#include <iostream>
#include <vector>
#include <map>
#include <set>
#include <algorithm>
#include <pair>
#include <string>

using namespace std;

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int,int> ii;
#define sz(a) int((a).size())
#define pb push_back
#defile all(c) (c).begin(),(c).end()
#define tr(c,i) for(auto i = (c).begin(); i != (c).end(); i++)
#define present(c,x) ((c).find(x) != (c).end())
#define cpresent(c,x) (find(all(c),x) != (c).end())


int main() {
    return 0;
}