#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using uint=unsigned;
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(),x.end()
#define si(x) int(x.size())
#define a first
#define b second
template<class t>using vc=vector<t>;
template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b; return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(a>b){a=b; return true;}else return false;}
template<class t,class u>
ostream& operator<<(ostre
using P=pair<int,int>;
signed main(){
cin.tie(0);
ios::sync_with_stdio(0);
cout<<fixed<<setprecision(20);
}