#include <bits/stdc++.h>
 
#define mp       make_pair
#define pb       push_back
#define all(x)   (x).begin(),(x).end()

#define _D(p) std::cout<<"L"<<__LINE__<<" : " #p " = "<<(p)<<std::endl;
#define _D2(p,q) std::cout<<"L"<<__LINE__<<" : " #p " = "<<(p) << ", " #q " = "<<(q)<<std::endl;
#define _DN(v) std::cout<<"L"<<__LINE__<<" : " #v " = ["; rep(i,(v).size()) {std::cout<<v[i]<<(i==v.size()-1?"":", ");}std::cout<<"]"<<std::endl;
#define _DNN(v) std::cout<<"L"<<__LINE__<<" : " #v " = [" << std::endl; rep(i,(v).size()) {std::cout<<"	[";rep(j,(v)[0].size()){std::cout<<v[i][j]<<(j==v[0].size()-1?"":", ");}std::cout<<"],"<<std::endl;}std::cout<<"]"<<std::endl;
 
using namespace std;
 
typedef    long long          ll;
typedef    unsigned long long ull;
typedef    vector<int>        vi;
typedef    vector<vi>         vvi;
typedef    pair<int,int>      pii;
 
const int INF=1<<29;
const double EPS=1e-9;
 
const int dx[]={1,0,-1,0},dy[]={0,-1,0,1};

int main() {

	return 0;
}