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
INF = 10 **9 
v , e = map(int,input().split())
route = [[] for i in range(v)]
for i in range(e):
    s , t , d = map(int,input().split())
    route[s].append((t,d))

dp = [[INF for i in range(v)] for j in range(2**v)]

dp[0][0] = 0

for i in range(2**v):
    for j in range(v):
        for k , d in route[j]:
            if (i>>k) & 1 == 1:
                continue
            dp[i | (1<<k)][k] = min(dp[i | (1<<k)][k],dp[i][j] + d) 

print(dp[-1][0] if dp[-1][0] != INF else -1)
