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())
G = [[float('inf')]*v for _ in range(v)]
for _ in range(e):
    s, t, d = map(int, input().split())            
    G[s][t] = d
dist = [[float("inf")]*v for _ in range(1<<v)]
dist[1][0] = 0
for s in range(1<<v):
    for i in range(v):
        for j in range(v):
            # print(bin(s), dist[(1<<i)|s][i], dist[s][j], i, j, G[j][i])
            if (s>>i)&1 == 1:continue
            if (s>>j)&1 == 0:continue
            dist[(1<<i|s)][i] = min(dist[1<<i|s][i], dist[s][j] + G[j][i])

ans = float('inf')
for i in range(v):
    ans = min(ans, dist[(1<<v)-1][i] + G[i][0])
print(ans if ans != float('inf') else -1)

