#include "library/template/base.hpp"
#include "library/template/macro.hpp"
#include "library/template/type.hpp"
TYPES(T)
void input(T &...a) { (std::cin >> ... >> a); }
#define INPUT(T, ...) \
T __VA_ARGS__; \
input(__VA_ARGS__);
#define INT(...) INPUT(int, __VA_ARGS__)
#define STR(...) INPUT(std::string, __VA_ARGS__)
#define LL(...) INPUT(long long, __VA_ARGS__)
#define CHR(...) INPUT(char, __VA_ARGS__)
#define DBL(...) INPUT(double, __VA_ARGS__)
#define VI2(n, v) \
vi v(n); \
input(v);
#define VI3(n, v, w) \
vi v(n), w(n); \
input(v, w);
#define VI4(n, v, w, x) \
vi v(n), w(n), x(n); \
input(v, w, x);
#define VI(...) overload5(__VA_ARGS__, VI4, VI3, VI2)(__VA_ARGS__)
#define VLL2(n, v) \
vll v(n); \
input(v);
#define VLL3(n, v, w) \
vll v(n), w(n); \
input(v, w);
#define VLL4(n, v, w, x) \
vll v(n), w(n), x(n); \
input(v, w, x);
#define VLL(...) overload5(__VA_ARGS__, VLL4, VLL3, VLL2)(__VA_ARGS__)
#define VS2(n, v) \
vs v(n); \
input(v);
#define VS3(n, v, w) \
vs v(n), w(n); \
input(v, w);
#define VS4(n, v, w, x) \
vs v(n), w(n), x(n); \
input(v, w, x);
#define VS(...) overload5(__VA_ARGS__, VS4, VS3, VS2)(__VA_ARGS__)
#define VVI(n, m, v) \
vvi v(n, vi(m)); \
input(v);
#define VVLL(n, m, v) \
vvll v(n, vll(m)); \
input(v);
#line 1 "library/template/base.hpp"
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#line 1 "library/template/base.hpp"
#pragma GCC optimize("Ofast")
#line 2 "library/template/macro.hpp"
#define overload2(a, b, c, ...) c
#define overload3(a, b, c, d, ...) d
#define overload4(a, b, c, d, e, ...) e
#define overload5(a, b, c, d, e, f, ...) f
#define REP4(i, s, n, d) for (int i = (s); i < (n); i += (d))
#define REP3(i, s, n) REP4(i, s, n, 1)
#define REP2(i, n) REP3(i, 0, n)
#define REP1(n) REP2(tomato, n)
#define REP(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
#define RREP4(i, n, s, d) for (int i = (n)-1; i >= (s); i -= (d))
#define RREP3(i, n, s) RREP4(i, n, s, 1)
#define RREP2(i, n) RREP3(i, n, 0)
#define RREP1(n) RREP2(tomato, n)
#define RREP(...) overload4(__VA_ARGS__, RREP4, RREP3, RREP2, RREP1)(__VA_ARGS__)
#define FOR4(a, b, c, d, v) for (auto [a, b, c, d] : v)
#define FOR3(a, b, c, v) for (auto [a, b, c] : v)
#define FOR2(a, b, v) for (auto [a, b] : v)
#define FOR1(a, v) for (auto a : v)
#define FOR(...) overload5(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define AFOR4(a, b, c, d, v) for (auto &[a, b, c, d] : v)
#define AFOR3(a, b, c, v) for (auto &[a, b, c] : v)
#define AFOR2(a, b, v) for (auto &[a, b] : v)
#define AFOR1(a, v) for (auto &a : v)
#define AFOR(...) overload5(__VA_ARGS__, AFOR4, AFOR3, AFOR2, AFOR1)(__VA_ARGS__)
#define CFOR4(a, b, c, d, v) for (const auto &[a, b, c, d] : v)
#define CFOR3(a, b, c, v) for (const auto &[a, b, c] : v)
#define CFOR2(a, b, v) for (const auto &[a, b] : v)
#define CFOR1(a, v) for (const auto &a : v)
