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
ii = lambda : int(input())
mi = lambda : map(int,input().split())
li = lambda : list(map(int,input().split()))


v,e = mi()
sb = [[]for i in range(e)]
ub = [[]for i in range(e)]
w = [[float('inf')] * v for i in range(v)]
dp = [[-1] * v for i in range(2**v +1) ] 


for i in range(e):
    s,t,d = mi()
    sb[s].append(t)
    w[s][t] = d

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

    res = float('inf')
    for i in sb[p]:
        if (s >> i&1) == 0:
            a = rec(s|(1<<i), i,dp) + w[p][i]
            res = min(res, a)
    
    dp[s][p] = res
    return res

if v >= 3 and e >= 3:
    ans = rec(0,0,dp)
else:
    ans = -1

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