template

#include <bits/stdc++.h>

using namespace std;

#define st first
#define nd second
#define pb push_back
#define db(x) cerr << #x << " == " << x << endl

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ll, pll> plll;
typedef vector<int> vi;
typedef vector<vi> vii;
const ld EPS = 1e-9, PI = acos(-1.);
const ll LINF = 0x3f3f3f3f3f3f3f3f;
const int INF = 0x3f3f3f3f, MOD = 1e9 + 7;
const int N = 1e5 + 5;

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    return 0;
}