/* codeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed by squishy1337 */

#include <bits/stdc++.h>

using namespace std;

#define sz(s) (int)(s).size()
#define all(v) (v).begin(), (v).end()
#define fst first
#define snd second
#define fastio ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ull> vul;
typedef vector<string> vstr;
typedef vector<bool> vbl;
typedef vector<pii> vii;
typedef vector<pll> vll;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef vector<char> vchr;

const ll INF = INT_MAX, LNF = 1e9;
const double EPS = 1e-9, PI = acos(-1);
const int MOD = 1e9 + 7, P = 239;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

signed main() {
    fastio;
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
#endif



    return 0;
}