結果
問題 | No.2414 2 KA 3 KA |
ユーザー |
![]() |
提出日時 | 2023-08-12 13:31:27 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 39,244 bytes |
コンパイル時間 | 5,113 ms |
コンパイル使用メモリ | 215,388 KB |
最終ジャッジ日時 | 2025-02-16 02:53:17 |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 28 |
ソースコード
// made by https://github.com/094-gengar/add_lib_to_templ#if !__INCLUDE_LEVEL__#include __FILE__int main(){using namespace std;using namespace m9;INT(a, b, c);int x = a * b + b * c + c * a; x *= 2;int y = a * b * c;print(x > y ? 2 : 3);}#else// #line 2 "graph/Graph.hpp"#include <cassert>#include <iostream>#include <vector>#include <queue>#include <algorithm>#include <limits>namespace m9 {template<class T> struct Graph {template<class _T> inline bool chmin(_T& a, const _T& b){if(b < a) { a = b; return true; }else return false;}int SIZ;// bool isOffset;// bool isDirected;std::vector<std::vector<T>> G;Graph() = default;Graph(int n) : SIZ(n) {}// Graph(int n, bool offset, bool directed) : SIZ(n), isOffset(offset), isDirected(directed), G(n) {}void init(std::vector<std::vector<T>> g) { SIZ = g.size(); G = g; }std::vector<T> bfs(T s, T t = -1){assert(0 <= s and s < SIZ);assert((t == -1) or (0 <= s or s < SIZ));std::vector<T> dist(SIZ, std::numeric_limits<T>::max() / 2);std::vector<std::int8_t> vis(SIZ, false);dist[s] = 0;std::queue<T> q{};q.emplace(s);while(!q.empty()){T cur = q.front(); q.pop();for(const auto& e : G[cur])if(chmin(dist[e], dist[cur] + 1))q.emplace(e);}return (t == -1 ? dist : std::vector<T>{dist[t]});}};// #include <utility>template<class T> struct weightedGraph {using PTT = std::pair<T, T>;template<class _T> inline bool chmin(_T& a, const _T& b){if(b < a) { a = b; return true; }else return false;}int SIZ;// bool isOffset;// bool isDirected;std::vector<std::vector<PTT>> G;weightedGraph() = default;weightedGraph(int n) : SIZ(n) {}// weightedGraph(int n, bool os, bool drc) : SIZ(n), isOffset(os), isDirected(drc), G(n) {}void init(std::vector<std::vector<PTT>> g) { SIZ = g.size(); G = g; }std::vector<T> bfs(T s, T t = -1){assert(0 <= s and s < SIZ);assert((t == -1) or (0 <= s or s < SIZ));std::vector<T> dist(SIZ, std::numeric_limits<T>::max() / 2);std::vector<std::int8_t> vis(SIZ, false);dist[s] = 0;std::queue<PTT> q{};q.emplace(0, s);while(!q.empty()){const auto [curCst, curE]= q.front(); q.pop();if(curCst > dist[curE])continue;for(const auto&[cst, e] : G[curE])if(chmin(dist[e], dist[curE] + cst))q.emplace(dist[e], e);}return (t == -1 ? dist : std::vector<T>{dist[t]});}std::vector<T> dijk(T s, T t = -1){assert(0 <= s and s < SIZ);assert((t == -1) or (0 <= s or s < SIZ));std::vector<T> dist(SIZ, std::numeric_limits<T>::max() / 2);std::vector<std::int8_t> vis(SIZ, false);dist[s] = 0;std::priority_queue<PTT, std::vector<PTT>, std::greater<>> pq{};pq.emplace(0, s);while(!pq.empty()){const auto [curCst, curE]= pq.top(); pq.pop();if(curCst > dist[curE])continue;for(const auto&[cst, e] : G[curE])if(chmin(dist[e], dist[curE] + cst))pq.emplace(dist[e], e);}return (t == -1 ? dist : std::vector<T>{dist[t]});}};} // namespace m9// #line 2 "graph/LCA.hpp"#include <vector>// Euler Tourもしてるやつ → https://atcoder.jp/contests/abc294/submissions/39948286namespace m9 {struct LCA {std::vector<std::vector<int>> par;std::vector<int> dis;LCA(const std::vector<std::vector<int>>& g, int root = 0) { init(g, root); }void init(const std::vector<std::vector<int>>& g, int root = 0){int v = g.size(), k = 1;for(; 1 << k < v; k++) {}par.assign(k, std::vector<int>(v, -1));dis.assign(v, -1);dfs(g, root, -1, 0);for(int i = 0; i < k - 1; i++)for(int j = 0; j < v; j++){if(par[i][j] < 0)par[i + 1][j] = -1;else par[i + 1][j] = par[i][par[i][j]];}}void dfs(const std::vector<std::vector<int>>& g, int v, int p, int d){par[0][v] = p;dis[v] = d;for(int e : g[v])if(e != p)dfs(g, e, v, d + 1);}int run(int u, int v){if(dis[u] < dis[v])std::swap(u, v);int k = par.size();for(int i = 0; i < k; i++)if(dis[u] - dis[v] >> i & 1)u = par[i][u];if(u == v)return u;for(int i = k - 1; i >= 0; i--)if(par[i][u] != par[i][v]){u = par[i][u];v = par[i][v];}return par[0][u];}int distance(int u, int v) { return dis[u] + dis[v] - dis[run(u, v)] * 2; }bool isOnPath(int u, int v, int a) { return distance(u, a) + distance(a, v) == distance(u, v); }};} // namespace m9// #line 2 "heuristic/RandInt.hpp"#include <random>#include <ctime>namespace m9 {struct RandInt {private:std::mt19937 mt;public:RandInt() { mt.seed((unsigned int)time(0)); }auto seed() -> std::mt19937 { return mt; }unsigned int next() { return mt(); }unsigned int roll(int high){std::uniform_int_distribution<unsigned