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
INF = 10**10
v, e = map(int, input().split())
dis = [[INF]*v for _ in range(v)]

for i in range(e):
    frm, to, d = map(int, input().split())
    dis[frm][to] = d
  
mem = {}
end = 2**v-1

def minCost(state, pos):
    if state==end:
        return dis[pos][0]
    
    if (state,pos) in mem:
        return mem[(state, pos)]
    
    nxt = 1
    ret = INF
    
    for to in range(v):
        if 1<<to & state:
            continue
        
        ret = min(ret, minCost(state|1<<to, to) + dis[pos][to])
        
    mem[(state, pos)] = ret
    
    return ret

ans = minCost(1, 0)

if ans>=INF:
    print(-1)
else:
    print(ans)
