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())

dis = [[float("inf")] * V for _ in range(V)]
for i in range(E):
	s, t, d = map(int, input().split())
	dis[s][t] = d

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

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

	if s == (1<<V) -1 and v == 0:
		dp[s][v] = 0
		return 0
	
	res = float("inf")
	for u in range(V):
		if not s >> u&1:
			res = min(res, rec(s|(1<<u), u)+dis[v][u])
	
	dp[s][v] = res
	return res

res = rec(0, 0)
if res == float("inf"):
	print(-1)
else:
	print(res)

