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
#!/usr/bin/env python3
import sys
from collections import defaultdict

rl = sys.stdin.buffer.readline
INF = sys.maxsize

V, E = map(int, rl().split())
ES = [tuple(map(int, rl().split())) for i in range(E)]



# グラフを初期化する
G = defaultdict(lambda: defaultdict(lambda: INF))
for e in ES:
  G[e[0]][e[1]] = e[2]


dp = defaultdict(lambda: defaultdict(lambda: INF))
dp[0][0] = 0

for s in range(1 << V):
  for v in range(V):
    if s & (1 << v) == 0: # s に頂点v が含まれていないときを考える
      for u in range(V):
        dp[s | (1 << v)][v] = min(dp[s | (1 << v)][v], dp[s][u] + G[u][v])


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