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
import sys
from typing import List, Tuple


def rec(state: int, v: int, dp: List[List[int]],
        edges: List[List[Tuple[int, int]]]) -> int:
    if (dp[state][v] >= 0):
        return dp[state][v]
    if ((1 << V) - 1 == state and v == 0):
        # Reach all vertices and get back to the starting point.
        dp[state][0] = 0
        return 0

    ans = sys.maxsize
    for to, cost in edges[v]:
        if (not (state >> to & 1)):
            ans = min(ans, rec(state | 1 << to, to, dp, edges) + cost)
    dp[state][v] = ans
    return ans


if __name__ == "__main__":
    V, E = map(lambda x: int(x), input().split())
    edges: List[List[Tuple[int, int]]] = [[] for _ in range(V)]
    for _ in range(E):
        source, target, cost = map(lambda x: int(x), input().split())
        edges[source].append((target, cost))

    dp = [[-1] * V for _ in range(1 << V)]
    print(dp[0][0] if rec(0, 0, dp, edges) != sys.maxsize else -1)

