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
# http://www.geocities.jp/m_hiroi/light/pyalgo65.html

def memoize(f):
    table = {}
    def func(*args):
        if not args in table:
            table[args] = f(*args)
        return table[args]
    return func

@memoize
def tsp(p, v):
    if (1 << point_size) - 1 == v:
        return distance_table[p][0]
    else:
        return min(distance_table[p][x] + tsp(x, v | (1 << x)) for x in range(point_size) if not (v & (1 << x)))

from sys import stdin
from collections import defaultdict
from math import isinf

readline = stdin.readline

point_size, e = map(int, readline().split())
distance_table = [[float('inf')] * point_size for _ in range(point_size)]
for _ in range(e):
    s, t, d = map(int, readline().split())
    distance_table[s][t] = d
ans = tsp(0,1)
print(-1 if isinf(ans) else ans)