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

constexpr int inf = 0x3f3f3f3f;
constexpr ll linf = 0x3f3f3f3f3f3f3f3fLL;

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int v, e; cin >> v >> e;
    vector<vector<int>> g(v, vector<int>(v, inf));
    for (int i = 0; i < e; i++) {
        int s, t, d; cin >> s >> t >> d;
        g[s][t] = d;
    }

    vector<vector<int>> dp(1 << v, vector<int>(v, inf));
    dp[0][0] = 0;
    for (int i = 0; i < (1 << v); i++) {
        for (int j = 0; j < v; j++) {
            if ((i >> j) & 1) continue;
            for (int k = 0; k < v; k++) {
                if (g[j][k] >= inf) continue;
                dp[i | (1 << j)][k] = min(dp[i | (1 << j)][k], dp[i][j] + g[j][k]);
            }
        }
    }
    cout << (dp[(1 << v) - 1][0] < inf ? dp[(1 << v) - 1][0] : -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 <bits/stdc++.h>
using namespace std;
using ll = long long;

constexpr int inf = 0x3f3f3f3f;
constexpr ll linf = 0x3f3f3f3f3f3f3f3fLL;

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int v, e; cin >> v >> e;
    vector<vector<int>> g(v, vector<int>(v, inf));
    for (int i = 0; i < e; i++) {
        int s, t, d; cin >> s >> t >> d;
        g[s][t] = d;
    }

    vector<vector<int>> dp(1 << v, vector<int>(v, inf));
    dp[0][0] = 0;
    for (int i = 0; i < (1 << v); i++) {
        for (int j = 0; j < v; j++) {
            if ((i >> j) & 1) continue;
            for (int k = 0; k < v; k++) {
                if (g[j][k] >= inf) continue;
                dp[i | (1 << j)][k] = min(dp[i | (1 << j)][k], dp[i][j] + g[j][k]);
            }
        }
    }
    cout << (dp[(1 << v) - 1][0] < inf ? dp[(1 << v) - 1][0] : -1) << endl;
    return 0;
}


```