int> die(0, high - 1);return die(mt);}} ri;} // namespace m9using m9::ri;// #line 2 "heuristic/Timer.hpp"#include <chrono>namespace m9 {struct Timer {private:std::chrono::system_clock::time_point m_start;public:Timer() : m_start(std::chrono::system_clock::time_point::min()) { (*this).start(); }void clear() { m_start = std::chrono::system_clock::time_point::min(); }bool is_started() const { return (m_start.time_since_epoch() != std::chrono::system_clock::duration(0)); }void start() { m_start = std::chrono::system_clock::now(); }unsigned long long get_time(){if(is_started()){std::chrono::system_clock::duration diff;diff = std::chrono::system_clock::now() - m_start;return (unsigned long long)std::chrono::duration_cast<std::chrono::milliseconds>(diff).count() + 50;}return 0;}} timer;} // namespace m9using m9::timer;// #line 2 "io/FastIO.hpp"#include <cstdint>#include <cassert>#include <cmath>#include <unistd.h>#include <string>#include <array>#include <vector>#include <set>#define MY_FASTIO_VER2//#define IS_OUTPUT_ONLYnamespace m9 {struct fastin{std::array<signed char, 1048576> _buf;ssize_t n_w, n_r;#ifdef IS_OUTPUT_ONLYfastin() {}#elsefastin() { _do_read(); }#endiflong long rd_ll() noexcept{long long ret = 0, sgn = 1;signed char ch = _current_char();while(ch == ' ' || ch == '\n')ch = _next_char();if(ch == '-') sgn *= -1, ch = _next_char();for(; '0' <= ch && ch <= '9'; ch = _next_char()){ret = (ret * 10) + ch - '0';}return sgn * ret;}double rd_dbl() noexcept{double ret{}, sgn = 1;signed char ch = _current_char();while(ch == ' ' or ch == '\n')ch = _next_char();if(ch == '-')sgn *= -1, ch = _next_char();bool foundDot = false;double mul = 1;for(; ('0' <= ch && ch <= '9') or ch == '.'; ch = _next_char()){if(ch == '.') { foundDot = true; continue; }if(foundDot) { ret = ret + (ch - '0') / (mul *= 10); }else { ret = (ret * 10) + ch - '0'; }}return sgn * ret;}int rd_int() noexcept{long long _result = rd_ll();assert(-2147483648ll <= _result && _result <= 2147483647ll);return static_cast<int>(_result);}std::string rd_str() noexcept{std::string _res{};signed char ch = _current_char();while(ch == ' ' || ch == '\n')ch = _next_char();for(; ch != -1 && ch != '\n' && ch != ' '; ch = _next_char()){_res += std::string(1, ch);}return _res;}char rd_chr() noexcept{signed char ch = _current_char();while(ch == ' ' || ch == '\n')ch = _next_char();_next_char();// signed char discard = _next_char();return ch;}private:void _do_read() noexcept{ssize_t r = read(0, &_buf[0], _buf.size());assert(r >= 0);n_w = r, n_r = 0;}inline signed char _next_char() noexcept{if(++n_r == n_w)_do_read();return _current_char();}inline signed char _current_char() noexcept{return (n_r == n_w ? -1 : _buf[n_r]);}} fi;struct fastout{unsigned _wt_double_digit = 15;inline void wt_bool(bool x) noexcept { putchar_unlocked(x ? '1' : '0'); }inline void wt_ll(long long x) noexcept{std::array<signed char, 32> _buf;ssize_t _siz = 0;if(x < 0){x *= -1;putchar_unlocked('-');}if(x == 0)putchar_unlocked('0');while(x > 0){_buf[_siz++] = x % 10 + '0';x /= 10;}while(_siz--)putchar_unlocked(_buf[_siz]);}inline void wt_int(int x) noexcept { wt_ll(static_cast<long long>(x)); }inline void wt_ull(unsigned long long x) noexcept{std::array<signed char, 32> _buf;ssize_t _siz = 0;if(x == 0)putchar_unlocked('0');while(x > 0){_buf[_siz++] = x % 10 + '0';x /= 10;}while(_siz--)putchar_unlocked(_buf[_siz]);}inline void wt_chr(char x) noexcept { putchar_unlocked(x); }inline void wt_str(std::string x) noexcept{ssize_t _siz = static_cast<ssize_t>(x.length());for(ssize_t i = 0; i < _siz; i++)putchar_unlocked(x[i]);}inline void wt_dbl(double x) noexcept{int k, r = 0;double v = 1;if(x < 0){x *= -1;putchar_unlocked('-');}x += 0.5 * pow(0.1, _wt_double_digit);while(x >= 10 * v)v *= 10, r++;while(r-- >= 0){k = floor(x / v);if(k >= 10)k = 9;if(k <= -1)k = 0;x -= k * v;v *= 0.1;putchar_unlocked(k + '0');}if(_wt_double_digit > 0){putchar_unlocked('.');v = 1;for(ssize_t _ = 0; _ < _wt_double_digit; _++){v *= 0.1;k = floor(x / v);if(k >= 10)k = 9;if(k <= -1)k = 0;x -= k * v;putchar_unlocked(k + '0');}}}// const char* const END = "\n";// const char* const SPLIT = " ";} fo;inline void set_digit(unsigned d) { fo._wt_double_digit = d; }inline void scan(int& x) noexcept { x = fi.rd_int(); }inline void scan(long& x) noexcept { x = (sizeof(long) == 32 ? fi.rd_int() : fi.rd_ll()); }inline void scan(long long& x) noexcept { x = fi.rd_ll(); }inline void scan(unsigned& x) noexcept{int a = fi.rd_int();assert(a >= 0);x = a;}inline void scan(unsigned long& x) noexcept{long a;scan(a);assert(a >= 0l);x = a;}inline void scan(unsigned long long& x) noexcept{long long a = fi.rd_ll();assert(a >= 0ll);x = a;}// inline void scan(double& x) noexcept { x = static_cast<double>(fi.rd_ll()); }inline void scan(double& x) noexcept { x = fi.rd_dbl(); }inline void scan(char& x) noexcept { x = fi.rd_chr(); }inline void scan(std::string& x) noexcept { x = fi.rd_str(); }template<class T, class U>inline void scan(std::pair<T, U>& x) { scan(x.first); scan(x.second); }template<class T>inline void scan(std::vector<T>& x) { for(auto& e : x)scan(e); }void IN() {}template<class Car, class... Cdr>void IN(Car&& car, Cdr &&...cdr){scan(car);IN(std::forward<Cdr>(cdr)...);}inline void wt_any(const bool& x) noexcept { fo.wt_bool(x); }inline void wt_any(const int& x) noexcept { fo.wt_int(x); }inline void wt_any(const long& x) noexcept { fo.wt_ll(static_cast<long>(x)); }inline void wt_any(const long long& x) noexcept { fo.wt_ll(x); }inline void wt_any(const unsigned& x) noexcept { fo.wt_ull(static_cast<unsigned long long>(x)); }inline void wt_any(const unsigned long& x) noexcept { fo.wt_ull(static_cast<unsigned long long>(x)); }inline void wt_any(const unsigned long long& x) noexcept { fo.wt_ull(x); }inline void wt_any(const double& x) noexcept { fo.wt_dbl(x); }inline void wt_any(const char& x) noexcept { fo.wt_chr(x); }inline void wt_any(const char x[]) noexcept{size_t _siz = 0;while(x[_siz] != '\0')fo.wt_chr(x[_siz++]);}inline void wt_any(const std::string& x) noexcept { fo.wt_str(x); }template<class T, class U>inline void wt_any(const std::pair<T, U>& x){wt_any(x.first);wt_any(" ");wt_any(x.second);}template<class T>inline void wt_any(const std::vector<T>& x){size_t _siz = x.size();for(size_t i = 0; i < _siz - 1; i++)wt_any(x[i]), wt_any(" ");if(not x.empty())wt_any(x.back());}template<class T>inline void wt_any(const std::set<T>& x){for(const auto& e : x)wt_any(e), wt_any(' ');}int print() { wt_any("\n"); return 0; }template<class T>int print(const T& t){wt_any(t);wt_any("\n");return 0;}template<class T>int print(const std::vector<std::vector<T>>& x){for(const auto& v : x)print(v);return 0;}template<class Car, class... Cdr>int print(const Car& car, const Cdr &...cdr){wt_any(car);wt_any(" ");print(cdr...);return 0;}template<class T>int wt(const T& t){wt_any(t);return 0;}template<class Car, class... Cdr>int wt(const Car& car, const Cdr &...cdr){wt_any(car);wt(cdr...);return 0;}void yn(bool fl = true) { print(fl ? "Yes" : "No"); }template<class... T>void drop(const T&... x) { print(x...); exit(0); }void dyn(bool fl = true) { print(fl ? "Yes" : "No"); exit(0); }// void setEND(const char* c) { fo.END = c; }// void setSPLIT(const char* c) { fo.SPLIT = c; }#define INT(...) int __VA_ARGS__; IN(__VA_ARGS__)#define LL(...) long long __VA_ARGS__; IN(__VA_ARGS__)#define ULL(...) unsigned long long __VA_ARGS__; IN(__VA_ARGS__)#define STR(...) std::string __VA_ARGS__; IN(__VA_ARGS__)#define CHR(...) char __VA_ARGS__; IN(__VA_ARGS__)#define DBL(...) double __VA_ARGS__; IN(__VA_ARGS__)using ll = long long;using ull = unsigned long long;using pii = std::pair<int, int>;using pll = std::pair<ll, ll>;#define VEC(a, type, n) std::vector<type> (a)(n); IN(a)#define VVEC(a, type, h, w) std::vector<std::vector<type>> (a)(h, std::vector<type>(w)); IN(a)#define VI(a, n) VEC(a, int, n)#define VVI(a, h, w) VVEC(a, int, h, w)#define VPII(a, n) VEC(a, pii, n)#define VVPII(a, h, w) VVEC(a, pii, h, w)#define VLL(a, n) VEC(a, ll, n)#define VVLL(a, h, w) VVEC(a, ll, h, w)#define VPLL(a, n) VEC(a, pll, n)#define VVPLL(a, h, w) VVEC(a, pll, h, w)#define VULL(a, n) VEC(a, ull, n)#define VVULL(a, h, w) VVEC(a, ull, h, w)#define VC(a, n) VEC(a, char, n)#define VVC(a, h, w) VVEC(a, char, h, w)#define VD(a, n) VEC(a, double, n)#define VVD(a, h, w) VVEC(a, double, h, w)#define VS(a, n) VEC(a, std::string, n)} // namespace m9// #line 2 "math/Argsort.hpp"// #include <utility>#include <iostream>namespace m9 {template<class T> bool arg_cmp(const std::pair<T, T>& p, const std::pair<T, T>& q){auto area = [](const std::pair<T, T>& a) -> int {const auto&[x, y] = a;if(y < 0)return -1;else if(y == 0 and 0 <= x)return 0;else return 1;};const int ap = area(p);const int aq = area(q);if(ap != aq)return ap < aq;else{const auto& [px, py] = p;const auto& [qx, qy] = q;return (0 < (px * qy - py * qx));}}} // namespace m9// #line 2 "math/ChineseRemainderTheorem.hpp"#include <vector>#include <cassert>namespace m9 {using ll = long long;namespace m9_cht {template<class T> T ext_gcd(T a, T b, T &x, T &y){if(b == 0){x = 1, y = 0;return a;}T d = ext_gcd(b, a % b, y, x);y -= a / b * x;return