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
V, E = map(int, input().split())
graph = [[] for _ in range(V)]

for _ in range(E):
    s, t, d = map(int, input().split())
    graph[s].append((t, d))

case = 2**V
INF = 10**7

dp = [[-1]*case for _ in range(V)]

def dfs(now, dist, checked):
    if checked==(1<<V)-1:
        if now==s:
            return dist
        else:
            return INF
    r = dp[now][checked]
    if r!=-1:
        return r+dist
    ret = INF
    try:
        for q, d in graph[now]:
            if not (checked>>q)&1 and dist+d<ans:
                ret = min(ret, dfs(q, dist+d, checked|(1<<q)))
    except:
        return ret
    dp[now][checked] = ret - dist
    return ret

ans = INF
# for i in range(V):
s = 0
ans = min(ans, dfs(0, 0, 0))

if ans<=10**6:
    print(ans)
else:
    print(-1)
