็ตๆ
ๅ้ก | No.2878 ๐๐พโ๐๐๐๐โ |
ใฆใผใถใผ |
๐ ![]() |
ๆๅบๆฅๆ | 2024-09-08 12:54:17 |
่จ่ช | C++23 (gcc 13.3.0 + boost 1.87.0) |
็ตๆ |
AC
|
ๅฎ่กๆ้ | 2 ms / 2,000 ms |
ใณใผใ้ท | 45,373 bytes |
ใณใณใใคใซๆ้ | 2,220 ms |
ใณใณใใคใซไฝฟ็จใกใขใช | 176,468 KB |
ๅฎ่กไฝฟ็จใกใขใช | 6,940 KB |
ๆ็ตใธใฃใใธๆฅๆ | 2024-09-08 12:54:20 |
ๅ่จใธใฃใใธๆ้ | 2,987 ms |
ใธใฃใใธใตใผใใผID ๏ผๅ่ๆ ๅ ฑ๏ผ |
judge4 / judge2 |
๏ผ่ฆใญใฐใคใณ๏ผ
ใใกใคใซใใฟใผใณ | ็ตๆ |
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other | AC * 8 |
ใฝใผในใณใผใ
#ifdef __LOCAL#include <mytemplate.hpp> // ใใชใณใณใใคใซๆธใฟใใใ ~/local/include/mytemplate.hpp.gch#else#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <climits>#include <cmath>#include <deque>#include <functional>#include <iomanip>#include <iostream>#include <iterator>#include <list>#include <map>#include <memory>#include <numeric>#include <optional>#include <queue>#include <random>#include <set>#include <stack>#include <string>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>#endifusing namespace std;// #pragma GCC target "no-avx" // gcc12.2ใฎใใฐๅ้ฟ็จใboostไฝฟ็จๆใฏใณใกใณใใขใฆใใฎไบ// #include <boost/multiprecision/cpp_int.hpp>// using bint = boost::multiprecision::cpp_int;using ll = long long;using vl = vector<ll>;using vvl = vector<vl>;using vb = vector<bool>;using vvb = vector<vb>;using vd = vector<double>;using vvd = vector<vd>;using vc = vector<char>;using vvc = vector<vc>;using pll = pair<ll, ll>;template <class T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;#define REP1(i, n) REP3(i, 0, n, 1)#define REP2(i, s, n) REP3(i, s, n, 1)#define REP3(i, s, n, d) for (ll i = (ll)(s); i < (ll)(n); i += (d))#define REP_OVERLOAD(e1, e2, e3, e4, NAME, ...) NAME#define rep(...) REP_OVERLOAD(__VA_ARGS__, REP3, REP2, REP1)(__VA_ARGS__)#define DEP1(i, n) DEP3(i, n, -1, 1)#define DEP2(i, n, s) DEP3(i, n, s, 1)#define DEP3(i, n, s, d) for (ll i = (ll)(n); (ll)(s) < i; i -= (d))#define DEP_OVERLOAD(e1, e2, e3, e4, NAME, ...) NAME#define dep(...) DEP_OVERLOAD(__VA_ARGS__, DEP3, DEP2, DEP1)(__VA_ARGS__)#define fore(e, a) for (auto&& e : (a))#define len(a) (ll)(a).size()#define all(a) (a).begin(), (a).end()#define rall(a) (a).rbegin(), (a).rend()#define pb push_back#define eb emplace_back#define fi first#define se second#define th third#define fo fourth/********* C O N S T A N T **********/constexpr ll INF = LONG_LONG_MAX / 2 - 10000LL; // 4,611,686,018,427,377,903 ~= 4.6e+18, 19ๆกconst double PI = acos(-1);/********* 1 2 8 b i t ๆด ๆฐ **********/using int128 = __int128_t;istream& operator>>(istream& stream, int128& val);ostream& operator<<(ostream& stream, const int128& val_);/********* P A I R **********/// ๅ้ ๆผ็ฎๅญ๏ผ+ -๏ผtemplate <class T, class U> pair<T, U> operator+(pair<T, U> a);template <class T, class U> pair<T, U> operator-(pair<T, U> a);// ่คๅไปฃๅ ฅๆผ็ฎๅญtemplate <class T, class U> pair<T, U>& operator+=(pair<T, U>& a, const pair<T, U> b);template <class T, class U> pair<T, U>& operator-=(pair<T, U>& a, const pair<T, U> b);template <class T, class U> pair<T, U>& operator*=(pair<T, U>& a, const pair<T, U> b);template <class T, class U> pair<T, U>& operator/=(pair<T, U>& a, const pair<T, U> b);template <class T, class U> pair<T, U>& operator%=(pair<T, U>& a, const pair<T, U> b);template <class T, class U, class V> pair<T, U>& operator+=(pair<T, U>& a, const V b);template <class T, class U, class V> pair<T, U>& operator-=(pair<T, U>& a, const V b);template <class T, class U, class V> pair<T, U>& operator*=(pair<T, U>& a, const V b);template <class T, class U, class V> pair<T, U>& operator/=(pair<T, U>& a, const V b);template <class T, class U, class V> pair<T, U>& operator%=(pair<T, U>& a, const V b);// ็ฎ่กๆผ็ฎๅญtemplate <class T, class U, class V> pair<T, U> operator+(pair<T, U> a, const V& b);template <class T, class U, class V> pair<T, U> operator-(pair<T, U> a, const V& b);template <class T, class U, class V> pair<T, U> operator*(pair<T, U> a, const V& b);template <class T, class U, class V> pair<T, U> operator/(pair<T, U> a, const V& b);template <class T, class U, class V> pair<T, U> operator%(pair<T, U> a, const V& b);// ๅ ฅๅบๅtemplate <class T, class U> istream& operator>>(istream& stream, pair<T, U>& a);template <class T, class U> ostream& operator<<(ostream& stream, const pair<T, U>& a);/********* V E C T O R **********/// ๅ้ ๆผ็ฎๅญ๏ผ+ -๏ผtemplate <class T> vector<T> operator+(vector<T> a);template <class T> vector<T> operator-(vector<T> a);// ่คๅไปฃๅ ฅๆผ็ฎๅญtemplate <class T> vector<T>& operator+=(vector<T>& a, const vector<T> b);template <class T> vector<T>& operator-=(vector<T>& a, const vector<T> b);template <class T> vector<T>& operator*=(vector<T>& a, const vector<T> b);template <class T> vector<T>& operator/=(vector<T>& a, const vector<T> b);template <class T> vector<T>& operator%=(vector<T>& a, const vector<T> b);template <class T, class U> vector<T>& operator+=(vector<T>& a, const U b);template <class T, class U> vector<T>& operator-=(vector<T>& a, const