#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector< int > vi;
typedef vector< vi > vvi;
typedef vector< vvi > vvvi;
typedef vector< vvvi > vvvvi;
typedef vector< vvvvi > vvvvvi;
typedef vector< ll > vl;
typedef vector< vl > vvl;
typedef vector< vvl > vvvl;
typedef vector< vvvl > vvvvl;
typedef vector< vvvvl > vvvvvl;
typedef pair< int, int > pii;
typedef vector< pii > vp;
typedef vector< vp > vvp;
typedef vector < string > vs;
typedef vector< vs > vvs;
typedef vector< double > vd;
typedef vector< vd > vvd;
typedef vector< vvd > vvvd;
typedef vector< bool > vb;
typedef vector< vb > vvb;
const int INF = 0x3f3f3f3f;
const int MOD7 = ( int ) 1e9 + 7;
template< class T1, class T2 >
int upmin( T1 &x, T2 v ){
if( x > v ){
x = v;
return 1;
}
return 0;
}
template< class T1, class T2 >
int upmax( T1 &x, T2 v ){
if( x < v ){
x = v;
return 1;
}
return 0;
}
void init(){
}
void preprocess(){
}
void solve(){
}
signed main(){
ios::sync_with_stdio( 0 );
init();
preprocess();
solve();
return 0;
}