#pragma GCC optimize "Ofast"
#pragma GCC optimize "unroll-loops"
#pragma GCC optimize "omit-frame-pointer"
#pragma GCC optimize "prefetch-loop-arrays"
#pragma GCC target "sse,sse2,sse3,sse4,abm,avx,aes,sse4a,sse4.1,sse4.2,mmx,popcnt,tune=native"
#include <bits/stdc++.h>
using namespace std;

#define scan(x) do{while((_n=getchar())<45);if(_n-45)x=_n;else x=getchar();for(x-=48;47<(_=getchar());x=(x<<3)+(x<<1)+_-48);if(_n<46)x=-x;}while(0)
char _, _n;

int __attribute__((optimize("-O3"))) main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    return 0;
}