#include<bits/stdc++.h>

using namespace std;

const int INF=1e9+10;


int main()
{
    int V,E;
    ios::sync_with_stdio(false);
    cin.tie(0);
    while(cin>>V>>E)
    {
        vector<vector<int> > mat(20,vector<int>(20));
        vector<vector<int> > dp(1<<V,vector<int>(V));
        for(int i=0;i<mat.size();i++)
        {
            fill(mat[i].begin(),mat[i].end(),INF);
        }
        for(int i=0;i<E;i++)
        {
            int s,t,d;
            cin>>s>>t>>d;
            mat[s][t]=d;

        }
        for(int i=0;i<dp.size();i++)
        {
            fill(dp[i].begin(),dp[i].end(),INF);
        }
        dp[0][0]=0;
        for(int i=0;i<(1<<V);i++)
        {
            for(int j=0;j<V;j++)
            {
                for(int k=0;k<V;k++)
                {
                    if(!(i>>k&1))
                    {
                        dp[i^(1<<k)][k]=min(dp[i][j]+mat[j][k],dp[i^(1<<k)][k]);
                    }
                }
            }
        }
        cout<<(dp[(1<<V)-1][0]==INF?-1:dp[(1<<V)-1][0])<<endl;
    }

    return 0;
}


### Prompt

Please formulate 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>

using namespace std;

const int INF=1e9+10;


int main()
{
    int V,E;
    ios::sync_with_stdio(false);
    cin.tie(0);
    while(cin>>V>>E)
    {
        vector<vector<int> > mat(20,vector<int>(20));
        vector<vector<int> > dp(1<<V,vector<int>(V));
        for(int i=0;i<mat.size();i++)
        {
            fill(mat[i].begin(),mat[i].end(),INF);
        }
        for(int i=0;i<E;i++)
        {
            int s,t,d;
            cin>>s>>t>>d;
            mat[s][t]=d;

        }
        for(int i=0;i<dp.size();i++)
        {
            fill(dp[i].begin(),dp[i].end(),INF);
        }
        dp[0][0]=0;
        for(int i=0;i<(1<<V);i++)
        {
            for(int j=0;j<V;j++)
            {
                for(int k=0;k<V;k++)
                {
                    if(!(i>>k&1))
                    {
                        dp[i^(1<<k)][k]=min(dp[i][j]+mat[j][k],dp[i^(1<<k)][k]);
                    }
                }
            }
        }
        cout<<(dp[(1<<V)-1][0]==INF?-1:dp[(1<<V)-1][0])<<endl;
    }

    return 0;
}


```