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())

dp = [[float("inf")] * (v) for _ in range(1 << v)]
edges = [[float("inf")] * v for _ in range(v)]


for edge in range(e):
    frm, to, w = map(int, input().split())
    edges[frm][to] = w

dp[1][0] = 0

for i in range(1 << v):
    for j in range(v):
        if dp[i][j] == float("inf"):
            continue
        for k in range(v):
            if (i >> k) % 2 == 1:
                continue
            next_d = dp[i][j] + edges[j][k]
            next_i = i | (1 << k)

            dp[next_i][k] = min(dp[next_i][k], next_d)

all = (1 << v) - 1
ans = float("inf")

for i in range(1, v):
    ans = min(ans, dp[all][i] + edges[i][0])

if ans == float("inf"):
    print(-1)
else:
    print(ans)

