#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef vector<ll> vi;
typedef vector<vector<ll>> vvi;
typedef pair<ll,ll> pii;
typedef vector<pair<ll,ll>> vpii;
typedef vector<vector<pair<ll,ll>>> vvpii;
typedef vector<bool> vb;
typedef vector<vector<bool>> vvb;
#define REP(i,a,b) for(ll i=a;i<b;i++)
#define REPR(i,a,b) for(ll i=b;i>=a;i--)
#define show(a) REP(i,0,a.size()){cout<<a[i]<<" ";}
#define show2(a) REP(i,0,a.size()){REP(j,0,a[i].size()){cout<<a[i][j]<<" ";}cout<<endl;}
#define pb push_back
#define mp make_pair
#define min(a,b) (a<b?a:b)
#define min2(a,b,c) (a<b?(a<c?a:c):(b<c?b:c))
#define max(a,b) (a>b?a:b)
#define max2(a,b,c) (a>b?(a>c?a:c):(b>c?b:c))

int main(){
	std::ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	
	return 0;
}