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 collections import defaultdict

v, e = map(int, input().split())

links = [set() for _ in range(v)]
bests = [None] * (1 << v)

for _ in range(e):
    s, t, d = map(int, input().split())
    links[s].add((t, d))

bests[0] = {0: 0}

for visited, best in enumerate(bests):
    if best is None:
        continue
    for last, cost in best.items():
        for t, d in links[last]:
            new_visited = visited | (1 << t)
            if visited == new_visited:
                continue
            new_best = bests[new_visited]
            if new_best is None:
                bests[new_visited] = defaultdict(lambda: 15001, [(t, cost + d)])
            else:
                new_best[t] = min(new_best[t], cost + d)

result = bests[-1]
print(-1 if result is None else -1 if result[0] == 15001 else result[0])