#include <bits/stdc++.h>
using namespace std;
#define ll long long 
const ll INF = 1e18;
//
#define fi first
#define se second
#define pb push_back
//
#define all(x) (x).begin(), (x).end()
#define v1(name,n) vector<ll> name((n)+1)
#define v2(name,n,m) vector<vector<ll>> name((n)+1,vector<ll>((m)+1))
//
#define FOR(i, a, b) for (ll i = (a); i <= (b); ++i)
#define F0R(i, n) for (ll i = 0; i < (n); ++i)
#define FORK(i, a, b, k) for(ll i=(a) ; i<= (b) ; i+=k)
#define REP(i, a, b) for (ll i = (a); i >= (b); --i)
//
#define TIME (1.0* clock()/CLOCKS_PER_SEC)
#define file(name) if(fopen(name".inp","r")){freopen(name".inp","r",stdin); freopen(name".out","w",stdout);}
#define FAST_IO ios_base::sync_with_stdio(false); cin.tie(nullptr)
//

void solve(){
   

}



int main(){
   FAST_IO;
   //file("");
   
   //code
   

   //time
   cerr << "Time elapsed: " << TIME << "s.\n";
   return 0;
}