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():
    inf = 1000000000
    n,m = map(int,input().split())
    d = [[inf]*n for _ in range(n)]
    for _ in range(m):
        a,b,c = map(int,input().split())
        d[a][b] = c
    dp = [[inf]*n for _ in range(1<<n)]
    dp[0][0] = 0
    for bits in range(1<<n):
        for i in range(n):
            if bits&(1<<i):continue
            for j in range(n):
                dp[(1<<i)|bits][i] = min(dp[(1<<i)|bits][i],dp[bits][j]+d[i][j])
    if dp[(1<<n)-1][0]==inf:print (-1)
    else                   :print (dp[(1<<n)-1][0])


if __name__ == '__main__':
    main()


