#include <iostream>
#include <cstdio>
#include <fstream>
#include <algorithm>
#include <iterator>
#include <math.h>
#include <cmath>
#include <stdlib.h>
#include <vector>
#include <queue>
#include <stack>
#include <set>
#include <regex>
#include <stdexcept>
#include <unordered_set>
#include <string>
#include <map>
#include <iomanip>
#include <sstream>
#include <cassert>
#include <time.h>
#include <numeric>
#include <complex>


using namespace std;
using ull = unsigned long long;
using ll = long long;
using ld = long double;
using D = double;
using ii = pair<int, int>;
using vi = vector<int>;
using vii = vector<ii>;

#define pb push_back
#define mp make_pair
#define all(x) x.begin(),x.end()
#define makeunique(x) sort(all(x)), (x).resize(unique(all(x)) - (x).begin())
#define rep(i, x)  for(int i = 0; i < (x); i++)
#define rrep(i, x) for(int i = (x - 1); i >= 0; i--)
#define sqrt(x) sqrt(abs(x))
#define y1 y1_1234413
#define j1 j1_235
#define y0 y0_235
#define j0 j0_256
#define fi first
#define se second
#define re return
#define prev PREV
#define next NEXT
#define sz(x) ((int)x.size())

template<typename T> T sqr(T a) { re a * a; }
template<typename T> T gcd(T a, T b) { re b ? gcd(b, a % b) : a; }
template<typename T> T sgn(T a) { re a > 0 ? 1 : (a < 0 ? -1 : 0); }
template<typename T> T abs(T a) { re a > 0 ? a : -a; }

const int inf = 2e9;
const ld pi = acos((ld)-1);
const int MAXN = 300001;

#define FILENAME ""

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(NULL);
    //  freopen(FILENAME ".in", "r", stdin);
    //  freopen(FILENAME ".out", "w", stdout);
return 0;
}