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 main():
    n,m=map(int,input().split())
    inf=10**6
    edges=[[inf]*n for i in range(n)]

    for i in range(m):
        a,b,c=map(int,input().split())
        a-=1
        b-=1
        edges[a][b]=c
    
    
    dp=[[inf]*n for i in range(1<<n)]
    dp[0][0]=0

    for s in range(1<<n):
        for v in range(n):
            for j in range(n):
                if (s>>j)&1 and v!=j and edges[j][v]<10**5:
                    dp[s][v]=min(dp[s][v],dp[s^(1<<j)][j]+edges[j][v])
                    
    if dp[-1][0]>10**5:
        print(-1)
    else:
        print(dp[-1][0])
    
if __name__=='__main__':
    main()
