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())

#distance_list[j][i] = 頂点j→iの距離（有向）
distance_list = [[float('inf') for i in range(V)] for j in range(V)]
for i in range(V):
    distance_list[i][i] = 0
for node in range(E):
    start, goal, distance = map(int, input().split())
    distance_list[start][goal] = distance

dp = [[-1 for v in range(V)] for S in range(1 << V)]
def TSP(S, v):
    if dp[S][v] >= 0:
        return dp[S][v]
    else:
        if S == (1 << V) - 1 and v == 0:
            dp[S][v] = 0
            return 0
        else:
            ans = float('inf')
            for u in range(V):
                if (S >> u) & 1 == 0:
                    ans = min(ans, TSP(S | (1 << u), u) + distance_list[v][u])
            dp[S][v] = ans
            return ans
if TSP(0,0) == float('inf'):
    print(-1)
else:
    print(TSP(0,0))

