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
def dp(S, v):
    if memo[S][v] != -1:
        return memo[S][v]
    if not S&(1<<v):
        memo[S][v] = inf
        return inf
    res = inf
    for i in range(n):
        if S&(1<<i) and d[i][v] != inf and i != v:
            res = min(res, dp(S&(~(1<<v)), i)+d[i][v])
    memo[S][v] = res
    return res

n, m = map(int, input().split())
inf = 10**10
d = [[inf for i in range(n)] for j in range(n)]
for i in range(m):
    s, t, dis = map(int, input().split())
    d[s][t] = dis

memo = [[-1 for i in range(n)] for j in range(2**n)]
memo[1][0] = 0

ans = min([dp(2**n-1, v)+d[v][0] for v in range(n)])
print(-1 if ans>=inf else ans)
