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
#!python3

iim = lambda: map(int, input().rstrip().split())

from heapq import heappush, heappop

def resolve():
    V, E = iim()
    inf = float("inf")
    ad = [[inf]*V for i in range(V)]

    for i in range(E):
        s, t, d = iim()
        ad[s][t] = d

    bi = [1<<i for i in range(V)]
    goal = (1<<V) - 1

    dp = dict()
    q = []
    heappush(q, (0, 0, 1))
    ans = inf
    while q:
        cost, v, state = heappop(q)

        vs = (v, state)
        if vs in dp:
            if dp[vs] <= cost:
                continue
        dp[vs] = cost

        if state == goal:
            cost += ad[v][0]
            if cost < ans:
                ans = cost
            continue

        for i in range(V):
            if bi[i] & state:
                continue
            heappush(q, (cost + ad[v][i], i, state | bi[i]))
    print(ans if ans != inf else -1)
    #print(dp[(0, goal)])

if __name__ == "__main__":
    resolve()

