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
import sys

def rec(p, V, bit, dist, matrix):
  if 2 ** V - 1 == bit and p == 0:
    return dist

  mindist = sys.maxint
  for i in range(V):
    if bit & 2 ** i == 0 and matrix[p][i] != sys.maxint:
      mindist = min(mindist, rec(i, V, bit | 2 ** i, dist + matrix[p][i], matrix))
  return mindist

ipt = raw_input().split()
V = int(ipt[0])
E = int(ipt[1])
s = {}
t = {}
d = {}
matrix = [[sys.maxint for i in range(V)] for j in range(V)]

for i in range(E):
  ipt = raw_input().split()
  matrix[int(ipt[0])][int(ipt[1])] = int(ipt[2])

ans = rec(0, V, 0, 0, matrix)
if ans == sys.maxint:
  print "-1"
else:
  print ans