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
num_V, num_E = map(int, input().split())
inf = float('inf')

d = [[inf] * num_V for _ in range(num_V)]

for _ in range(num_E):
	ts,tt,td = map(int, input().split())
	d[ts][tt] = td

dp = [[-1] * num_V for _ in range(1 << num_V)]

def solve(s,v,dp):
	if dp[s][v] >= 0:
		return dp[s][v]

	if s == ((1 << num_V) - 1) and v == 0:
		return 0

	tmp = inf
	for u in range(num_V):
		if s >> u & 1 == 0:
			tmp = min(tmp, solve(s|1 << u, u, dp) + d[v][u])

	dp[s][v] = tmp
	return dp[s][v]

ans = solve(0,0,dp)
if ans == inf:
	print(-1)
else:
	print(ans)
