Given an asymmetric adjacency matrix, determine the number of unique directed cycles.

For example, the graph represented by adjacency matrix

A = [
  0 1 1 0;
  1 1 0 1;
  1 0 0 1;
  1 1 0 0];

has 7 cycles. They are:

[2 -> 2]
[1 -> 2 -> 1]
[1 -> 3 -> 1]
[2 -> 4 -> 2]
[1 -> 2 -> 4 -> 1]
[1 -> 3 -> 4 -> 1]
[1 -> 3 -> 4 -> 2 -> 1]

The input is an adjacency matrix of 0s and 1s, and the output should be the number of unique (simple) directed cycles in the graph.