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
N, M = map(int, input().split())
INF = float('inf')
G = [[INF] * N for i in range(N)]
for i in range(M):
    s, t, d = map(int, input().split())
    G[s][t] = d


dp = [[INF] * N for i in range(1 << N)]
dp[1][0] = 0
for bs in range(1 << N):
    for n in range(N):
        if dp[bs][n] == INF:
            continue
        for to in range(N):
            if bs & (1 << to):
                continue
            next_index = bs | (1 << to)
            dp[next_index][to] = min(dp[next_index][to], dp[bs][n] + G[n][to])


ans = INF
for fr in range(1, N):
    ans = min(ans, dp[-1][fr] + G[fr][0])
print(ans if ans != INF else -1)