U b);template <class T, class U> vector<T>& operator*=(vector<T>& a, const U b);template <class T, class U> vector<T>& operator/=(vector<T>& a, const U b);template <class T, class U> vector<T>& operator%=(vector<T>& a, const U b);// ็ฎ่กๆผ็ฎๅญtemplate <class T, class U> vector<T> operator+(vector<T> a, const U& b);template <class T, class U> vector<T> operator-(vector<T> a, const U& b);template <class T, class U> vector<T> operator*(vector<T> a, const U& b);template <class T, class U> vector<T> operator/(vector<T> a, const U& b);template <class T, class U> vector<T> operator%(vector<T> a, const U& b);// ๅ ฅๅบๅtemplate <class T> istream& operator>>(istream& stream, vector<T>& a);template <class T> ostream& operator<<(ostream& stream, const vector<T>& v);template <class T> ostream& operator<<(ostream& stream, const vector<vector<T>>& vv);// ่จ็ฎtemplate <class T> T Sum(const vector<T>& v);template <class T> T Max(const vector<T>& v);template <class T> T Min(const vector<T>& v);template <class T> ll Argmax(const vector<T>& v);template <class T> ll Argmin(const vector<T>& v);template <class T, class U> bool Contains(const vector<T>& v, const U& a);template <class T> void Unique(vector<T>& v);// ็ๆtemplate <class T, class U> vector<T> make_vector(int n, U v);template <class T, class... Args> auto make_vector(int n, Args... args) {auto val = make_vector<T>(args...);return make_vector<decltype(val)>(n, move(val));}/********* S E T **********/template <class T> istream& operator>>(istream& stream, set<T>& st);template <class T> ostream& operator<<(ostream& stream, const set<T>& st);template <class T> T Max(const set<T>& st);template <class T> T Min(const set<T>& st);/********* M U L T I S E T **********/template <class T> istream& operator>>(istream& stream, multiset<T>& st);template <class T> ostream& operator<<(ostream& stream, const multiset<T>& st);template <class T> T Max(const multiset<T>& st);template <class T> T Min(const multiset<T>& st);template <class T> bool EraseOne(multiset<T>& st, const T& x);/********* C H A R **********/bool IsUpper(const char& c);bool IsLower(const char& c);char ToUpper(const char& c);char ToLower(const char& c);/********* S T R I N G **********/string ToUpper(const string& s);string ToLower(const string& s);bool IsPalindrome(const string& S);/********* T R I O **********/template <class T1, class T2, class T3> struct trio {T1 first;T2 second;T3 third;// ใณใณในใใฉใฏใฟใปไปฃๅ ฅๆผ็ฎๅญtrio();trio(const T1& x);trio(const T1& x, const T2& y, const T3& z);trio(const trio& t);trio& operator=(const trio& t);// ๆฏ่ผๆผ็ฎๅญbool operator<(const trio& t) const;bool operator==(const trio& t) const;bool operator!=(const trio& t) const;bool operator>(const trio& t) const;bool operator<=(const trio& t) const;bool operator>=(const trio& t) const;// ๅ้ ๆผ็ฎๅญ๏ผ+ -๏ผtrio operator+() const;trio operator-() const;// ๅ ฅๅบๅtemplate <class U1, class U2, class U3> friend istream& operator>>(istream&, trio<U1, U2, U3>&);template <class U1, class U2, class U3> friend ostream& operator<<(ostream&, const trio<U1, U2, U3>&);// `tie(a, b, c) = tll{3, 5, 7}`ใใใใฎใซๅฟ ่ฆ๏ผใณใณใใคใฉใ่ญฆๅ๏ผใๅบใใฎใงใใใงๅฎ็พฉ๏ผoperator tuple<T1&, T2&, T3&>() {return tie(first, second, third);}};// ่คๅไปฃๅ ฅๆผ็ฎๅญtemplate <class T1, class T2, class T3>trio<T1, T2, T3>& operator+=(trio<T1, T2, T3>& a, const trio<T1, T2, T3> b);template <class T1, class T2, class T3>trio<T1, T2, T3>& operator-=(trio<T1, T2, T3>& a, const trio<T1, T2, T3> b);template <class T1, class T2, class T3>trio<T1, T2, T3>& operator*=(trio<T1, T2, T3>& a, const trio<T1, T2, T3> b);template <class T1, class T2, class T3>trio<T1, T2, T3>& operator/=(trio<T1, T2, T3>& a, const trio<T1, T2, T3> b);template <class T1, class T2, class T3>trio<T1, T2, T3>& operator%=(trio<T1, T2, T3>& a, const trio<T1, T2, T3> b);template <class T1, class T2, class T3, class U> trio<T1, T2, T3>& operator+=(trio<T1, T2, T3>& a, const U b);template <class T1, class T2, class T3, class U> trio<T1, T2, T3>& operator-=(trio<T1, T2, T3>& a, const U b);template <class T1, class T2, class T3, class U> trio<T1, T2, T3>& operator*=(trio<T1, T2, T3>& a, const U b);template <class T1, class T2, class T3, class U> trio<T1, T2, T3>& operator/=(trio<T1, T2, T3>& a, const U b);template <class T1, class T2, class T3, class U> trio<T1, T2, T3>& operator%=(trio<T1, T2, T3>& a, const U b);// ็ฎ่กๆผ็ฎๅญtemplate <class T1, class T2, class T3, class U> trio<T1, T2, T3> operator+(trio<T1, T2, T3> a, const U& b);template <class T1, class T2, class T3, class U> trio<T1, T2, T3> operator-(trio<T1, T2, T3> a, const U& b);template <class T1, class T2, class T3, class U> trio<T1, T2, T3> operator*(trio<T1, T2, T3> a, const U& b);template <class T1, class T2, class T3, class U> trio<T1, T2, T3> operator/(trio<T1, T2, T3> a, const U& b);template <class T1, class T2, class T3, class U> trio<T1, T2, T3> operator%(trio<T1, T2, T3> a, const U& b);using tll = trio<ll, ll, ll>;/********* Q U A R T E T **********/template <class T1, class T2, class T3, class T4> struct quartet {T1 first;T2 second;T3 third;T4 fourth;// ใณใณในใใฉใฏใฟใปไปฃๅ ฅๆผ็ฎๅญquartet();quartet(const T1& x);quartet(const T1& x, const T2& y, const T3& z, const T4& w);quartet(const quartet& t);quartet& operator=(const quartet& t);// ๆฏ่ผๆผ็ฎๅญbool operator<(const quartet& t) const;bool operator==(const quartet& t) const;bool operator!