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
INF = 10 ** 10
v, e = map(int, input().split())
adj = [[INF] * v for _ in range(v)]
for _ in range(e):
    s, t, d = map(int, input().split())
    adj[s][t] = d

mem = {}
end = 2 ** v - 1
def minCost(state, pos):
    if (state, pos) in mem:
        return mem[(state, pos)]

    if state == end:
        return adj[pos][0]

    mask = 1
    ret = INF
    for to in range(v):
        if mask & state:
            mask <<= 1
            continue

        ret = min(ret, adj[pos][to] + minCost(state | mask, to))
        mask <<= 1

    mem[(state, pos)] = ret
    return ret

result = minCost(1, 0)
if result >= INF:
    print(-1)
else:
    print(result)

