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 itertools
V, E = [int(_) for _ in input().split()]
STD = [[int(_) for _ in input().split()] for _ in range(E)]
G = [[float('inf')] * V for _ in range(V)]
for s, t, d in STD:
    G[s][t] = d
ans = float('inf')
dp = [[float('inf')] * V for _ in range(2**V)]
#for start in range(V):
for start in range(1):
    dp[(2**V - 1)][start] = 0
    for S in range(2**V - 1 - 2**start, -1, -1):
        for v in range(V):
            for u in range(V):
                if not (S >> u & 1):
                    dp[S][v] = min(dp[S][v], dp[S | 1 << u][u] + G[v][u])
    ans = min(ans, dp[0][start])
if ans == float('inf'):
    print(-1)
else:
    print(ans)
# http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_2_A&lang=jp

