p02323 Traveling Salesman Problem
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
```python
v,e=[int(j) for j in input().split()]
d=[[10**18]*v for i in range(v)]
dp=[[-1]*v for i in range(1<<v)]
for i in range(e):
    s,t,w=[int(j) for j in input().split()]
    d[s][t]=w


def f(s,n,dp):
    if dp[s][n]>=0:
        return dp[s][n]
    if s==(1<<v)-1 and n==0:
        dp[s][n]=0
        return 0
    tmp=10**18
    for u in range(v):
        if (s>>u&1)==0:
            tmp=min(tmp,f(s|(1<<u),u,dp)+d[n][u])
    dp[s][n]=tmp
    return tmp

ans=f(0,0,dp)
if ans==10**18:
    print(-1)
else:
    print(ans)


```