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
from sys import stdin
from math import isinf

readline = stdin.readline


min_cost = float('inf')


def main():
    v, e = map(int, readline().split())
    g = [[float('inf')] * v for _ in range(v)]
    for _ in range(e):
        s, t, d = map(int, readline().split())
        g[s][t] = d
    dfs(g, 0, 0, set(range(1, v)))
    global min_cost
    print(-1 if isinf(min_cost) else min_cost)


def dfs(g, cost, last, vs):
    global min_cost
    if min_cost < cost:
        return
    if vs:
        for v in vs:
            if isinf(g[last][v]):
                continue
            dfs(g, cost + g[last][v], v, vs - {v})
    elif min_cost > cost + g[last][0]:
        min_cost = cost + g[last][0]

main()