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 rec(visited,curpos):
    if (dp[visited][curpos] >= 0): return dp[visited][curpos]

    if (curpos == 0) & (visited == ((1 << v) - 1)) : 
        dp[visited][curpos] = 0
        return 0
    ret = float('inf')
    for i in range(v):
        if not ((visited >> i) & 1):
            ret = min(ret , rec((visited | 1 << i) , i ) + dis[curpos][i])
    dp[visited][curpos] = ret
    return ret

v,e = map(int, input().split())
dis = [[float('inf') for i in range(v)] for j in range(v)]
dp = [[-1 for j in range(v)] for k in range(1 << v)]

for i in range(e):
    s,t,d = map(int, input().split())
    dis[s][t] = d

ans = float('inf')
rec(0,0)
ans = min(ans , dp[0][0])

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