#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>

using namespace std;

typedef long long ll;
#define vll vector< ll >
#define pll pair<ll, ll>
#define vpll vector<pll>
#define vvll vector<vector< ll > >
#define fo(in, out) freopen(in, "r", stdin);freopen(out, "w", stdout);
#define int ll
#define debug(a) cerr << #a << " = " << a << '\n';
#define debug2(a, b) cerr << #a << " = " << a << ", " << #b << " = " << b <<'\n';
#define debug3(a, b, c) cerr << #a << " = " << a << ", " << #b << " = " << b << ", " << #c << " = " << c << '\n';