=(const quartet& other) const;bool operator>(const quartet& other) const;bool operator<=(const quartet& other) const;bool operator>=(const quartet& other) const;// ๅ้ ๆผ็ฎๅญ๏ผ+ -๏ผquartet operator+() const;quartet operator-() const;// ๅ ฅๅบๅtemplate <class U1, class U2, class U3, class U4>friend istream& operator>>(istream&, quartet<U1, U2, U3, U4>&);template <class U1, class U2, class U3, class U4>friend ostream& operator<<(ostream&, const quartet<U1, U2, U3, U4>&);// `tie(a, b, c, d) = qll{3, 5, 7, 9}`ใใใใฎใซๅฟ ่ฆ๏ผใณใณใใคใฉใ่ญฆๅ๏ผใๅบใใฎใงใใใงๅฎ็พฉ๏ผoperator tuple<T1&, T2&, T3&, T4&>() {return tie(first, second, third, fourth);}};// ่คๅไปฃๅ ฅๆผ็ฎๅญtemplate <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>& operator+=(quartet<T1, T2, T3, T4>& a, const quartet<T1, T2, T3, T4> b);template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>& operator-=(quartet<T1, T2, T3, T4>& a, const quartet<T1, T2, T3, T4> b);template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>& operator*=(quartet<T1, T2, T3, T4>& a, const quartet<T1, T2, T3, T4> b);template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>& operator/=(quartet<T1, T2, T3, T4>& a, const quartet<T1, T2, T3, T4> b);template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>& operator%=(quartet<T1, T2, T3, T4>& a, const quartet<T1, T2, T3, T4> b);template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4>& operator+=(quartet<T1, T2, T3, T4>& a, const U b);template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4>& operator-=(quartet<T1, T2, T3, T4>& a, const U b);template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4>& operator*=(quartet<T1, T2, T3, T4>& a, const U b);template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4>& operator/=(quartet<T1, T2, T3, T4>& a, const U b);template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4>& operator%=(quartet<T1, T2, T3, T4>& a, const U b);// ็ฎ่กๆผ็ฎๅญtemplate <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4> operator+(quartet<T1, T2, T3, T4> a, const U& b);template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4> operator-(quartet<T1, T2, T3, T4> a, const U& b);template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4> operator*(quartet<T1, T2, T3, T4> a, const U& b);template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4> operator/(quartet<T1, T2, T3, T4> a, const U& b);template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4> operator%(quartet<T1, T2, T3, T4> a, const U& b);using qll = quartet<ll, ll, ll, ll>;/********* R A N D O M **********/struct Random {mt19937_64 rnd;Random();Random(ll seed);ll randint(ll a, ll b);double randreal(double a, double b);char randchar(char a, char b);template <class T> void shuffle(vector<T>& vec);};/********* T I M E R **********/struct Timer {int time_limit;int start_time;Timer(double time_limit_sec);bool is_time_up() const;double get_elapsed_ratio() const;};/********* P R I N T **********/template <class T> void print(const T& e);template <class H, class... T> void print(const H& h, const T&... t);template <class... T> void End(const T&... t);/********* D E B U G **********/#ifdef __LOCAL#define debug(...) \if (DEBUG) do { \cout << '[' << #__VA_ARGS__ << "] "; \debug_(__VA_ARGS__); \} while (0)#else#define debug(...)#endifvoid dbg_(const long long& e);template <class T> void dbg_(const T& e);template <class T, class U> void dbg_(const pair<T, U>& p);template <class T1, class T2, class T3> void dbg_(const trio<T1, T2, T3>& t);template <class T1, class T2, class T3, class T4> void dbg_(const quartet<T1, T2, T3, T4>& t);template <class T> void debug_(const T& e);template <class T> void debug_(const vector<T>& v);template <class T> void debug_(const vector<vector<T>>& vv);template <class T, class U> void debug_(const map<T, U>& mp);template <class T, class U> void debug_(const vector<map<T, U>>& vm);template <class T> void debug_(const set<T>& st);template <class T> void debug_(const multiset<T>& st);template <class T> void debug_(const vector<set<T>>& vs);template <class T> void debug_(const vector<multiset<T>>& vs);template <class H, class... T> void debug_(const H& h, const T&... t);/********* O T H E R S **********/template <class T, class U> bool chmin(T& a, U b);template <class T, class U> bool chmax(T& a, U b);template <class T, class U> T Mod(const T& a, const U& m);template <class T, class U> T Ceil(const T& x, const U& y);template <class T, class U> T Floor(const T& x, const U& y);template <class T> ll