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())
L=[[]for i in range(N+1)]
for i in range(M):
    s,t,d=map(int,input().split())
    L[s].append([t,d])

D=[{}for i in range(N+1)]
D[0][(0,0)]=0
#print(D)


for i in range(1,N+1):
    for k,v in D[i-1].items():
        P,dist=k
        for to,d in L[P]:
            Ndist=dist|1<<to
            if Ndist!=dist:
                if (to,Ndist) not in D[i]:
                    D[i][(to,Ndist)]=v+d
                else:
                    D[i][(to,Ndist)]=min(v+d,D[i][(to,Ndist)])
#print(D)
if len(D[-1])==0:
    print(-1)
else:
    for k,v in D[-1].items():
        if k[0]==0:
            print(v)
            exit()
    print(-1)
