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
V,E=map(int,input().split())
d=[[float('inf')]*V for _ in range(V)]
for i in range(E):
    com=list(map(int,input().split()))
    d[com[0]][com[1]]=com[2]
for i in range(V):
    d[i][i]=0
S=pow(2,V-1)
dp=[[0]+[float('inf')]*(S-1) for _ in range(V)]
for i in range(1,V):
    dp[i][1<<(i-1)]=d[0][i]
for i in range(1,S):
    for v in range(1,V):
        if i>>(v-1) & 1:
            #print(i,v)
            #print(*dp,sep='\n')
            dp[v][i]=min([float('inf')]+[dp[v][i]]+[dp[u][i-(1<<(v-1))]+d[u][v] for u in range(1,V) if i>>(u-1) & 1 and u!=v])
ans=min([dp[i][S-1]+d[i][0] for i in range(V)])
if ans==float('inf'):
    print(-1)
else:
    print(ans)