d;}} // m9_chttemplate<class T>std::pair<T, T> ChnRemThm(std::vector<T>& r, std::vector<T>& m){assert(r.size() == m.size());int n = r.size();ll ret_r{0}, ret_m{1};for(int i{0}; i < n; i++){assert(m[i] >= 1);ll p{}, q{};ll g = m9_cht::ext_gcd(ret_m, m[i], p, q);if((r[i] - ret_r) % g != 0) { return std::make_pair((T)0, (T)0); }ll tmp = (r[i] - ret_r) / g * p % (m[i] / g);ret_r += ret_m * tmp;ret_m *= m[i] / g;ret_r = (ret_r % ret_m + ret_m) % ret_m;}return std::make_pair(ret_r, ret_m);}} // namespace m9// #line 2 "math/Combination.hpp"#include <cassert>#include <vector>namespace m9 {template<class T> struct combination {using ll = long long;ll N;std::vector<T> fct;combination(ll n) : N(n){fct.resize(N + 1);fct[0] = 1;for(ll i{1}; i <= N; i++)fct[i] = fct[i - 1] * i;}T nPr(ll n, ll r) { return n < 0 || r < 0 || n < r ? (T)(0) : fct[n] / fct[n - r]; }T nCr(ll n, ll r) { return n < 0 || r < 0 || n < r ? (T)(0) : nPr(n, r) / fct[r]; }T nHr(ll n, ll r) {return n < 0 || r + n - 1 < 0 || n < r + n - 1 ? (T)(0) : nCr(r + n - 1, r); }};} // namespace m9// #line 2 "math/DivisorList.hpp"#include <vector>#include <algorithm>namespace m9 {template<class T> std::vector<T> divisorList(const T& N){std::vector<T> result{};for(T i{1}; i * i <= N; i++){if(N % i == 0){result.emplace_back(i);if(i * i != N)result.emplace_back(N / i);}}std::sort(std::begin(result), std::end(result));return result;}} // namespace m9// #line 2 "math/ModInt.hpp"#include <iostream>namespace m9 {#define MY_MODINTtemplate<long long Mod> struct modInt {long long x;constexpr modInt() noexcept : x() {}template<class T>constexpr modInt(T v = 0) noexcept : x(v% Mod) { if(x < 0)x += Mod; }constexpr long long val() const noexcept { return x; }constexpr modInt operator-() const noexcept { return x ? Mod - x : 0; }constexpr modInt operator+(const modInt& r) const noexcept { return modInt(*this) += r; }constexpr modInt operator-(const modInt& r) const noexcept { return modInt(*this) -= r; }constexpr modInt operator*(const modInt& r) const noexcept { return modInt(*this) *= r; }constexpr modInt operator/(const modInt& r) const noexcept { return modInt(*this) /= r; }constexpr modInt& operator+=(const modInt& r) noexcept { x += r.x; if(x >= Mod)x -= Mod; return *this; }constexpr modInt& operator-=(const modInt& r) noexcept { x -= r.x; if(x < 0)x += Mod; return *this; }constexpr modInt& operator*=(const modInt& r) noexcept { x = x * r.x % Mod; return *this; }constexpr modInt& operator/=(const modInt& r) noexcept { x = x * r.inv().val() % Mod; return *this; }constexpr modInt powm(long long n) noexcept{if(n < 0)return powm(-n).inv();modInt x = *this, r = 1;for(; n; x *= x, n >>= 1)if(n & 1)r *= x;return r;}constexpr modInt inv() const noexcept{long long a = x, b = Mod, u = 1, v = 0;while(b){long long t = a / b;a -= t * b;std::swap(a, b);u -= t * v;std::swap(u, v);}return modInt(u);}constexpr modInt comb(long long a) noexcept{modInt n = *this, s = 1;for(int i = 0; i < a; i++)s *= (n - modInt(i));modInt m = 1;for(int i = 1; i <= a; i++)m *= modInt(i);return s * m.powm(Mod - 2);}constexpr bool operator==(const modInt& r) { return this->x == r.x; }constexpr bool operator!=(const modInt& r) { return this->x != r.x; }friend std::ostream& operator<<(std::ostream& os, const modInt<Mod>& a) { return os << a.x; }friend std::istream& operator>>(std::istream& is, modInt<Mod>& a){long long v;is >> v;a = modInt<Mod>(v);return is;}};using mint = modInt<1000000007>;using mint2 = modInt<998244353>;} // namespace m9// #line 2 "math/PrimeFactor.hpp"#include <vector>namespace m9 {template<class T> std::vector<std::pair<T, T>> prime_factor(T n){std::vector<std::pair<T, T>> ret;for(T i{2}; i * i <= n; i++){if(n % i != 0)continue;T tmp = 0;while(n % i == 0){tmp++;n /= i;}ret.push_back(std::make_pair(i, tmp));}if(n != 1)ret.push_back(std::make_pair(n, 1));return ret;}} // namespace m9// #line 2 "math/PrimeFactorPollard.hpp"#include <vector>#include <numeric>#include <algorithm>namespace m9 {using ll = long long;namespace m9_pfp {template<class T> T PM(T X, T N, T M){T ret{1};while(N > 0){if(N & 1) { (ret *= X) %= M; }(X *= X) %= M;N >>= 1;}return ret;}bool IP(ll N){if(N <= 1) { return false; }if(N == 2 || N == 3) { return true; }if(N % 2 == 0) { return false; }auto A = std::vector<ll>{2, 325, 9375, 28178, 450775, 9780504, 1795265022};ll s{}, d{N - 1};while(d % 2 == 0) { s++; d >>= 1; }for(const auto& a : A){if(a % N == 0) { return true; }ll t, x = PM<__int128_t>(a, d, N);if(x != 1){for(t = 0; t < s; t++){if(x == N - 1) { break; }x = (__int128_t)(x) * x % N;}if(t == s) { return