#include <iostream>
using namespace std;
#define MAX 15
#define INF 10000


int main()
{
    int v, e, s, t, p;
    int d[MAX][MAX];
    for (int i = 0; i < MAX; i++) {
        for (int j = 0; j < MAX; j++) {
            d[i][j] = INF;
        }
    }
    for (int i = 0; i < MAX; i++) {
        d[i][i] = 0;
    }
    cin >> v >> e;
    for (int i = 0; i < e; i++) {
        cin >> s >> t >> p;
        d[s][t] = p;
    }
    
    int dp[1<<MAX][MAX];
    for (s = 0; s < 1 << v; s++) {
        fill(dp[s], dp[s] + v, INF);
    }
    dp[(1 << v) - 1][0] = 0;
    for (int s = (1 << v) - 2; s >= 0; s--) {
        for (int i = 0; i < v; i++) {
            for (int j = 0; j < v; j++) {
                if (!(s >> j & 1)) {
                    dp[s][i] = min(dp[s][i], dp[s | 1 << j][j] + d[i][j]);
                }
            }
        }
    }
    if (dp[0][0] == INF) {
        cout << -1 << endl;
    }else{
        cout << dp[0][0] << endl;
    }
    
    

    return 0;
}
### Prompt

Please formulate a CPP solution 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 <iostream>
using namespace std;
#define MAX 15
#define INF 10000


int main()
{
    int v, e, s, t, p;
    int d[MAX][MAX];
    for (int i = 0; i < MAX; i++) {
        for (int j = 0; j < MAX; j++) {
            d[i][j] = INF;
        }
    }
    for (int i = 0; i < MAX; i++) {
        d[i][i] = 0;
    }
    cin >> v >> e;
    for (int i = 0; i < e; i++) {
        cin >> s >> t >> p;
        d[s][t] = p;
    }
    
    int dp[1<<MAX][MAX];
    for (s = 0; s < 1 << v; s++) {
        fill(dp[s], dp[s] + v, INF);
    }
    dp[(1 << v) - 1][0] = 0;
    for (int s = (1 << v) - 2; s >= 0; s--) {
        for (int i = 0; i < v; i++) {
            for (int j = 0; j < v; j++) {
                if (!(s >> j & 1)) {
                    dp[s][i] = min(dp[s][i], dp[s | 1 << j][j] + d[i][j]);
                }
            }
        }
    }
    if (dp[0][0] == INF) {
        cout << -1 << endl;
    }else{
        cout << dp[0][0] << endl;
    }
    
    

    return 0;
}
```