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

int n;
long long int d[16][16];

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

const long long int INF = 10000000000;

long long int rec(int s,int v){

    if(dp[s][v] >= 0){
        return dp[s][v];
    }

    if(s == (1 << n) -1 && v == 0){
        return dp[s][v] = 0;
    }

    long long int res = INF;

    for(int u=0; u<n; u++){
        if(!(s >> u & 1)){
            //?¬????u????§??????????
            res = min(res, rec(s | 1 << u ,u) + d[v][u]);
        }
    }

    return dp[s][v] = res;

}

int main() {

    int e;

    cin >> n >> e;

    int s,t,dd;

    for(int i=0;i<=15;i++){
        for(int j=0;j<=15;j++){
            d[i][j] = INF;
        }
    }

    for(int i=0; i<e; i++){
        scanf(" %d %d %d",&s,&t,&dd);
        d[s][t] = dd;
    }

    for(int i=0;i < (1<<15) ; i++){
        for(int j=0;j<15;j++){
            dp[i][j] = -1;
        }
    }

    long long int ans = rec(0,0);

    if(ans==INF){
        ans = -1;
    }

    cout << ans << endl;

    return 0;
}
### Prompt

Please create a solution in Cpp to 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 <bits/stdc++.h>
using namespace std;

int n;
long long int d[16][16];

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

const long long int INF = 10000000000;

long long int rec(int s,int v){

    if(dp[s][v] >= 0){
        return dp[s][v];
    }

    if(s == (1 << n) -1 && v == 0){
        return dp[s][v] = 0;
    }

    long long int res = INF;

    for(int u=0; u<n; u++){
        if(!(s >> u & 1)){
            //?¬????u????§??????????
            res = min(res, rec(s | 1 << u ,u) + d[v][u]);
        }
    }

    return dp[s][v] = res;

}

int main() {

    int e;

    cin >> n >> e;

    int s,t,dd;

    for(int i=0;i<=15;i++){
        for(int j=0;j<=15;j++){
            d[i][j] = INF;
        }
    }

    for(int i=0; i<e; i++){
        scanf(" %d %d %d",&s,&t,&dd);
        d[s][t] = dd;
    }

    for(int i=0;i < (1<<15) ; i++){
        for(int j=0;j<15;j++){
            dp[i][j] = -1;
        }
    }

    long long int ans = rec(0,0);

    if(ans==INF){
        ans = -1;
    }

    cout << ans << endl;

    return 0;
}
```