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())
dist = [[float('inf')]*V for _ in range(V)]
for _ in range(E):
  s,t,d = map(int,input().split())
  s -= 1
  t -= 1
  dist[s][t] = d

# dp[mask][destination]
dp = [ [-1]*V for _ in range(1<<V) ]
VISITED_ALL = (1<<V)-1

def tsp(mask, pos):
  if mask == VISITED_ALL:
    return dist[pos][0]

  if dp[mask][pos] != -1:
    return dp[mask][pos]

  ans = float('inf')
  for city in range(V):
    if (1<<city)&mask == 0:
      newAns = dist[pos][city] + tsp(mask | (1<<city), city)
      ans = min(ans, newAns)

  dp[mask][pos] = ans
  return ans

res = tsp(1,0)
if res == float('inf'):
  print(-1)
else:
  print(res)

