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 dfs(g, last, vs, first):
    if vs:return min(g[last][v] + dfs(g, v, vs - {v}, first) for v in vs)
    else:return g[last][first]

from sys import stdin
from collections import defaultdict
from math import isinf

readline = stdin.readline

v, e = map(int, readline().split())
g = [[float('inf')] * v for _ in range(v)]
for _ in range(e):
    s, t, d = map(int, readline().split())
    g[s][t] = d

cost = []
vs = set(range(v))

first = 0
for second in range(1, v):
    if isinf(g[first][second]):continue
    cost.append(g[first][second] + dfs(g, second, vs - {first,second}, first))
        
print(min(cost) if cost else -1)