#define CFOR(...) overload5(__VA_ARGS__, CFOR4, CFOR3, CFOR2, CFOR1)(__VA_ARGS__)
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define SORT(v) std::sort(ALL(v))
#define RSORT(v) std::sort(RALL(v))
#define REVERSE(v) std::reverse(ALL(v))
#define UNIQUE(v) SORT(v), v.erase(std::unique(ALL(v)), v.end())
#define PFOR(v) for (bool f = true; (f ? std::exchange(f, false) : std::next_permutation(ALL(v)));)
#line 1 "library/template/base.hpp"
#pragma GCC optimize("Ofast")
#line 2 "library/template/type.hpp"
#define TYPE1(T) template <class T>
#define TYPE2(T, U) template <class T, class U>
#define TYPE3(T, U, V) template <class T, class U, class V>
#define TYPE4(T, U, V, W) template <class T, class U, class V, class W>
#define TYPE5(T, U, V, W, X) \
template <class T, class U, class V, class W, class X>
#define TYPE(...) \
overload5(__VA_ARGS__, TYPE5, TYPE4, TYPE3, TYPE2, TYPE1)(__VA_ARGS__)
#define TYPES1(T) template <class... T>
#define TYPES2(H, T) template <class H, class... T>
#define TYPES(...) overload2(__VA_ARGS__, TYPES2, TYPES1)(__VA_ARGS__)
TYPE(T)
using vec<T> = std::vector<T>;
TYPE(T)
using vvec<T> = vec<vec<T>>;
TYPE(T)
using vvvec<T> = vec<vvec<T>>;
TYPE(T)
using vvvvec<T> = vec<vvvec<T>>;
TYPE(T)
using ptt<T> = std::pair<T, T>;
using ll = long long;
using ld = long double;
using vi = vec<int>;
using vvi = vvec<int>;
using vvvi = vvvec<int>;
using vvvvi = vvvvec<int>;
using vll = vec<ll>;
using vvll = vvec<ll>;
using vvvll = vvvec<ll>;
using vvvvll = vvvvec<ll>;
using vs = vec<std::string>;
using pi = ptt<int>;
using pll = ptt<ll>;
TYPE(T)
using pq = std::priority_queue<T>;
TYPE(T)
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;
#line 4 "library/template/input.hpp"
TYPES(T)
void input(T &...a) { (std::cin >> ... >> a); }
#define INPUT(T, ...) \
T __VA_ARGS__; \
input(__VA_ARGS__);
#define INT(...) INPUT(int, __VA_ARGS__)
#define STR(...) INPUT(std::string, __VA_ARGS__)
#define LL(...) INPUT(long long, __VA_ARGS__)
#define CHR(...) INPUT(char, __VA_ARGS__)
#define DBL(...) INPUT(double, __VA_ARGS__)
#define VI2(n, v) \
vi v(n); \
input(v);
#define VI3(n, v, w) \
vi v(n), w(n); \
input(v, w);
#define VI4(n, v, w, x) \
vi v(n), w(n), x(n); \
input(v, w, x);
#define VI(...) overload5(__VA_ARGS__, VI4, VI3, VI2)(__VA_ARGS__)
#define VLL2(n, v) \
vll v(n); \
input(v);
#define VLL3(n, v, w) \
vll v(n), w(n); \
input(v, w);
#define VLL4(n, v, w, x) \
vll v(n), w(n), x(n); \
input(v, w, x);
#define VLL(...) overload5(__VA_ARGS__, VLL4, VLL3, VLL2)(__VA_ARGS__)
#define VS2(n, v) \
vs v(n); \
input(v);
#define VS3(n, v, w) \
vs v(n), w(n); \
input(v, w);
#define VS4(n, v, w, x) \
vs v(n), w(n), x(n); \
input(v, w, x);
#define VS(...) overload5(__VA_ARGS__, VS4, VS3, VS2)(__VA_ARGS__)
#define VVI(n, m, v) \
vvi v(n, vi(m)); \
input(v);
#define VVLL(n, m, v) \
vvll v(n, vll(m)); \
input(v);
library/template/input.hpp
build/pch/stdc++.hpp