false; }}}return true;}} // namespace m9_pfpll pollard(ll N){if(N % 2 == 0)return 2;if(m9_pfp::IP(N)) { return N; }auto f = [&](ll x) -> ll {return ((__int128_t(x) * x + 1) % N);};ll step{};while(true){step++;ll x = step;ll y = f(x);while(true){ll p = std::gcd(y - x + N, N);if(p == 0 || p == N) { break; }if(p != 1) { return p; }x = f(x);y = f(f(y));}}}std::vector<ll> primeFactPollard(ll N){if(N == 1) { return std::vector<ll>{}; }ll p = pollard(N);if(p == N) { return std::vector<ll>{p}; }std::vector<ll> L = primeFactPollard(p), R = primeFactPollard(N / p);L.insert(std::end(L), std::begin(R), std::end(R));std::sort(std::begin(L), std::end(L));return L;}}// #line 2 "other/Integers.hpp"#include <iostream>namespace m9 {struct cent_t {private:__int128_t N;public:template<class T>constexpr cent_t(T n) : N(static_cast<__int128_t>(n)) {}friend std::ostream& operator<<(std::ostream& os, const cent_t& a){ if(a.N > INT64_MAX)return os << "too big integer"; else return os << static_cast<long long>(a.N); }friend std::istream& operator>>(std::istream& is, cent_t& a){ long long tmp{}; is >> tmp; a.N = static_cast<__int128_t>(tmp); return is; }constexpr __int128_t val() const noexcept { return N; }constexpr cent_t operator-() const noexcept { return -N; }template<class INTEGER> constexpr cent_t operator+(const INTEGER& x) const noexcept { return N + x.N; }template<class INTEGER> constexpr cent_t operator-(const INTEGER& x) const noexcept { return N - x.N; }template<class INTEGER> constexpr cent_t operator*(const INTEGER& x) const noexcept { return N * x.N; }template<class INTEGER> constexpr cent_t operator/(const INTEGER& x) const noexcept { return N / x.N; }template<class INTEGER> constexpr cent_t operator<<(const INTEGER& x) const noexcept { return N << x; }template<class INTEGER> constexpr cent_t operator>>(const INTEGER& x) const noexcept { return N >> x; }template<class INTEGER> constexpr cent_t operator+=(const INTEGER& x) noexcept { N += x.N; return *this; }template<class INTEGER> constexpr cent_t operator-=(const INTEGER& x) noexcept { N -= x.N; return *this; }template<class INTEGER> constexpr cent_t operator*=(const INTEGER& x) noexcept { N *= x.N; return *this; }template<class INTEGER> constexpr cent_t operator/=(const INTEGER& x) noexcept { N /= x.N; return *this; }template<class INTEGER> constexpr cent_t operator<<=(const INTEGER& x) const noexcept { N <<= x.N; return *this; }template<class INTEGER> constexpr cent_t operator>>=(const INTEGER& x) const noexcept { N >>= x.N; return *this; }constexpr cent_t operator++() noexcept { N += 1; return *this; }constexpr cent_t operator--() noexcept { N -= 1; return *this; }template<class INTEGER> constexpr bool operator==(const INTEGER& x) { return this->N == x.N; }template<class INTEGER> constexpr bool operator!=(const INTEGER& x) { return this->N != x.N; }template<class INTEGER> constexpr bool operator<(const INTEGER& x) { return this->N < x.N; }template<class INTEGER> constexpr bool operator>(const INTEGER& x) { return this->N > x.N; }template<class INTEGER> constexpr bool operator<=(const INTEGER& x) { return this->N <= x.N; }template<class INTEGER> constexpr bool operator>=(const INTEGER& x) { return this->N >= x.N; }};} // namespace m9using i8 = signed char;using u8 = unsigned char;using i32 = signed int;using u32 = unsigned int;using i64 = signed long long;using u64 = unsigned long long;i8 operator"" _i8(unsigned long long x) { return static_cast<i8>(x); }u8 operator"" _u8(unsigned long long x) { return static_cast<u8>(x); }i32 operator"" _i32(unsigned long long x) { return static_cast<i32>(x); }u32 operator"" _u32(unsigned long long x) { return static_cast<u32>(x); }i64 operator"" _i64(unsigned long long x) { return static_cast<i64>(x); }u64 operator"" _u64(unsigned long long x) { return static_cast<u64>(x); }m9::cent_t operator"" _i128(unsigned long long x) { return m9::cent_t(x); }using f32 = float;using f64 = double;double operator"" _f32(unsigned long long x) { return static_cast<f32>(x); }double operator"" _f64(unsigned long long x) { return static_cast<f64>(x); }// #line 2 "other/gridtoInt.hpp"// #include <utility>#include <iostream>namespace m9 {template<class T> auto GridtoT(const T width, const T x, const T y) -> T {return x * width + y;}template<class T> auto GridtoT(const T width, const std::pair<T, T> p) -> T {return p.first * width + p.second;}template<class T> auto TtoGrid(const T width, const T N) -> std::pair<T, T> {return std::make_pair(N / width, N % width);}} // namespace m9// #line 2 "other/others.hpp"#include <cstdlib>#include <cmath>#include <climits>#include <cfloat>#include <map>// #include <utility>#include <set>#include <iostream>#include <memory>#include <string>#include <vector>#include <algorithm>#include <functional>#include <sstream>#include <deque>#include <complex>#include <stack>#include <queue>#include <cstdio>#include <cctype>#include <cstdint>#include <cstring>#include <ctime>#include <chrono>//#include <bit>#include <iterator>#include <bitset>#include <numeric>#include <list>#include <iomanip>#include <cassert>#include <array>#include <tuple>#include <initializer_list>#include <unordered_set>#include <unordered_map>#include <forward_list>#include <random>#include <regex>//#define INCLUDE_BOOST#ifdef INCLUDE_BOOST#if __has_include(<boost/range/irange.hpp>)#include <boost/range/irange.hpp>#include <boost/algorithm/string/split.hpp>#include <boost/algorithm/string/join.hpp>#include <boost/algorithm/string/replace.hpp>#include <boost/algorithm/string/classification.hpp>#endif#endif//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,fma,abm,mmx,avx,avx2")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")#define all(x) std::begin(x), std::end(x)#define Sort(x) sort(all(x))#define rSort(x) sort(all(x)); reverse(all(x))#define UNIQUE(v) v.erase(unique(all(v)), v.end())#define uniq(v) sort(all(v)); UNIQUE(v)#define l_b(c, x) distance(begin(c), lower_bound(all(c), (x)))#define u_b(c, x) distance(begin(c), upper_bound(all(c), (x)))#define fi first#define se second#define m_p make_pair#define m_t make_tuple#define pb push_back#define eb emplace_back#define cauto const auto&#define _rep_overload(_1, _2, _3, _4, name, ...) name#define _rep1(i, n) _rep2(i, 0, n)#define _rep2(i, a, b) for(ll i = (a); i < (b); i++)#define _rep3(i, a, b, c) for(ll i = (a); i < (b); i += c)#define rep(...) _rep_overload(__VA_ARGS__, _rep3, _rep2, _rep1)(__VA_ARGS__)#define myceil(a, b) ((a) + ((b) - 1)) / (b)#define continue_with(...) ({__VA_ARGS__; continue;})#define break_with(...) ({__VA_ARGS__; break;})// #include <utility>//#define int long longusing ll = long long;using ull = unsigned long long;using pii = std::pair<int, int>;using pll = std::pair<ll, ll>;#include <vector>#include <string>template<class T>using Vec = std::vector<T>;using vb = Vec<std::int8_t>;using vi = Vec<int>;using vu = Vec<unsigned>;using vll = Vec<ll>;using vull = Vec<ull>;using vd = Vec<double>;using vc = Vec<char>;using vs = Vec<std::string>;using vpii = Vec<pii>;using vpll = Vec<pll>;using vvb = Vec<vb>;using vvi = Vec<vi>;using vvu = Vec<vu>;using vvll = Vec<vll>;using vvull = Vec<vull>;using vvd = Vec<vd>;using vvc = Vec<vc>;using vvs = Vec<vs>;using vvpii = Vec<vpii>;using vvpll = Vec<vpll>;template <class T>inline bool chmin(T& a, const T& b) { if(b < a) { a = b; return true; } return false; }template <class T>inline bool chmax(T& a, const T& b) { if(a < b) { a = b; return true; } return false; }ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }ll fact(ll n, ll m) { ll f = n; for(ll i = n - 1; i >= 1; i--) { f *= i; if(m != -1)f %= m; } return f; }constexpr ll inf = 0x1fffffffffffffff;constexpr ll mod = 1000000007LL;constexpr ll mod2 = 998244353LL;constexpr double eps = 1e-8;constexpr double pi = 3.141592653589793238462643383279;#include <vector>#include <algorithm>#include <string>struct sorted_operator {template<class T> friend std::vector<T> operator>>(std::vector<T>a, sorted_operator){ std::sort(std::begin(a), std::end(a)); return a; }friend std::string operator>>(std::string a, sorted_operator){ std::sort(std::begin(a), std::end(a)); return a; }} Sor;struct reversed_operator {template<class T> friend std::vector<T> operator>>(std::vector<T> a, reversed_operator){ std::reverse(std::begin(a), std::end(a)); return a; }friend std::string operator>>(std::string a, reversed_operator){ std::reverse(std::begin(a), std::end(a)); return a; }} Rev;struct unique_operator {template<class T> friend std::vector<T> operator>>(std::vector<T> a, unique_operator){ a.erase(unique(std::begin(a), std::end(a)), std::end(a)); return a; }friend std::string operator>>(std::string a, unique_operator){ a.erase(unique(std::begin(a), std::end(a)), std::end(a)); return a; }} Set;template <class T>void INCVEC(std::vector<T>& a) { for(T& e : a)e++; }template <class T>void DECVEC(std::vector<T>& a) { for(T& e : a)e--; }struct inc_operator {template<class T> friend std::vector<T> operator>>(std::vector<T> a, inc_operator){ INCVEC(a); return a; }} Inc;struct dec_operator {template<class T> friend std::vector<T> operator>>(std::vector<T> a, dec_operator){ DECVEC(a); return a; }} Dec;template <class T, class F>auto operator>> (std::vector<T> a, F f) -> std::vector<decltype(f(a.front()))>{std::vector<decltype(f(a.front()))> res{};for(const T& e : a)res.emplace_back(f(e));return res;}#include <iostream>namespace m9 {#ifdef ONLINE_JUDGE#define dbg(...) void(0)#else#define dbg(...) _DEBUG(#__VA_ARGS__, __VA_ARGS__)template<class Car, class... Cdr>void _DEBUG(const char* s, Car&& car, Cdr&&... cdr){constexpr const char* open_br = sizeof...