#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;
const int INF = (int)1e9 + 7;

template<class T>
vector<vector<T>> TSP(const vector<vector<T>>& dist) {
    int n = dist.size();
    vector<vector<T>> dp(1 << n, vector<T>(n, INF));
    dp[0][0] = 0;
    for (int s = 0; s < 1 << n; s++) {
        for (int cur = 0; cur < n; cur++) {
            if (dp[s][cur] == INF) continue;
            for (int to = 0; to < n; to++) {
                if (s & (1 << to)) continue;
                if (dist[cur][to] < 0) continue;
                T& res = dp[s | 1 << to][to];
                res = min(res, dp[s][cur] + dist[cur][to]);
            }
        }
    }
    return dp;
}

int main() {
    int n, m; cin >> n >> m;
    vector<vector<int>> dist(n, vector<int>(n, -1));
    for (int i = 0; i < m; i++) {
        int s, t, d; cin >> s >> t >> d;
        dist[s][t] = d;
    }
    vector<vector<int>> dp = TSP(dist);
    int ans = dp[(1 << n) - 1][0];
    cout << (ans == INF ? -1 : ans) << endl;
    return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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 <vector>
using namespace std;
const int INF = (int)1e9 + 7;

template<class T>
vector<vector<T>> TSP(const vector<vector<T>>& dist) {
    int n = dist.size();
    vector<vector<T>> dp(1 << n, vector<T>(n, INF));
    dp[0][0] = 0;
    for (int s = 0; s < 1 << n; s++) {
        for (int cur = 0; cur < n; cur++) {
            if (dp[s][cur] == INF) continue;
            for (int to = 0; to < n; to++) {
                if (s & (1 << to)) continue;
                if (dist[cur][to] < 0) continue;
                T& res = dp[s | 1 << to][to];
                res = min(res, dp[s][cur] + dist[cur][to]);
            }
        }
    }
    return dp;
}

int main() {
    int n, m; cin >> n >> m;
    vector<vector<int>> dist(n, vector<int>(n, -1));
    for (int i = 0; i < m; i++) {
        int s, t, d; cin >> s >> t >> d;
        dist[s][t] = d;
    }
    vector<vector<int>> dp = TSP(dist);
    int ans = dp[(1 << n) - 1][0];
    cout << (ans == INF ? -1 : ans) << endl;
    return 0;
}

```