Sign(const T& x);ll Isqrt(ll n);ll Comb(ll n, ll r);template <class T> T Pow(T x, ll n);template <class T> T Aseries(T a, T d, ll n);template <class T> T Gseries(T a, T r, ll n);bool Bit(ll b, int i);ll Popcount(ll b);ll Mask(ll n);ll Mask(ll n, ll m);pll GetOverlap(ll l1, ll r1, ll l2, ll r2);bool IsOverlap(ll l1, ll r1, ll l2, ll r2);void PrintYesNo(bool b);/********* M O D **********/// #include <atcoder/modint> // https://atcoder.github.io/ac-library/production/document_ja/// using namespace atcoder;// using mint = modint998244353; // modint1000000007;// istream& operator >>(istream& stream, mint& e) {ll n; stream >> n; e = n; return stream; }// ostream& operator <<(ostream& stream, const mint& e) { stream << e.val(); return stream; }// using vm = vector<mint>;// using vvm = vector<vm>;/***************************************/constexpr bool DEBUG = true;int main() {cin.tie(nullptr);cout << fixed << setprecision(10);ll i;cin >> i;i--;string s = "IGNITION";print(s[i]);}/********* 1 2 8 b i t ๆด ๆฐ *********/// 128bitๆดๆฐใๅ ฅๅ. LONG_LONG_MAX่ถ ้/LONG_LONG_MINๆชๆบใOK.istream& operator>>(istream& stream, int128& val) {string s;stream >> s;assert(s.size() > 0);val = 0;bool is_minus = false;for (int i = 0; i < (int)s.size(); i++) {if (i == 0 && s[i] == '-') {assert(s.size() > 1);is_minus = true;} else {assert('0' <= s[i] && s[i] <= '9');val *= 10;val += s[i] - '0';}}if (is_minus) val *= -1;return stream;}// 128bitๆดๆฐใๅบๅ.ostream& operator<<(ostream& stream, const int128& val_) {auto val(val_);if (val == 0) return stream << 0;if (val < 0) {stream << '-';val *= -1;}string s;while (val > 0) {s += (val % 10) + '0';val /= 10;}reverse(all(s));return stream << s;}/********* P A I R **********//* ๅ้ ๆผ็ฎๅญ๏ผ+ -๏ผ */template <class T, class U> pair<T, U> operator+(pair<T, U> a) {return a;}template <class T, class U> pair<T, U> operator-(pair<T, U> a) {return a * (-1);}/* ่คๅไปฃๅ ฅๆผ็ฎๅญ (pair) */template <class T, class U> pair<T, U>& operator+=(pair<T, U>& a, const pair<T, U> b) {a.fi += b.fi;a.se += b.se;return a;}template <class T, class U> pair<T, U>& operator-=(pair<T, U>& a, const pair<T, U> b) {a.fi -= b.fi;a.se -= b.se;return a;}template <class T, class U> pair<T, U>& operator*=(pair<T, U>& a, const pair<T, U> b) {a.fi *= b.fi;a.se *= b.se;return a;}template <class T, class U> pair<T, U>& operator/=(pair<T, U>& a, const pair<T, U> b) {a.fi /= b.fi;a.se /= b.se;return a;}template <class T, class U> pair<T, U>& operator%=(pair<T, U>& a, const pair<T, U> b) {a.fi %= b.fi;a.se %= b.se;return a;}template <class T, class U, class V> pair<T, U>& operator+=(pair<T, U>& a, const V b) {a.fi += b;a.se += b;return a;}template <class T, class U, class V> pair<T, U>& operator-=(pair<T, U>& a, const V b) {a.fi -= b;a.se -= b;return a;}template <class T, class U, class V> pair<T, U>& operator*=(pair<T, U>& a, const V b) {a.fi *= b;a.se *= b;return a;}template <class T, class U, class V> pair<T, U>& operator/=(pair<T, U>& a, const V b) {a.fi /= b;a.se /= b;return a;}template <class T, class U, class V> pair<T, U>& operator%=(pair<T, U>& a, const V b) {a.fi %= b;a.se %= b;return a;}/* ็ฎ่กๆผ็ฎๅญ (pair) */template <class T, class U, class V> pair<T, U> operator+(pair<T, U> a, const V& b) {return a += b;}template <class T, class U, class V> pair<T, U> operator-(pair<T, U> a, const V& b) {return a -= b;}template <class T, class U, class V> pair<T, U> operator*(pair<T, U> a, const V& b) {return a *= b;}template <class T, class U, class V> pair<T, U> operator/(pair<T, U> a, const V& b) {return a /= b;}template <class T, class U, class V> pair<T, U> operator%(pair<T, U> a, const V& b) {return a %= b;}// ๅ ฅๅบๅtemplate <class T, class U> istream& operator>>(istream& stream, pair<T, U>& a) {stream >> a.fi >> a.se;return stream;}template <class T, class U> ostream& operator<<(ostream& stream, const pair<T, U>& a) {stream << a.fi << " " << a.se;return stream;}/********* V E C T O R **********//* ๅ้ ๆผ็ฎๅญ๏ผ+ -๏ผ */template <class T> vector<T> operator+(vector<T> a) {return a;}template <class T> vector<T> operator-(vector<T> a) {return a * (-1);}/* ่คๅไปฃๅ ฅๆผ็ฎๅญ (vector) */template <class T> vector<T>& operator+=(vector<T>& a, const vector<T> b) {assert(a.size() == b.size());rep(i, 0, a.size()) a[i] += b[i];return a;}template <class T> vector<T>& operator-=(vector<T>& a, const vector<T> b) {assert(a.size() == b.size());rep(i, 0, a.size()) a[i] -= b[i];return a;}template <class T> vector<T>& operator*=(vector<T>& a, const vector<T> b) {assert(a.size() == b.size());rep(i, 0, a.size()) a[i] *= b[i];return a;}template <class T> vector<T>& operator/=(vector<T>& a, const vector<T> b) {assert(a.size() == b.size());rep(i, 0, a.size()) a[i] /= b[i];return a;}template <class T> vector<T>& operator%=(vector<T>& a, const vector<T> b) {assert(a.size() == b.size());rep(i, 0, a.size()) a[i] %= b[i];return a;}template <class T, class U> vector<T>& operator+=(vector<T>& a, const U b) {fore(e, a) e += b;return