#include <bits/stdc++.h>
     
#define REP( i, n )     for( int (i) = 0; (i) < (n); (i)++ )
#define ALL( a )        (a).begin(), (a).end()
     
using namespace std;
using ll = long long;
using P = pair<int, int>;
     
template<class T>bool chmax( T& a, const T& b ) { if( a < b ) { a = b; return 1; } return 0; }
template<class T>bool chmin( T& a, const T& b ) { if( a > b ) { a = b; return 1; } return 0; }
     
const int INF = 1e9;
const ll LINF = 1e18;
const int MOD = 1e9 + 7;

int G[20][20];
int dp[1 << 15][20];

int rec( int S, int v, int n ){
  if( dp[S][v] >= 0 ){
    return dp[S][v];
  }

  if( S == ( 1 << n ) - 1 && v == 0 ){
    return dp[S][v] = 0;
  }

  int res = INF;
  REP( i, n ){
    if( !( S >> i & 1 ) ){
      chmin( res, rec( S | 1 << i, i, n ) + G[v][i] );
    }
  }
  
  return dp[S][v] = res;
}

int main(){
  int v, e; cin >> v >> e;

  fill( G[0], G[v], INF );
  
  REP( i, e ){
    int f, t, d; cin >> f >> t >> d;
    G[f][t] = d;
  }

  fill( dp[0], dp[1 << 15], -1 );

  int ans = rec( 0, 0, v );
  if( ans != INF ){
    cout << ans << endl;
  }else{
    cout << -1 << endl;
  }
}


### Prompt

Your challenge is to write a CPP solution to the following problem:

For a given weighted directed graph G(V, E), find the distance of the shortest route that meets the following criteria:

* It is a closed cycle where it ends at the same point it starts.
* It visits each vertex exactly once.

Constraints

* 2 ≤ |V| ≤ 15
* 0 ≤ di ≤ 1,000
* There are no multiedge

Input


|V| |E|
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1


|V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target vertices of i-th edge (directed) and di represents the distance between si and ti (the i-th edge).

Output

Print the shortest distance in a line. If there is no solution, print -1.

Examples

Input

4 6
0 1 2
1 2 3
1 3 9
2 0 1
2 3 6
3 2 4


Output

16


Input

3 3
0 1 1
1 2 1
0 2 1


Output

-1

### Response

```cpp
#include <bits/stdc++.h>
     
#define REP( i, n )     for( int (i) = 0; (i) < (n); (i)++ )
#define ALL( a )        (a).begin(), (a).end()
     
using namespace std;
using ll = long long;
using P = pair<int, int>;
     
template<class T>bool chmax( T& a, const T& b ) { if( a < b ) { a = b; return 1; } return 0; }
template<class T>bool chmin( T& a, const T& b ) { if( a > b ) { a = b; return 1; } return 0; }
     
const int INF = 1e9;
const ll LINF = 1e18;
const int MOD = 1e9 + 7;

int G[20][20];
int dp[1 << 15][20];

int rec( int S, int v, int n ){
  if( dp[S][v] >= 0 ){
    return dp[S][v];
  }

  if( S == ( 1 << n ) - 1 && v == 0 ){
    return dp[S][v] = 0;
  }

  int res = INF;
  REP( i, n ){
    if( !( S >> i & 1 ) ){
      chmin( res, rec( S | 1 << i, i, n ) + G[v][i] );
    }
  }
  
  return dp[S][v] = res;
}

int main(){
  int v, e; cin >> v >> e;

  fill( G[0], G[v], INF );
  
  REP( i, e ){
    int f, t, d; cin >> f >> t >> d;
    G[f][t] = d;
  }

  fill( dp[0], dp[1 << 15], -1 );

  int ans = rec( 0, 0, v );
  if( ans != INF ){
    cout << ans << endl;
  }else{
    cout << -1 << endl;
  }
}


```