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=float("inf")
v,e=map(int,input().split())
STD=[list(map(int,input().split())) for _ in range(e)]

D=[[inf for _ in range(v)] for _ in range(v)]
for s,t,d in STD:
    D[s][t]=d

DP=[[-1 for _ in range(v)] for _ in range(1<<v)]


def bitDP(s,g,DP):
    if DP[s][g]>=0:return DP[s][g]
    if s==(1<<v)-1 and g==0:
        DP[s][g]=0
        return 0

    ans=inf
    for i in range(v):
        if (s>>i & 1)==0:
            ans=min(ans,bitDP(s|(1<<i),i,DP)+D[g][i])
    DP[s][g]=ans
    return ans


ans=bitDP(0,0,DP)
print(ans if ans!=inf else -1)
