#include <algorithm>
#include <iostream>
#include <utility>
#include <vector>

using namespace std;
typedef long long ll;

ll dp[(1 << 16) + 1][20];
ll G[20][20];
int main() {
    int n, m, i, j, k;
    cin >> n >> m;
    for(i = 0; i <= n; i++) {
        for(j = 0; j <= n; j++) {
            G[i][j] = 1e9;
        }
    }
    for(i = 0; i < m; i++) {
        int s, t, d;
        cin >> s >> t >> d;
        G[s][t] = d;
    }

    for(i = 0; i < 1 << n; i++) {
        for(j = 0; j < n; j++) {
            dp[i][j] = 1e9;
        }
    }
    dp[1][0] = 0; //始点は0に固定
    for(i = 0; i < 1 << n; i++) {
        for(j = 0; j < n; j++) {
            if(i >> j & 1) {
                for(k = 0; k < n; k++) {
                    if(j != k && (i >> k & 1)) dp[i][j] = min(dp[i][j], dp[i ^ (1 << j)][k] + G[k][j]);
                }
            }
        }
    }
    ll ret = 1e9;
    for(i = 0; i < n; i++) {
        ret = min(dp[(1 << n) - 1][i] + G[i][0], ret);
    }
    cout << (ret != 1e9 ? ret : -1) << 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 <algorithm>
#include <iostream>
#include <utility>
#include <vector>

using namespace std;
typedef long long ll;

ll dp[(1 << 16) + 1][20];
ll G[20][20];
int main() {
    int n, m, i, j, k;
    cin >> n >> m;
    for(i = 0; i <= n; i++) {
        for(j = 0; j <= n; j++) {
            G[i][j] = 1e9;
        }
    }
    for(i = 0; i < m; i++) {
        int s, t, d;
        cin >> s >> t >> d;
        G[s][t] = d;
    }

    for(i = 0; i < 1 << n; i++) {
        for(j = 0; j < n; j++) {
            dp[i][j] = 1e9;
        }
    }
    dp[1][0] = 0; //始点は0に固定
    for(i = 0; i < 1 << n; i++) {
        for(j = 0; j < n; j++) {
            if(i >> j & 1) {
                for(k = 0; k < n; k++) {
                    if(j != k && (i >> k & 1)) dp[i][j] = min(dp[i][j], dp[i ^ (1 << j)][k] + G[k][j]);
                }
            }
        }
    }
    ll ret = 1e9;
    for(i = 0; i < n; i++) {
        ret = min(dp[(1 << n) - 1][i] + G[i][0], ret);
    }
    cout << (ret != 1e9 ? ret : -1) << endl;
    return 0;
}

```