#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> P;

int MOD=1e9+7;
ll INF=1e18;

int dx[]={1, -1, 0, 0};
int dy[]={0, 0, 1, -1};

int main(){
    int V, E; cin>>V>>E;
    ll dist[V][V];

    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;
    }

    ll dp[(1<<V)][V];
    for(int i=0; i<(1<<V); i++){
        for(int j=0; j<V; j++){
            dp[i][j]=INF;
        }
    }
    dp[0][0]=0;

    for(int S=1; S<(1<<V); S++){
        for(int v=0; v<V; v++){
            for(int j=0; j<V; j++){
                if((1<<v) & S){
                    dp[S][v]=min(dp[S][v], dp[S-(1<<v)][j]+dist[j][v]);
                }
            }
        }
    }
    if(dp[(1<<V)-1][0] == INF) cout << -1 << endl;
    else cout << dp[(1<<V)-1][0] << endl;
}

### 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<int, int> P;

int MOD=1e9+7;
ll INF=1e18;

int dx[]={1, -1, 0, 0};
int dy[]={0, 0, 1, -1};

int main(){
    int V, E; cin>>V>>E;
    ll dist[V][V];

    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;
    }

    ll dp[(1<<V)][V];
    for(int i=0; i<(1<<V); i++){
        for(int j=0; j<V; j++){
            dp[i][j]=INF;
        }
    }
    dp[0][0]=0;

    for(int S=1; S<(1<<V); S++){
        for(int v=0; v<V; v++){
            for(int j=0; j<V; j++){
                if((1<<v) & S){
                    dp[S][v]=min(dp[S][v], dp[S-(1<<v)][j]+dist[j][v]);
                }
            }
        }
    }
    if(dp[(1<<V)-1][0] == INF) cout << -1 << endl;
    else cout << dp[(1<<V)-1][0] << endl;
}

```