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
# Acceptance of input
import sys

file_input = sys.stdin

V, E = map(int, file_input.readline().split())

D = [[] for i in range(V)]

for line in file_input:
    s, t, d = map(int, line.split())
    D[s].append((t, d))

max_d = 15001

# Full search with bit mask
def tsp(v, b):
    if b == (1 << V) - 1:
        if D[v]:
            t, d = min(D[v])
            if t == 0:
                return d
            else:
                return max_d
        else:
            return max_d
    res = max_d
    for t, d in D[v]:
        if b & (1 << t):
            continue
        res = min(res, d + tsp(t, b | (1 << t)))
    return res

# Output
ans = tsp(0, 1)

if ans == max_d:
    print(-1)
else:
    print(ans)