a;}template <class T, class U> vector<T>& operator-=(vector<T>& a, const U b) {fore(e, a) e -= b;return a;}template <class T, class U> vector<T>& operator*=(vector<T>& a, const U b) {fore(e, a) e *= b;return a;}template <class T, class U> vector<T>& operator/=(vector<T>& a, const U b) {fore(e, a) e /= b;return a;}template <class T, class U> vector<T>& operator%=(vector<T>& a, const U b) {fore(e, a) e %= b;return a;}/* ็ฎ่กๆผ็ฎๅญ (vector) */template <class T, class U> vector<T> operator+(vector<T> a, const U& b) {return a += b;}template <class T, class U> vector<T> operator-(vector<T> a, const U& b) {return a -= b;}template <class T, class U> vector<T> operator*(vector<T> a, const U& b) {return a *= b;}template <class T, class U> vector<T> operator/(vector<T> a, const U& b) {return a /= b;}template <class T, class U> vector<T> operator%(vector<T> a, const U& b) {return a %= b;}/* ๅ ฅๅบๅ (vector) */// ใใฏใใซใๅ ฅๅtemplate <class T> istream& operator>>(istream& stream, vector<T>& a) {fore(e, a) stream >> e;return stream;}// ใใฏใใซใ็ฉบ็ฝๅบๅใใงๅบๅtemplate <class T> ostream& operator<<(ostream& stream, const vector<T>& v) {if (v.size()) {stream << v[0];rep(i, 1, v.size()) cout << " " << v[i];}return stream;}// 2ๆฌกๅ ใใฏใใซใ็ฉบ็ฝ/ๆน่กๅบๅใใงๅบๅtemplate <class T> ostream& operator<<(ostream& stream, const vector<vector<T>>& vv) {if (vv.size()) {stream << vv[0];rep(i, 1, vv.size()) cout << '\n' << vv[i];}return stream;}/* ่จ็ฎ (vector) */// ๅ่จใv.size() == 0 ใฎใจใ T() ใ่ฟใtemplate <class T> T Sum(const vector<T>& v) {return reduce(all(v));}template <class T> T Max(const vector<T>& v) {assert(v.size());return *max_element(all(v));}template <class T> T Min(const vector<T>& v) {assert(v.size());return *min_element(all(v));}// ๆๅคง่ฆ็ด ใๆใๆๅใฎไฝ็ฝฎใ่ฟใ๏ผ0-origin๏ผ, O(N).template <class T> ll Argmax(const vector<T>& v) {assert(v.size());return max_element(all(v)) - v.begin();}// ๆๅฐ่ฆ็ด ใๆใๆๅใฎไฝ็ฝฎใ่ฟใ๏ผ0-origin๏ผ, O(N).template <class T> ll Argmin(const vector<T>& v) {assert(v.size());return min_element(all(v)) - v.begin();}// ่ฆ็ด `a`ใใใฏใใซ`v`ใซ1ใคไปฅไธๅซใพใใใใฉใใtemplate <class T, class U> bool Contains(const vector<T>& v, const U& a) {return find(all(v), a) != v.end();}// ใฝใผใใใใใฆใใผใฏๅคใฎใใฏใใซใซinplaceใงๆธใๆใใ, O(NlogN).template <class T> void Unique(vector<T>& v) {sort(all(v));v.erase(unique(all(v)), v.end());}/* ็ๆ (vector) */template <class T, class U> vector<T> make_vector(int n, U v) {return vector<T>(n, v);}/********* S E T **********/// ไธ่ฆ็ด ใๅ ฅๅtemplate <class T> istream& operator>>(istream& stream, set<T>& st) {T e;stream >> e;st.insert(e);return stream;}// ็ฉบ็ฝๅบๅใใงๅบๅtemplate <class T> ostream& operator<<(ostream& stream, const set<T>& st) {if (st.size()) {auto it = st.begin();stream << *it++;for (; it != st.end(); it++)cout << " " << *it;}return stream;}template <class T> T Max(const set<T>& st) {assert(st.size());return *prev(st.end());}template <class T> T Min(const set<T>& st) {assert(st.size());return *st.begin();}/********* M U L T I S E T **********/// ไธ่ฆ็ด ใๅ ฅๅtemplate <class T> istream& operator>>(istream& stream, multiset<T>& st) {T e;stream >> e;st.insert(e);return stream;}// ็ฉบ็ฝๅบๅใใงๅบๅtemplate <class T> ostream& operator<<(ostream& stream, const multiset<T>& st) {if (st.size()) {auto it = st.begin();stream << *it++;for (; it != st.end(); it++)cout << " " << *it;}return stream;}template <class T> T Max(const multiset<T>& st) {assert(st.size());return *prev(st.end());}template <class T> T Min(const multiset<T>& st) {assert(st.size());return *st.begin();}// ่ฆ็ด xใ1ใคๅ้ค. ๆถใใใtrueใ่ฟใ.template <class T> bool EraseOne(multiset<T>& st, const T& x) {auto it = st.find(x);if (it != st.end()) {st.erase(it);return true;} elsereturn false;}/********* C H A R **********/// ๅคงๆๅญใใฉใใbool IsUpper(const char& c) {return isupper(c) > 0;}// ๅฐๆๅญใใฉใใbool IsLower(const char& c) {return islower(c) > 0;}// ๅคงๆๅญใธๅคๆchar ToUpper(const char& c) {string s{c}, t;t.resize(s.size());std::transform(all(s), t.begin(), ::toupper);return t[0];}// ๅฐๆๅญใธๅคๆchar ToLower(const char& c) {string s{c}, t;t.resize(s.size());std::transform(all(s), t.begin(), ::tolower);return t[0];}/********* S T R I N G **********/// ๅคงๆๅญใธๅคๆstring ToUpper(const string& s) {string t;t.resize(s.size());std::transform(all(s), t.begin(), ::toupper);return t;}// ๅฐๆๅญใธๅคๆstring ToLower(const string& s) {string t;t.resize(s.size());std::transform(all(s), t.begin(), ::tolower);return t;}// ๅๆๅคๅฎ, O(N). ็ฉบๆๅญใฎ่ฟใๅคใฏTrue.bool IsPalindrome(const string& S) {ll N = len(S);for (ll i = 0; 2 * i < N; i++)if (S[i] != S[N - i - 1]) return false;return true;}/********* T R I O **********/// ใณใณในใใฉใฏใฟใปไปฃๅ ฅๆผ็ฎๅญtemplate <class T1, class T2, class T3> trio<T1, T2, T3>::trio() {first = T1();second = T2();third = T3();}template <class T1, class T2, class T3> trio<T1, T2, T3>::trio(const T1& x) : first(x), second(x), third(x) {}template <class T1, class T2, class T3>trio<T1, T2, T3>::trio(const