Given a graph as an adjacency matrix, calculate the total number of distinct simple cycles.
Remember that ~A \to B \to C \to A~ is not the same as ~A \to C \to B \to A~, and that ~A \to B \to A~ is the same as ~B \to A \to B~.

Input Specification

~N \le 10~, the number of vertices.
The adjacency matrix - ~N~ rows of ~N~ numbers.
The first row represents the first vertex, and similarly the last row represents the last vertex.

Output Specification

The number of distinct simple cycles of any length.

Sample Input

3
0 1 0
0 0 1
1 0 0

Sample Output

1