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

sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7


def resolve():
    n, m = map(int, input().split())

    graph = [[f_inf] * n for _ in range(n)]
    for i in range(n):
        graph[i][i] = 0

    for _ in range(m):
        s, t, d = map(int, input().split())
        graph[s][t] = d

    dp = [[f_inf] * n for _ in range(1 << n)]
    dp[0][0] = 0

    for S in range(1 << n):
        for v in range(n):
            for u in range(n):
                if ((1 << v) & S) == 0:
                    if v != u:
                        idx = S | (1 << v)
                        dp[idx][v] = min(dp[idx][v], dp[S][u] + graph[u][v])

    print(dp[-1][0] if dp[-1][0] != f_inf else -1)


if __name__ == '__main__':
    resolve()

