#include<iostream>

using namespace std;

int main(){
  int V,E;
  cin>>V>>E;
  int d[15][15];
  for(int i=0;i<V;i++){
    for(int j=0;j<V;j++){
      d[i][j]=-1;
    }
  }
  while(E--){
    int s,t,d_;
    cin>>s>>t>>d_;
    d[s][t]=d_;
  }
  int dp[1<<15][15];
  for(int i=0;i<V-1;i++){
    if(d[V-1][i]>=0){
      dp[1<<i][i]=d[V-1][i];
    }else{
      dp[1<<i][i]=1e9;
    }
  }
  for(int i=0;i<1<<V-1;i++){
    if(!(i&i-1))continue;
    for(int j=0;j<V-1;j++){
      if(!(i>>j&1))continue;
      dp[i][j]=1e9;
      int p=i^1<<j;
      for(int k=0;k<V-1;k++){
	if(!(p>>k&1)||d[k][j]<0)continue;
	dp[i][j]=min(dp[i][j],dp[p][k]+d[k][j]);
      }
    }
  }
  int b=1e9;
  for(int i=0;i<V-1;i++){
    if(d[i][V-1]<0)continue;
    b=min(b,dp[(1<<V-1)-1][i]+d[i][V-1]);
  }
  cout<<(b>1e8?-1:b)<<endl;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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>

using namespace std;

int main(){
  int V,E;
  cin>>V>>E;
  int d[15][15];
  for(int i=0;i<V;i++){
    for(int j=0;j<V;j++){
      d[i][j]=-1;
    }
  }
  while(E--){
    int s,t,d_;
    cin>>s>>t>>d_;
    d[s][t]=d_;
  }
  int dp[1<<15][15];
  for(int i=0;i<V-1;i++){
    if(d[V-1][i]>=0){
      dp[1<<i][i]=d[V-1][i];
    }else{
      dp[1<<i][i]=1e9;
    }
  }
  for(int i=0;i<1<<V-1;i++){
    if(!(i&i-1))continue;
    for(int j=0;j<V-1;j++){
      if(!(i>>j&1))continue;
      dp[i][j]=1e9;
      int p=i^1<<j;
      for(int k=0;k<V-1;k++){
	if(!(p>>k&1)||d[k][j]<0)continue;
	dp[i][j]=min(dp[i][j],dp[p][k]+d[k][j]);
      }
    }
  }
  int b=1e9;
  for(int i=0;i<V-1;i++){
    if(d[i][V-1]<0)continue;
    b=min(b,dp[(1<<V-1)-1][i]+d[i][V-1]);
  }
  cout<<(b>1e8?-1:b)<<endl;
}
```