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
def solve():
  ans = 0
  V, E = map(int, input().split())
  edge = [[] for _ in range(V)]
  for i in range(E):
    s,t,d = map(int, input().split())
    edge[s].append([t,d])
  dp = [[float('inf')]*V for _ in range(1<<V)]
  for v,d in edge[0]:
    dp[1<<v][v] = min(dp[1<<v][v],d)
  for S in range(2,1<<V,2):
    for u in range(V):
      if (S>>u)&1:
        for v,d in edge[u]:
          if not (S>>v)&1:
            dp[S+(1<<v)][v] = min(dp[S+(1<<v)][v],dp[S][u]+d)
  return dp[-1][0] if dp[-1][0]<float('inf') else -1
print(solve())
