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 read_list(t): return [t(x) for x in input().split()]
def read_line(t): return t(input())
def read_lines(t, N): return [t(input()) for _ in range(N)]

def rec(state, v):
    if dp[state][v] >= 0:
        return dp[state][v]
    if (1 << V) - 1 == state and v == 0:
        dp[state][0] = 0
        return 0

    ret = INF
    for to, cost in edge[v]:
        if not (state >> to & 1):
            ret = min(ret, rec(state | 1 << to, to) + cost)
    dp[state][v] = ret
    return ret

INF = 1<<27
V, E = read_list(int)
edge = [[] for _ in range(V)]
for _ in range(E):
    fr, to, cost = map(int, input().split())
    edge[fr].append((to, cost))

dp = [[-1] * V for _ in range(1<<V)]
print(dp[0][0] if rec(0, 0) != INF else -1)