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
import sys
read = sys.stdin.read
readline = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 8)
INF = float('inf')
MOD = 10 ** 9 + 7


def main():
    V, E = map(int, readline().split())
    dist = [[INF] * V for _ in range(V)]
    for i in range(E):
        u, v, cost = map(int, readline().split())
        dist[u][v] = cost
    dp = [[-1] * V for _ in range(1<<V)]

    def rec(s, v, dp):
        if dp[s][v] >= 0:
            return dp[s][v]

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

        res = INF
        for u in range(V):
            if ((s >> u) & 1) == 0:
                res = min(res, rec(s | (1 << u), u, dp) + dist[v][u])
        dp[s][v] = res
        return res

    ans = rec(0, 0, dp)
    if ans==INF:
        print(-1)
    else:
        print(ans)
if __name__ == '__main__':
    main()