(cdr) == 0 ? "" : "(";constexpr const char* close_br = sizeof...(cdr) == 0 ? "" : ")";#ifdef MY_FASTIOio.wt_any(open_br); io.wt_any(s); io.wt_any(close_br);io.wt_any(" : ");io.wt_any(open_br); io.wt_any(std::forward<Car>(car));((io.wt_any(", "), io.wt_any(std::forward<Cdr>(cdr))), ...);io.wt_any(close_br); io.wt_any("\n");#else#ifdef MY_FASTIO_VER2wt_any(open_br); wt_any(s); wt_any(close_br);wt_any(" : ");wt_any(open_br); wt_any(std::forward<Car>(car));((wt_any(", "), wt_any(std::forward<Cdr>(cdr))), ...);wt_any(close_br); wt_any("\n");#elsestd::cerr << open_br << s << close_br << " : " << open_br << std::forward<Car>(car);((std::cerr << ", " << std::forward<Cdr>(cdr)), ...);std::cerr << close_br << "\n";#endif#endif}#endif} // namespace m9// #line 2 "structure/BinaryIndexedTree.hpp"#include <cassert>#include <vector>namespace m9 {template<class T> class BIT {int SIZ;std::vector<T> tree;public:BIT(int n = 0, T x = 0) : SIZ(n), tree(n, x) {}T sum(int i){assert(0 <= i and i <= SIZ);T result{0};for(; i > 0; i -= (i & -i))result += tree[i - 1];return result;}T sum(int l, int r) { return sum(r) - sum(l); }void add(int i, T a) { assert(0 <= i and i < SIZ); for(i++; i <= SIZ; i += (i & -i))tree[i - 1] += a; }int lowerBound(T k){if(k <= 0)return 0;int result{0}, i{1};for(; (i << 1) <= SIZ; )i <<= 1;for(; i; i >>= 1)if(result + i <= SIZ and tree[result + i] < k)k -= tree[result += i];return result;}};} // namespace m9// #line 2 "structure/CompressVec.hpp"#include <map>namespace m9 {template<class T> struct compress {private:int SIZ;public:std::vector<T> C;compress(std::vector<T> a){SIZ = a.size();C = a;std::map<T, T> mp{};for(int i{}; i < SIZ; i++)mp[C[i]] = -1;int c{};for(auto&[key, value] : mp)value = c++;for(int i{}; i < SIZ; i++)C[i] = mp[C[i]];}void init(std::vector<T> a){SIZ = a.size();C = a;std::map<T, T> mp{};for(int i{}; i < SIZ; i++)mp[C[i]] = -1;int c{};for(auto&[key, value] : mp)value = c++;for(int i{}; i < SIZ; i++)C[i] = mp[C[i]];}T operator[](int idx) { assert(0 <= idx and idx < SIZ); return C[idx]; }};} // namespace m9// #line 2 "structure/Cumsum.hpp"#include <cassert>namespace m9 {template<class T> struct cumsum {private:int SIZ;public:std::vector<T> S;cumsum(std::vector<T> a){SIZ = a.size();S.assign(SIZ + 1, 0);for(int i{}; i < SIZ; i++)S[i + 1] = S[i] + a[i];}void init(std::vector<T> a){SIZ = a.size();S.assign(SIZ + 1, 0);for(int i{}; i < SIZ; i++)S[i + 1] = S[i] + a[i];}T operator[](int idx) { assert(0 <= idx and idx <= SIZ); return S[idx]; }};} // namespace m9// #line 2 "structure/RollingHash.hpp"#include <vector>#include <cassert>#include <cmath>namespace m9 {using ll = long long;template<class T> struct RollingHash {private:int N;const ll MOD = (1ll << 61) - 1;ll base;std::vector<ll> Hs{}, Pw{};ll mul(ll x, ll y) const { return (__int128_t)(x) * y % MOD; }public:RollingHash() = default;RollingHash(const T& s, ll base = -1) : N(s.size()) {if(base == -1){ base = base = 1e9 + 7; }Hs.assign(N + 1, 0); Pw.assign(N + 1, 1);for(int i{}; i < N; i++){Hs[i + 1] = (mul(Hs[i], base) + s[i]) % MOD;Pw[i + 1] = (mul(Pw[i], base)) % MOD;}}ll get(const int l, const int r) const{assert(l <= r and 0 <= l and r <= N);return (Hs[r] - mul(Hs[l], Pw[r - l]) % MOD + MOD) % MOD;}ll getAll() const { return get(0, N);}int getLCP(const int a, const int b) const{assert(a >= 0 and b >= 0 and a < N and b < N);int ok{0}, ng{std::min(N - a, N - b)};while(abs(ok - ng) > 1){int mid = (ok + ng) / 2;(get(a, a + mid) != get(b, b + mid) ? ng : ok) = mid;}return ok;}};}// #line 2 "structure/SegmentTree.hpp"#include <cassert>#include <vector>namespace m9 {template<class M> class segmentTree {using T = typename M::valueType;std::vector<T> seg;int SIZ;public:segmentTree(int n) { for(SIZ = 1; SIZ < n; )SIZ <<= 1; seg.assign(2 * SIZ, M::id);}void update(int k, const T& x) { assert(0 <= k and k < SIZ); for(seg[k += SIZ] = x; k>>= 1; )seg[k] = M::op(seg[2 * k], seg[2 * k + 1]); }void set(int k, const T& x) { assert(0 <= k and k < SIZ); seg[k + SIZ] = x; }T operator[](const int& k) const { assert(0 <= k and k < SIZ); return seg[k + SIZ]; }void build() { for(int k = SIZ - 1; k > 0; k--)seg[k] = M::op(seg[2 * k], seg[2 * k + 1]); }T query(int a, int b){assert(0 <= a and a <= b and b <= SIZ);auto L = M::id;auto R = M::id;for(a += SIZ, b += SIZ; a < b; a >>= 1, b >>= 1){if(a & 1)L = M::op(L, seg[a++]);if(b & 1)R = M::op(seg[--b], R);}return M::op(L, R);}template<class C> int findSubtree(int a, const C& check, T& mono, bool type){for(; a < SIZ; ){auto next = M::op(seg[2 * a + type], mono);if(check(next))a = 2 * a + type;else mono = next, a = 2 * a + !type;}return (a - SIZ);}template<class C> int findFirst(int a, const C& check){assert(0 <= a and a <= SIZ);auto L = M::id;if(a <= 0)return (check(M::op(L, seg[1])) ? findSubtree(1, check, L, false) : -1);int b = SIZ;for(a += SIZ, b += SIZ; a < b; a >>= 1, b >>= 1){if(a & 1){auto next = M::op(L, seg[a]);if(check(next))return findSubtree(a, check, L, false);L = next;a++;}}return -1;}template<class C> int findLast(int b, const C& check){assert(0 <= b and b <= SIZ);auto R = M::id;if(b >= SIZ)return (check(M::op(seg[1], R)) ? findSubtree(1, check, R, true) : -1);int a = SIZ;for(b += SIZ; a < b; a >>= 1, b >>= 1){if(b & 1){auto next = M::op(seg[--b], R);if(check(next))return findSubtree(b, check, R, true);R = next;}}return -1;}};struct RSumQ {using valueType = int;static int op(int a, int b) { return a + b; }static inline int id{0};};struct RSumQLL {using valueType = long long;static long long op(long long a, long long b) { return a + b; }static inline long long id{0};};struct RMaxQ {using valueType = int;static int op(int a, int b) { return std::max(a, b); }static inline int id{-(1 << 29)};};struct RMaxQLL {using valueType = long long;static long long op(long long a, long long b) { return std::max(a, b); }static inline long long id{-(1ll << 60)};};struct RminQ {using valueType = int;static int op(int a, int b) { return std::min(a, b); }static inline int id{1 << 29};};struct RminQLL {using valueType = long long;static long long op(long long a, long long b) { return std::min(a, b); }static inline long long id{1ll << 60};};} // namespace m9// #line 2 "structure/Trie.hpp"#include <string>#include <algorithm>#include <vector>namespace m9 {template<int BAND_SIZE> struct TrieSub {int16_t C{};int common;std::vector<int> child;std::vector<int> accept{};TrieSub(int16_t C) : C(C), common(0){child.assign(BAND_SIZE, -1);}};template<int BAND_SIZE, int16_t BASE_CHAR> struct Trie {using Node = TrieSub<BAND_SIZE>;std::vector<Node> Nodes{};int root{0};Trie() { Nodes.emplace_back(Node(root)); }void insert(const std::string& word, int word_id){int len = word.length();int node_id{0};for(int i{0}; i < len; i++){int16_t c = (int16_t)(word[i]) - BASE_CHAR;int& next_id = Nodes[node_id].child[c];if(next_id == -1){next_id = (int)(Nodes.size());Nodes.emplace_back(Node(c));}Nodes[node_id].common++;node_id = next_id;}Nodes[node_id].common++;Nodes[node_id].accept.emplace_back(word_id);}void insert(const std::string& word){insert(word, Nodes[0].common);}bool search(const std::string& word, bool prefix = false){int len = word.length();int node_id{0};for(int i{0}; i < len; i++){int16_t C = (int16_t)(word[i]) - BASE_CHAR;int& next_id = Nodes[node_id].child[C];if(next_id == -1) { return false; }node_id = next_id;}return (prefix || (Nodes[node_id].accept.size() > 0));}bool search_prefix(const std::string& prefix){return search(prefix, true);}int count() const { return (Nodes.front().common); }long long size() const { return Nodes.size(); }};} // namespace m9// #line 2 "structure/UnionFind.hpp"#include <cassert>#include <vector>#include <algorithm>namespace m9 {class UnionFind {int SIZ;std::vector<int> a;public:UnionFind(int n) : SIZ(n), a(n) { for(int i{}; i < SIZ; i++)a[i] = -1; }int root(int x) { assert(x < SIZ); return (a[x] < 0 ? x : (a[x] = root(a[x]))); }bool same(int x, int y) { assert(x < SIZ); assert(y < SIZ); return root(x) == root(y); }void merge(int x, int y){assert(x < SIZ);assert(y < SIZ);x = root(x), y = root(y);if(x == y)return;if(a[x] > a[y])std::swap(x, y);a[x] += a[y], a[y] = x;}int size(int x) { assert(x < SIZ); return -a[root(x)]; }std::vector<std::vector<int>> groups(){std::vector<int> rootBuf(SIZ), groupSize(SIZ);for(int i{}; i < SIZ; i++)groupSize[rootBuf[i] = root(i)]++;std::vector<std::vector<int>> result(SIZ);for(int i{}; i < SIZ; i++)result[i].reserve(groupSize[i]);for(int i{}; i < SIZ; i++)result[rootBuf[i]].emplace_back(i);result.erase( \remove_if(std::begin(result),std::end(result),[&](const std::vector<int>& v) -> bool { return v.empty(); }),std::end(result));return result;}};using uni = UnionFind;} // namespace m9#endif