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
from sys import stdin
from sys import setrecursionlimit
setrecursionlimit(10**9)

readline=stdin.readline
n,w=map(int,readline().split())
INF=10**9
G=[[INF]*n for _ in range(n)]

for _ in range(w):
    s,t,d=map(int,readline().split())
    G[s][t]=d

dp=[[-1]*n for _ in range(1<<n)]

def func(s,v):
    if dp[s][v]>=0: return dp[s][v]

    if (s==(1<<n)-1) and v==0:
        dp[s][v]=0
        return dp[s][v]

    tmp=INF
    for u in range(n):
        t=(1<<u)|s
        if t==s: continue
        tmp=min(tmp,func(t,u)+G[v][u])
    dp[s][v]=tmp
    return dp[s][v]

ans=func(0,0)
print(ans if ans<INF else -1)
