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
n,m=map(int,input().split())
dist=[[INF for _ in range(n)]for _ in range(n)]
dp=[[INF for _ in range(n+1)]for _ in  range(1<<n)]
for _ in range(m):
  a,b,c=map(int,input().split())
  dist[a][b]=c
dp[(1<<n)-1][0]=0
for bit in range((1<<n)-2,-1,-1):
  for v in range(n):
    for u in range(n):
      if not ((bit>>u) & 1):
        dp[bit][v]=min(dp[bit][v],dp[bit|1<<u][u]+dist[u][v])
print(dp[0][0] if dp[0][0]!=INF else -1)
