#include<bits/stdc++.h>
using namespace std;
const int INF=1001001001;
struct edge{
    int to,cost;
    edge(int a,int b):to(a),cost(b){}
};

int dp[1<<16][15];
int N,M;
vector<edge>G[15];

int solve(int s){
    fill_n(*dp,(1<<16)*15,INF);
    dp[0][s]=0;

    for(int i=0;i<(1<<N);i++){
        for(int j=0;j<N;j++){
            if(dp[i][j]==INF)continue;
            for(int k=0;k<G[j].size();k++){
                edge &e=G[j][k];
                if(i>>e.to&1)continue;
                dp[i|(1<<e.to)][e.to]=min(dp[i|(1<<e.to)][e.to],dp[i][j]+e.cost);
            }
        }
    }

    return dp[(1<<N)-1][s];
}

int main(){
    cin>>N>>M;
    for(int i=0;i<M;i++){
        int a,b,c;cin>>a>>b>>c;
        G[a].push_back(edge(b,c));
    
    }

    int mi=INF;

    for(int i=0;i<N;i++)mi=min(mi,solve(i));

    if(mi==INF)cout<<-1<<endl;
    else cout<<mi<<endl;
    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<bits/stdc++.h>
using namespace std;
const int INF=1001001001;
struct edge{
    int to,cost;
    edge(int a,int b):to(a),cost(b){}
};

int dp[1<<16][15];
int N,M;
vector<edge>G[15];

int solve(int s){
    fill_n(*dp,(1<<16)*15,INF);
    dp[0][s]=0;

    for(int i=0;i<(1<<N);i++){
        for(int j=0;j<N;j++){
            if(dp[i][j]==INF)continue;
            for(int k=0;k<G[j].size();k++){
                edge &e=G[j][k];
                if(i>>e.to&1)continue;
                dp[i|(1<<e.to)][e.to]=min(dp[i|(1<<e.to)][e.to],dp[i][j]+e.cost);
            }
        }
    }

    return dp[(1<<N)-1][s];
}

int main(){
    cin>>N>>M;
    for(int i=0;i<M;i++){
        int a,b,c;cin>>a>>b>>c;
        G[a].push_back(edge(b,c));
    
    }

    int mi=INF;

    for(int i=0;i<N;i++)mi=min(mi,solve(i));

    if(mi==INF)cout<<-1<<endl;
    else cout<<mi<<endl;
    return 0;
}
```