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
def traveling_salesman(n,edge,INF=10**18):
    dist = [[INF for j in range(n)] for i in range(n)]
    for s,t,d in edge:
        dist[s][t] = d
    dp = [[INF for j in range(n)] for i in range(2**n)]
    dp[2**n-1][0] = 0
    for i in range(2**n-1)[::-1]:
        for j in range(n):
            for k in range(n):
                if not (i>>k & 1):
                    dp[i][j] = min(dp[i][j],dp[i|1<<k][k]+dist[j][k])
    return dp[0][0] if dp[0][0]!=INF else -1

V,E = map(int,input().split())
edge = [tuple(map(int,input().split())) for _ in range(E)]

print(traveling_salesman(V,edge))
