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
# 49

v, e = map(int, input().split())
n_l = [[float("Inf")] * v for y in range(v)]
for i in range(e):
    _s, _t, _d = map(int, input().split())
    n_l[_s][_t] = _d

ans = float("Inf")
dp = [[float("Inf")] * v for y in range(2**v)]
dp[1][0] = 0
for s in range(2**v):
    for i in range(v):
        if not((s>>i) & 1):
            continue
        _s = s & ~(1<<i)
        for j in range(v):
            if (_s>>j) & 1:
                dp[s][i] = min(dp[s][i], dp[_s][j] + n_l[j][i])

for i in range(v):
    ans = min(ans, dp[2**v-1][i] + n_l[i][0])
                
if ans != float("Inf"):
    print(ans)
else:
    print("-1")
                    
            

