#include<iostream>
#include<algorithm>
using namespace std;
const int INF=1<<29; 
int n;
int d[16][16];
int dp[1<<16][16];

int main(){
  int m;
  cin>>n>>m;
  for(int i=0;i<n;i++){
    for(int j=0;j<n;j++){
      d[i][j]=INF;
    }
  }
  int v1,v2,cost;
  for(int i=0;i<m;i++){
    cin>>v1>>v2>>cost;
    d[v1][v2]=cost; 
  }
  
  for(int S=0;S<1<<n;S++){
    fill(dp[S],dp[S]+n,INF);
  }
  dp[(1 << n)-1][0]=0;
  
  for(int S=(1<<n)-2;S>=0;S--){
    for(int v=0;v<n;v++){
      for(int u=0;u<n;u++){
	if(!(S>>u&1)){ 
	  dp[S][v]=min(dp[S][v],dp[S|1<<u][u]+d[v][u]);
	}
      }
    }
  }
  if(dp[0][0]==INF){
    cout<<-1<<"\n";
  }else{
    cout<<dp[0][0]<<"\n";
  }
  return 0;
}
  


### Prompt

Develop a solution in cpp to the problem described below:

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<iostream>
#include<algorithm>
using namespace std;
const int INF=1<<29; 
int n;
int d[16][16];
int dp[1<<16][16];

int main(){
  int m;
  cin>>n>>m;
  for(int i=0;i<n;i++){
    for(int j=0;j<n;j++){
      d[i][j]=INF;
    }
  }
  int v1,v2,cost;
  for(int i=0;i<m;i++){
    cin>>v1>>v2>>cost;
    d[v1][v2]=cost; 
  }
  
  for(int S=0;S<1<<n;S++){
    fill(dp[S],dp[S]+n,INF);
  }
  dp[(1 << n)-1][0]=0;
  
  for(int S=(1<<n)-2;S>=0;S--){
    for(int v=0;v<n;v++){
      for(int u=0;u<n;u++){
	if(!(S>>u&1)){ 
	  dp[S][v]=min(dp[S][v],dp[S|1<<u][u]+d[v][u]);
	}
      }
    }
  }
  if(dp[0][0]==INF){
    cout<<-1<<"\n";
  }else{
    cout<<dp[0][0]<<"\n";
  }
  return 0;
}
  


```