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
# -*- coding: utf-8 -*-
"""
Permutation/Path - Traveling Salesman Problem
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_2_A&lang=jp

"""


V, E = map(int, input().split())

d = [[float('inf')]*V for _ in range(V)]
for _ in range(E):
    f, t, dist = map(int, input().split())
    d[f][t] = dist
dp = [[-1]*V for _ in range(2**V)]


def solve(S, v):
    if dp[S][v] >= 0:
        return dp[S][v]
    if (S == 2**V-1) and (v == 0):
        dp[S][v] = 0
        return 0
    res = float('inf')
    for u in range(V):
        if not ((S >> u) & 1):
            res = min(res, solve(S | (1 << u), u) + d[v][u])
    dp[S][v] = res
    return res

ans = solve(0, 0)
if ans == float('inf'):
    print(-1)
else:
    print(ans)
