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
SENTINEL = 15001
v, e = map(int, input().split())

links = [set() for _ in range(v)]
bests = [[SENTINEL] * v for _ in range(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):
    for last, cost in enumerate(best):
        for t, d in links[last]:
            bit = 1 << t
            if visited & bit:
                continue
            new_best = bests[visited | bit]
            new_best[t] = min(new_best[t], cost + d)

print(-1 if bests[-1][0] == 15001 else bests[-1][0])