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