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 = float('inf')
n, k = map(int, input().split())
G = [[] for _ in range(n)]
_G = []
for _ in range(k):
    ss, t, d = map(int, input().split())
    G[ss].append((t,d))
    if t == 0:_G.append((ss,d))
    
dp = [[INF]*n for _ in range(1<<n)]
dp[1][0] = 0

for s in range(1,(1<<n)):
    for v in range(n):
        if dp[s][v] == INF:continue
        for t, d in G[v]:
            if not(s & (1<<t)):
                next_s = s | (1<<t)
                dp[next_s][t] = min(dp[next_s][t],dp[s][v]+d)
                    
                    
ans = INF
for pre, d in _G:
    ans = min(ans, dp[-1][pre]+d)
print(ans if ans != INF else -1)