T1& x, const T2& y, const T3& z) : first(x), second(y), third(z) {}template <class T1, class T2, class T3> trio<T1, T2, T3>::trio(const trio& t) {first = t.first;second = t.second;third = t.third;}template <class T1, class T2, class T3> trio<T1, T2, T3>& trio<T1, T2, T3>::operator=(const trio& t) {first = t.first;second = t.second;third = t.third;return *this;}// ๆฏ่ผๆผ็ฎๅญ (trio)template <class T1, class T2, class T3> bool trio<T1, T2, T3>::operator<(const trio& t) const {return tie(first, second, third) < tie(t.first, t.second, t.third);}template <class T1, class T2, class T3> bool trio<T1, T2, T3>::operator==(const trio& t) const {return tie(first, second, third) == tie(t.first, t.second, t.third);}template <class T1, class T2, class T3> bool trio<T1, T2, T3>::operator!=(const trio& t) const {return !(*this == t);}template <class T1, class T2, class T3> bool trio<T1, T2, T3>::operator>(const trio& t) const {return t < *this;}template <class T1, class T2, class T3> bool trio<T1, T2, T3>::operator<=(const trio& t) const {return !(*this > t);}template <class T1, class T2, class T3> bool trio<T1, T2, T3>::operator>=(const trio& t) const {return !(*this < t);}// ๅ้ ๆผ็ฎๅญ๏ผ+ -๏ผ (trio)template <class T1, class T2, class T3> trio<T1, T2, T3> trio<T1, T2, T3>::operator+() const {return *this;}template <class T1, class T2, class T3> trio<T1, T2, T3> trio<T1, T2, T3>::operator-() const {return (*this) * (-1);}// ๅ ฅๅบๅ (trio)template <class T1, class T2, class T3> istream& operator>>(istream& stream, trio<T1, T2, T3>& t) {return stream >> t.first >> t.second >> t.third;}template <class T1, class T2, class T3> ostream& operator<<(ostream& stream, const trio<T1, T2, T3>& t) {return stream << t.first << " " << t.second << " " << t.third;}/* ่คๅไปฃๅ ฅๆผ็ฎๅญ (trio) */template <class T1, class T2, class T3>trio<T1, T2, T3>& operator+=(trio<T1, T2, T3>& a, const trio<T1, T2, T3> b) {a.fi += b.fi;a.se += b.se;a.th += b.th;return a;}template <class T1, class T2, class T3>trio<T1, T2, T3>& operator-=(trio<T1, T2, T3>& a, const trio<T1, T2, T3> b) {a.fi -= b.fi;a.se -= b.se;a.th -= b.th;return a;}template <class T1, class T2, class T3>trio<T1, T2, T3>& operator*=(trio<T1, T2, T3>& a, const trio<T1, T2, T3> b) {a.fi *= b.fi;a.se *= b.se;a.th *= b.th;return a;}template <class T1, class T2, class T3>trio<T1, T2, T3>& operator/=(trio<T1, T2, T3>& a, const trio<T1, T2, T3> b) {a.fi /= b.fi;a.se /= b.se;a.th /= b.th;return a;}template <class T1, class T2, class T3>trio<T1, T2, T3>& operator%=(trio<T1, T2, T3>& a, const trio<T1, T2, T3> b) {a.fi %= b.fi;a.se %= b.se;a.th %= b.th;return a;}template <class T1, class T2, class T3, class U>trio<T1, T2, T3>& operator+=(trio<T1, T2, T3>& a, const U b) {a.fi += b;a.se += b;a.th += b;return a;}template <class T1, class T2, class T3, class U>trio<T1, T2, T3>& operator-=(trio<T1, T2, T3>& a, const U b) {a.fi -= b;a.se -= b;a.th -= b;return a;}template <class T1, class T2, class T3, class U>trio<T1, T2, T3>& operator*=(trio<T1, T2, T3>& a, const U b) {a.fi *= b;a.se *= b;a.th *= b;return a;}template <class T1, class T2, class T3, class U>trio<T1, T2, T3>& operator/=(trio<T1, T2, T3>& a, const U b) {a.fi /= b;a.se /= b;a.th /= b;return a;}template <class T1, class T2, class T3, class U>trio<T1, T2, T3>& operator%=(trio<T1, T2, T3>& a, const U b) {a.fi %= b;a.se %= b;a.th %= b;return a;}/* ็ฎ่กๆผ็ฎๅญ (trio) */template <class T1, class T2, class T3, class U> trio<T1, T2, T3> operator+(trio<T1, T2, T3> a, const U& b) {return a += b;}template <class T1, class T2, class T3, class U> trio<T1, T2, T3> operator-(trio<T1, T2, T3> a, const U& b) {return a -= b;}template <class T1, class T2, class T3, class U> trio<T1, T2, T3> operator*(trio<T1, T2, T3> a, const U& b) {return a *= b;}template <class T1, class T2, class T3, class U> trio<T1, T2, T3> operator/(trio<T1, T2, T3> a, const U& b) {return a /= b;}template <class T1, class T2, class T3, class U> trio<T1, T2, T3> operator%(trio<T1, T2, T3> a, const U& b) {return a %= b;}/********* Q U A R T E T **********/// ใณใณในใใฉใฏใฟใปไปฃๅ ฅๆผ็ฎๅญtemplate <class T1, class T2, class T3, class T4> quartet<T1, T2, T3, T4>::quartet() {first = T1();second = T2();third = T3();fourth = T4();}template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>::quartet(const T1& x) : first(x), second(x), third(x), fourth(x) {}template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>::quartet(const T1& x, const T2& y, const T3& z, const T4& w): first(x), second(y), third(z), fourth(w) {}template <class T1, class T2, class T3, class T4> quartet<T1, T2, T3, T4>::quartet(const quartet& t) {first = t.first;second = t.second;third = t.third;fourth = t.fourth;}template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>& quartet<T1, T2, T3, T4>::operator=(const quartet& t) {first = t.first;second = t.second;third = t.third;fourth = t.fourth;return *this;}// ๆฏ่ผๆผ็ฎๅญ (quartet)template <class T1, class T2, class T3, class T4>bool quartet<T1, T2, T3, T4>::operator<(const quartet& t) const {return tie(first, second, third, fourth) < tie(t.first, t.second, t.third, t.fourth);}template <class T1, class T2, class T3, class T4>bool quartet<T1, T2, T3, T4>::operator==(const quartet& t) const {return tie(first, second, third, fourth) == tie(t.first, t.second, t.third, t.fourth);}template <class T1, class T2, class T3, class T4>bool quartet<T1, T2, T3, T4>::operator!