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

int d[15][15];
int dp[1<<15][15];

int main(){
    int N, M; cin >> N >> M;
    int INF=pow(10,9);
    for(int i=0; i<N; i++){
        for(int j=0; j<N; j++){
            d[i][j]=INF;
        }
    }
    for(int i=0; i<M; i++){
        int s, t, di;
        cin >> s >> t >> di;
        d[s][t]=di;
    }
    for(int i=0; i< 1<<15; i++){
        for(int j=0; j<15; j++){
            dp[i][j]=INF;
        }
    }
    dp[(1<<N)-1][0]=0;
    for(int S=(1<<N)-2; S>=0; S--){
        for(int v=0; v<N; v++){
//            if( ! (1<<v &S) ) continue;
            for(int u=0; u<N; u++){
                if(!(S>>u &1)){
                    dp[S][v]=min(dp[S][v], dp[S|1<<u][u]+d[v][u]);
                }
            }
        }
    }
    if(dp[0][0]<INF){
    cout << dp[0][0] << endl;
    }
    else cout << -1 << endl;
}

### 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;

int d[15][15];
int dp[1<<15][15];

int main(){
    int N, M; cin >> N >> M;
    int INF=pow(10,9);
    for(int i=0; i<N; i++){
        for(int j=0; j<N; j++){
            d[i][j]=INF;
        }
    }
    for(int i=0; i<M; i++){
        int s, t, di;
        cin >> s >> t >> di;
        d[s][t]=di;
    }
    for(int i=0; i< 1<<15; i++){
        for(int j=0; j<15; j++){
            dp[i][j]=INF;
        }
    }
    dp[(1<<N)-1][0]=0;
    for(int S=(1<<N)-2; S>=0; S--){
        for(int v=0; v<N; v++){
//            if( ! (1<<v &S) ) continue;
            for(int u=0; u<N; u++){
                if(!(S>>u &1)){
                    dp[S][v]=min(dp[S][v], dp[S|1<<u][u]+d[v][u]);
                }
            }
        }
    }
    if(dp[0][0]<INF){
    cout << dp[0][0] << endl;
    }
    else cout << -1 << endl;
}

```