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**18
V,E=map(int,input().split())
G=[[INF]*V for i in range(V)]
for i in range(E):
    s,t,d=map(int,input().split())
    G[s][t]=d
ans=INF
dp=[[INF]*V for i in range(1<<V)]
dp[0][0]=0
    
for S in range(1<<V):
    for v in range(V):
        if S&(1<<v):
            for j in range(V):
                dp[S][v]=min(dp[S][v],dp[S-(1<<v)][j]+G[j][v])
print(dp[(1<<V)-1][0] if dp[(1<<V)-1][0]!=INF else -1)
