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
dp = []
dist = []
INF = 1000000000

def tsp(s, v, dp, n):
    if dp[s][v] >= 0:
        return dp[s][v]
    if s == (1<<n)-1 and v == 0:
        dp[s][v] = 0
        return 0
    res = INF
    for u in range(n):
        if (s >> u & 1) == 0:
            res = min(res, tsp(s | (1 << u), u, dp, n) + dist[v][u])
    dp[s][v] = res
    return res
    
line = input()
v, e = list(map(int, line.split()))
dp = [ [-1] * v for _ in range(0, 1 << v)]
dist = [ [INF] * v for _ in range(0, v)]
for _ in range(0, e):
    line = input()
    s, t, d = list(map(int, line.split()))
    dist[s][t] = d
ans = tsp(0, 0, dp, v)
print(ans if ans < INF else -1)
