#include<bits/stdc++.h>
using namespace std;
#define endl "n"
#define ll long long
#define file1 freopen(s, "r", stdin);
#define file2 freopen(s, "w", stdout);
#define all(v) ((v).begin()), ((v).end())
#define rall(v) ((v).rbegin()), ((v).rend())
#define fast ios::sync_with_stdio(0); cin.tie(0);
const double pi = acos(-1.0);//3.14
//cout << fixed << setprecision(9);
// transform(all(s),s.begin(),::tolower);
//string a(i.second/2,i.first);
//priority_queue<int, vector<int>, greater<int> > pq;
//int dx[8] = {0,1,0,-1,1,-1,1,-1};
//int dy[8] = {1,0,-1,0,1,1,-1,-1};
int32_t main() {
}