=(const quartet& t) const {return !(*this == t);}template <class T1, class T2, class T3, class T4>bool quartet<T1, T2, T3, T4>::operator>(const quartet& t) const {return t < *this;}template <class T1, class T2, class T3, class T4>bool quartet<T1, T2, T3, T4>::operator<=(const quartet& t) const {return !(*this > t);}template <class T1, class T2, class T3, class T4>bool quartet<T1, T2, T3, T4>::operator>=(const quartet& t) const {return !(*this < t);}// ๅ้ ๆผ็ฎๅญ๏ผ+ -๏ผ (quartet)template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4> quartet<T1, T2, T3, T4>::operator+() const {return *this;}template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4> quartet<T1, T2, T3, T4>::operator-() const {return (*this) * (-1);}// ๅ ฅๅบๅ (quartet)template <class T1, class T2, class T3, class T4>istream& operator>>(istream& stream, quartet<T1, T2, T3, T4>& t) {return stream >> t.first >> t.second >> t.third >> t.fourth;}template <class T1, class T2, class T3, class T4>ostream& operator<<(ostream& stream, const quartet<T1, T2, T3, T4>& t) {return stream << t.first << " " << t.second << " " << t.third << " " << t.fourth;}/* ่คๅไปฃๅ ฅๆผ็ฎๅญ (quartet) */template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>& operator+=(quartet<T1, T2, T3, T4>& a, const quartet<T1, T2, T3, T4> b) {a.fi += b.fi;a.se += b.se;a.th += b.th;a.fo += b.fo;return a;}template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>& operator-=(quartet<T1, T2, T3, T4>& a, const quartet<T1, T2, T3, T4> b) {a.fi -= b.fi;a.se -= b.se;a.th -= b.th;a.fo -= b.fo;return a;}template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>& operator*=(quartet<T1, T2, T3, T4>& a, const quartet<T1, T2, T3, T4> b) {a.fi *= b.fi;a.se *= b.se;a.th *= b.th;a.fo *= b.fo;return a;}template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>& operator/=(quartet<T1, T2, T3, T4>& a, const quartet<T1, T2, T3, T4> b) {a.fi /= b.fi;a.se /= b.se;a.th /= b.th;a.fo /= b.fo;return a;}template <class T1, class T2, class T3, class T4>quartet<T1, T2, T3, T4>& operator%=(quartet<T1, T2, T3, T4>& a, const quartet<T1, T2, T3, T4> b) {a.fi %= b.fi;a.se %= b.se;a.th %= b.th;a.fo %= b.fo;return a;}template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4>& operator+=(quartet<T1, T2, T3, T4>& a, const U b) {a.fi += b;a.se += b;a.th += b;a.fo += b;return a;}template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4>& operator-=(quartet<T1, T2, T3, T4>& a, const U b) {a.fi -= b;a.se -= b;a.th -= b;a.fo -= b;return a;}template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4>& operator*=(quartet<T1, T2, T3, T4>& a, const U b) {a.fi *= b;a.se *= b;a.th *= b;a.fo *= b;return a;}template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4>& operator/=(quartet<T1, T2, T3, T4>& a, const U b) {a.fi /= b;a.se /= b;a.th /= b;a.fo /= b;return a;}template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4>& operator%=(quartet<T1, T2, T3, T4>& a, const U b) {a.fi %= b;a.se %= b;a.th %= b;a.fo %= b;return a;}/* ็ฎ่กๆผ็ฎๅญ (quartet) */template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4> operator+(quartet<T1, T2, T3, T4> a, const U& b) {return a += b;}template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4> operator-(quartet<T1, T2, T3, T4> a, const U& b) {return a -= b;}template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4> operator*(quartet<T1, T2, T3, T4> a, const U& b) {return a *= b;}template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4> operator/(quartet<T1, T2, T3, T4> a, const U& b) {return a /= b;}template <class T1, class T2, class T3, class T4, class U>quartet<T1, T2, T3, T4> operator%(quartet<T1, T2, T3, T4> a, const U& b) {return a %= b;}/********* R A N D O M **********/// ๅผๆฐใชใ: seedใฏใฉใณใใRandom::Random() {random_device seed_gen;rnd.seed(seed_gen());}// ๅผๆฐ: seedRandom::Random(ll seed) {rnd.seed(seed);}// [a, b]ใใใฉใณใใ ใซๆดๆฐใ่ฟใll Random::randint(ll a, ll b) {uniform_int_distribution<ll> dist(a, b);return dist(rnd);}// [a, b]ใใใฉใณใใ ใซๆตฎๅๅฐๆฐ็นๆฐใ่ฟใdouble Random::randreal(double a, double b) {uniform_real_distribution<double> dist(a, b);return dist(rnd);}// [a, b]ใใใฉใณใใ ใซๆๅญใ่ฟใchar Random::randchar(char a, char b) {uniform_int_distribution<ll> dist(a, b);return dist(rnd);}// `vec`ใinplaceใงไธฆใณๆฟใใtemplate <class T> void Random::shuffle(vector<T>& vec) {std::shuffle(all(vec), rnd);}/********* T I M E R **********/// ๅผๆฐ: ใฟใคใ ใชใใใ๏ผ็ง๏ผTimer::Timer(double time_limit_sec) {assert(time_limit_sec > 0);this->time_limit = time_limit_sec * CLOCKS_PER_SEC;this->start_time = clock();}// ใฟใคใ ใชใใใใซๅฐ้ใใใใฉใใbool Timer::is_time_up() const {return clock() - this->start_time >= this->time_limit;}// ็ต้ๆ้ใฎๅฒๅใ[0.0, 1.0]ใง่ฟใdouble Timer::get_elapsed_ratio() const {double ratio = 1.0 * (clock() - this->start_time) / (this->time_limit - this->start_time);return min(1.0, ratio);}/********* P R I N T **********/template <class T> void print(const T& e) {cout << e << '\n';}template <class H, class... T> void print(const H& h, const T&... t) {cout << h << ' ';print(t...);}template <class... T> void End(const T&... t) {print(t...);exit(0);}/********* D E B U G *********/void dbg_(const long long& e) {if (e == INF)cout << "INF";else if (e == -INF)cout << "-INF";elsecout << e;}template <class T> void dbg_(const T& e) {cout << e;}template <class T, class U> void dbg_(const pair<T, U>& p) {cout << '(';dbg_(p.first);cout << ' ';dbg_(p.second);cout << ')';}template <class T1, class T2, class T3> void dbg_(const trio<T1, T2, T3>& t) {cout << '(';dbg_(t.first);cout << ' ';dbg_(t.second);cout << ' ';dbg_(t.third);cout << ')';}template <class T1, class T2, class T3, class T4> void dbg_(const quartet<T1, T2, T3, T4>& t) {cout << '(';dbg_(t.first);cout << ' ';dbg_(t.second);cout << ' ';dbg_(t.third);cout << ' ';dbg_(t.fourth);cout << ')';}template <class T> void debug_(const T& e) {dbg_(e);cout << '\n';}template <class T> void debug_(const vector<T>& v) {if (v.size()) {auto it = v.begin();dbg_(*it++);for (; it != v.end(); ++it) {cout << ' ';dbg_(*it);}}cout << '\n';}template <class T> void debug_(const vector<vector<T>>& vv) {cout << '\n';ll cnt = 0;for (auto&& v : vv) {cout << cnt++ << ": ";debug_(v);}}template <class T, class U> void debug_(const map<T, U>& mp) {if (mp.size()) {auto it = mp.begin();dbg_(*it++);for (; it != mp.end(); ++it) {cout << ' ';dbg_(*it);}}cout << '\n';}template <class T, class U> void debug_(const vector<map<T, U>>& vm) {cout << '\n';ll cnt = 0;for (auto&& mp : vm) {cout << cnt++ << ": ";debug_(mp);}}template <class T> void debug_(const set<T>& st) {if (st.size()) {auto it = st.begin();dbg_(*it++);for (; it != st.end(); ++it) {cout << ' ';dbg_(*it);}}cout << '\n';}template <class T> void debug_(const multiset<T>& st) {if (st.size()) {auto it = st.begin();dbg_(*it++);for (; it != st.end(); ++it) {cout << ' ';dbg_(*it);}}cout << '\n';}template <class T> void debug_(const vector<set<T>>& vs) {cout << '\n';ll cnt = 0;for (auto&& st : vs) {cout << cnt++ << ": ";debug_(st);}}template <class T> void debug_(const vector<multiset<T>>& vs) {cout << '\n';ll cnt = 0;for (auto&& st : vs) {cout << cnt++ << ": ";debug_(st);}}template <class H, class... T> void debug_(const H& h, const T&... t) {dbg_(h);cout << ", ";debug_(t...);}/********* O T H E R S **********/// a > b ใชใ a ใซ b ใไปฃๅ ฅ.template <class T, class U> bool chmin(T& a, U b) {if (a > b) {a = b;return true;}return false;}// a < b ใชใ a ใซ b ใไปฃๅ ฅ.template <class T, class U> bool chmax(T& a, U b) {if (a < b) {a = b;return true;}return false;}// a % mใ่ฟใ. aใฏ่ฒ ใOK.template <class T, class U> T Mod(const T& a, const U& m) {assert(m > 0);return (a % m + m) % m;}// ๅคฉไบ้ขๆฐ. xใฏ่ฒ ใOKtemplate <class T, class U> T Ceil(const T& x, const U& y) {assert(y > 0);return x < 0 ? x / y : (x + y - 1) / y;}// ๅบ้ขๆฐ. xใฏ่ฒ ใOKtemplate <class T, class U> T Floor(const T& x, const U& y) {assert(y > 0);return -(Ceil(-x, y));}// ็ฌฆๅท้ขๆฐ. ่ฟใๅค: -1, 0, +1ใฎใใใใtemplate <class T> ll Sign(const T& x) {return (x > T(0)) - (x < T(0));}// x * x <= nใๆบใใๆๅคงใฎๆดๆฐ`x`ใ่ฟใll Isqrt(ll n) {assert(n >= 0);ll x = round(sqrt(n));while (x * x > n)--x;return x;}// nCr. n=60, r=30ใพใงOK.ll Comb(ll n, ll r) {if (r < 0 || n < r) return 0;r = min(r, n - r);ll ret = 1;rep(i, r) {ret *= n - i;ret /= i + 1;}return ret;}// ในใไน. mintใOK.template <class T> T Pow(T x, ll n) {assert(n >= 0);T ret = 1;while (1) {if (n % 2) ret *= x;n /= 2;if (!n) return ret;x = x * x;}}// ็ญๅทฎ็ดๆฐ. mintใOK.template <class T> T Aseries(T a, T d, ll n) {assert(n >= 0);return a * n + n * (n - 1) / 2 * d;}// ็ญๆฏ็ดๆฐ. mintใOK.template <class T> T Gseries(T a, T r, ll n) {assert(n >= 0);if (r == 1)return a * n;elsereturn a * (1 - Pow(r, n)) / (1 - r);}// `b`ใฎ`i`็ช็ฎ๏ผ0 origin๏ผใฎใใใใ1ใใฉใใbool Bit(ll b, int i) {assert(0 <= i && i < 64);return (b >> i) & 1;}// `b`ใฎ็ซใฃใฆใใใใใๆฐll Popcount(ll b) {return __builtin_popcountll(b);}// [0, n)็ช็ฎใฎใใใใ็ซใฃใ64bitๆดๆฐใ่ฟใ.ll Mask(ll n) {assert(0 <= n && n < 63);return (1LL << n) - 1LL;}// [m, n)็ช็ฎใฎใใใใ็ซใฃใ64bitๆดๆฐใ่ฟใ.ll Mask(ll n, ll m) {assert(n >= m);return Mask(n) ^ Mask(m);}// [l1, r1)ใจ[l2, r2)ใฎ็ฉๅบ้ใ่ฟใ. ไพ: [3, 6) x [5, 7) = [5, 6)pll GetOverlap(ll l1, ll r1, ll l2, ll r2) {return {max(l1, l2), min(r1, r2)};}// [l1, r1)ใจ[l2, r2)ใง้ใชใใใใใใ่ฟใ. ๅผๆฐใ็ๆนใงใ็ฉบๅบ้ใชใfalse;bool IsOverlap(ll l1, ll r1, ll l2, ll r2) {return max(l1, l2) < min(r1, r2);}// b=trueใชใ"Yes\n", falseใชใ"No\n"ใๅบๅvoid PrintYesNo(bool b) {b ? print("Yes") : print("No");}