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
import sys
input = sys.stdin.readline
INF = float('inf')
N, M = map(int, input().split())
cost = [[INF]*N for _ in [0]*N]
to = [set() for _ in [0]*N]
for _ in [0]*M:
    a, b, c = map(int, input().split())
    cost[a][b] = c
    to[b].add(a)

K = 1 << N
dp = [[INF]*N for _ in range(K)]
dp[K-1][0] = 0

for bit in range(K-1, -1, -1):
    for i in range(N):
        tmp = [dp[bit|1<<j][j]+cost[j][i] for j in to[i] if bit>>j&1==0]
        if tmp:
            dist = min(tmp)
            if dp[bit][i] > dist:
                dp[bit][i] = dist

ans = dp[0][0]
print(ans if ans < INF else -1)

