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
N,e = map(int, input().split())
inf = float("inf")
adj = [[inf for _ in range(N)]  for _ in range(N)]
for _ in range(e):
    s,t,d = map(int, input().split())
    adj[s][t] = d

def memorize(f):
    cache = {}
    def func(*args):
        if args not in cache:
            cache[args] = f(*args)
        return cache[args]
    return func

@memorize
def tsp(v, b):
    if b == (1 << N) - 1:
        return adj[v][0]
    res = inf
    for w in range(N):
        if b & (1 << w): continue
        res = min(res, adj[v][w] + tsp(w, b | (1 << w)))
    return res

if tsp(0,1) == inf:
    print(-1)
else: print(tsp(0,1))