Traveling Salesman Problem

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

inputFormat

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).

outputFormat

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

样例

3 3
0 1 1
1 2 1
0 2 1

-1