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 functools


@functools.lru_cache(maxsize=None)
def rec(state, v):
    if state == (1 << V) - 1 and v == 0:
        return 0
    ret = INF
    for c, w in edge[v]:
        if not (state >> c & 1):
            ret = min(ret, rec(state | 1 << c, c) + w)
    return ret

INF = 10**6
V, E = map(int, input().split())
edge = [[] for _ in range(V)]
for _ in range(E):
    s, t, w = map(int, input().split())
    edge[s].append((t, w))
ans = rec(0, 0)
print(ans if ans != INF else -1)