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
# https://onlinejudge.u-aizu.ac.jp/problems/DPL_2_A


INF = float('inf')


def rec(bit, v):
    if dp[bit][v] != -1:
        return dp[bit][v]

    if (1 << V) - 1 == bit and v == 0:
        dp[bit][0] = 0
        return 0

    res = INF
    if v in D:
        for to, dist in D[v].items():
            if not (bit & (1 << to)):
                res = min(res, rec(bit | (1 << to), to) + dist)

    dp[bit][v] = res
    return res


if __name__ == "__main__":
    D = {}
    V, E = list(map(int, input().split()))
    for _ in range(E):
        s, t, d = list(map(int, input().split()))
        if s not in D:
            D[s] = {}
        D[s][t] = d

    dp = [[-1] * (V) for _ in range(1 << V)]

    print(dp[0][0] if rec(0, 0) != INF else -1)

