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
#include <iostream>
#include <algorithm>
using namespace std;
#define INF 1000000

int main()
{
    int v, e, s, t, d;
    int G[15][15];
    cin >> v >> e;
    for (int i = 0; i < v; i++) {
        fill(G[i], G[i] + v, INF);
    }
    for (int i = 0; i < v; i++) {
        G[i][i] = 0;
    }
    for (int i = 0; i < e; i++) {
        cin >> s >> t >> d;
        G[s][t] = d;
    }
    int dp[1 << 15][15];
    for (int i = 0; i < 1 << 15; i++) {
        fill(dp[i], dp[i] + 15, INF);
    }
    dp[0][0] = 0;
    
    for (int S = 0; S < 1 << v; S++) {
        for (int i = 0; i < v; i++) {
            for (int u = 0; u < v; u++) {
                if (!((S >> u) & 1)) {
                    dp[S | (1 << u)][u] = min(dp[S | (1 << u)][u], dp[S][i] + G[i][u]);
                }
            }
        }
    }
    if (dp[(1 << v) - 1][0] == INF) {
        cout << -1 << endl;
    }
    else {
        cout << dp[(1 << v) - 1][0] << endl;
    }
    return 0;
}