#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef pair<LL,LL> P;
const LL mod=1e9+7;
const LL LINF=1LL<<62;
const int INF=1<<17;

int main(){
    int V,E;
    cin >> V >> E;
    int dist[V][V];
    int dp[1<<V][V];
    for(int i=0;i<(1<<V);i++){
        for(int j=0;j<V;j++){
            dp[i][j]=INF;
        }
    }
    for(int i=0;i<V;i++){
        for(int j=0;j<V;j++){
            dist[i][j]=INF;
        }
    }
    for(int i=0;i<E;i++){
        int s,t,d;
        cin >> s >> t >> d;
        dist[s][t]=d;
    }
    dp[0][0]=0;
    for(int S=0;S<(1<<V);S++){
        for(int j=0;j<V;j++){
            if(dp[S][j]==INF) continue;
            for(int k=0;k<V;k++){
                if((S>>k)&1) continue;
                dp[S|(1<<k)][k]=min(dp[S|(1<<k)][k],dp[S][j]+dist[j][k]);
            }
        }
    }
    int ans=INF;
    ans=dp[(1<<V)-1][0];
    if(ans==INF) puts("-1");
    else cout << ans << endl;
    return 0;
}

### Prompt

Please provide a Cpp coded solution 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;
typedef long long LL;
typedef pair<LL,LL> P;
const LL mod=1e9+7;
const LL LINF=1LL<<62;
const int INF=1<<17;

int main(){
    int V,E;
    cin >> V >> E;
    int dist[V][V];
    int dp[1<<V][V];
    for(int i=0;i<(1<<V);i++){
        for(int j=0;j<V;j++){
            dp[i][j]=INF;
        }
    }
    for(int i=0;i<V;i++){
        for(int j=0;j<V;j++){
            dist[i][j]=INF;
        }
    }
    for(int i=0;i<E;i++){
        int s,t,d;
        cin >> s >> t >> d;
        dist[s][t]=d;
    }
    dp[0][0]=0;
    for(int S=0;S<(1<<V);S++){
        for(int j=0;j<V;j++){
            if(dp[S][j]==INF) continue;
            for(int k=0;k<V;k++){
                if((S>>k)&1) continue;
                dp[S|(1<<k)][k]=min(dp[S|(1<<k)][k],dp[S][j]+dist[j][k]);
            }
        }
    }
    int ans=INF;
    ans=dp[(1<<V)-1][0];
    if(ans==INF) puts("-1");
    else cout << ans << endl;
    return 0;
}

```