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#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#define int long long
#define double long double
#define uint unsigned long long
#define int128 __int128
#define uint128 unsigned __int128
using namespace std;
constexpr int INF = 1LL << 60;
template <class T>
bool chmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
template <class T>
bool chmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; }