<has_scan<T>::value>::type* = nullptr> void scan(T& a) { a.scan(*this); } void operator()() {} template<class Head, class... Args> void operator()(Head& head, Args&... args) { scan(head); operator()(args...); } template<class T> Scanner& operator>>(T& a) { scan(a); return *this; } explicit operator bool() const { return state; } friend Scanner& getline(Scanner& scan, std::string& a) { a.erase(); char c; if ((c = scan.scan_char()) == '\n' || c == '\0') return scan; a += c; while ((c = scan.scan_char()) != '\n' && c != '\0') a += c; scan.state = true; return scan; } }; Scanner<> scan(0);