#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

#define inf 1000000007
int dp[16][1<<16];

int main(){
    int n,m;
    cin >> n >> m;
    int dst[16][16]={};
    for(int i=0;i<16;i++){
        for(int j=0;j<16;j++){
            dst[i][j] = inf;
        }
    }
    for(int i=0;i<16;i++){
        for(int j=0;j<(1<<16);j++){
            dp[i][j] = inf;
        }
    }
    dp[0][0] = 0;
    for(int i=0;i<m;i++){
        int s,t,d;
        cin >> s >> t >> d;
        dst[s][t] = d;
    }
    for(int j=0;j<(1<<n);j++){
        for(int s=0;s<n;s++){
            for(int t=0;t<n;t++){
                if(s==t)continue;
                if((j&(1<<t))==0)dp[t][j+(1<<t)] = min(dp[t][j+(1<<t)],dp[s][j]+dst[s][t]);
            }
        }       
    }
    int ans = dp[0][(1<<n)-1];
    if(ans!=inf)cout << ans << endl;
    else cout << -1 << endl;
    return 0;
}

### Prompt

In cpp, your task is to solve 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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;

#define inf 1000000007
int dp[16][1<<16];

int main(){
    int n,m;
    cin >> n >> m;
    int dst[16][16]={};
    for(int i=0;i<16;i++){
        for(int j=0;j<16;j++){
            dst[i][j] = inf;
        }
    }
    for(int i=0;i<16;i++){
        for(int j=0;j<(1<<16);j++){
            dp[i][j] = inf;
        }
    }
    dp[0][0] = 0;
    for(int i=0;i<m;i++){
        int s,t,d;
        cin >> s >> t >> d;
        dst[s][t] = d;
    }
    for(int j=0;j<(1<<n);j++){
        for(int s=0;s<n;s++){
            for(int t=0;t<n;t++){
                if(s==t)continue;
                if((j&(1<<t))==0)dp[t][j+(1<<t)] = min(dp[t][j+(1<<t)],dp[s][j]+dst[s][t]);
            }
        }       
    }
    int ans = dp[0][(1<<n)-1];
    if(ans!=inf)cout << ans << endl;
    else cout << -1 << endl;
    return 0;
}

```