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,raw_input().split())
dist=[[float("inf")]*v for _ in xrange(v)]
for i in xrange(e):
    s,t,d=map(int,raw_input().split())
    dist[s][t]=d

dp=[[float('inf')]*(v) for _ in xrange(1<<v)]
dp[1][0]=0
for i in xrange(1<<v):
    for j in xrange(v):
        if dp[i][j]==float('inf'):continue
        for k in xrange(v):
            if not (i>>k)&1:
                nexti=i|1<<k
                nextdist=dp[i][j]+dist[j][k]
                dp[nexti][k]=min(dp[nexti][k],nextdist)

ans=float('inf')
for i in xrange(v):
    if dp[(1<<v)-1][i]==float('inf'):continue
    ans=min(ans,dp[(1<<v)-1][i]+dist[i][0])
if ans==float('inf'):
    print(-1)
else:
    print(ans)