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())
inf = float('inf')
graphs = [[inf for _ in range(V)] for _ in range(V)]


for i in range(E):
    s, t, d = map(int, input().split())
    graphs[s][t] = d
# print(graphs)


dps = [[inf for _ in range(V)] for _ in range(1 << V)]

dps[0][0] = 0

for S in range(1, 1 << V):
    for i in range(V):
        # 両方とも1のやつのみ残る。
        # 1100 と0100(1<<2)だったら0100になる。
        # 訪問済みであることがこれで確認できる。
        if S & (1 << i) == 0:
            continue
        prev_bit = S - (1 << i)
        for j in range(V):
            # print(S, prev_bit, i, j)
            dps[S][i] = min(dps[S][i], dps[prev_bit][j] + graphs[j][i])
# print(dps)
if dps[(1 << V) - 1][0] == inf:
    print(-1)
else:
    print(dps[(1 << V) - 1][0])

