A square piece of paper with integer dimensions NN is placed with a corner at the origin and two of its sides along the x- and y-axes. Then, we cut it up respecting the following rules:
Counting any reflections or rotations as distinct, we call C(N) the number of ways to cut an NN square. For example, C(1) = 2 and C(2) = 30 (shown below).
What is C(30) mod 108 ?