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**6
N, M = map(int, input().split())

edge = [[inf] * N for _ in range(N)]
for _ in range(M):
    s, t, c = map(int, input().split())
    edge[s][t] = c
for i in range(N):
    edge[i][i] = 0


# 0からスタートするよ
dp = [[inf] * (1 << N) for _ in range(N)]
dp[0][0] = 0

for bit in range(1 << N):
    for t in range(N):
        if bit & (1 << t):
            continue
        bit_next = bit | (1 << t)
        for s in range(N):
            dp[t][bit_next] = min(dp[t][bit_next], dp[s][bit] + edge[s][t])


if dp[0][(1 << N)-1] >= inf:
    print(-1)
else:
    print(dp[0][(1 << N) - 1])
