GAUSS8 2021 Problem 25

Square P Q R S has sides of length 8 . It is split into four rectangular regions by two line segments, one parallel to P Q and another parallel to Q R. There are N ways in which these lines can be drawn so that the area of each of the four rectangular regions is a positive integer. What is the remainder when N^{2} is divided by 100 ?

Answer Choices
A. 9
B. 61
C. 1
D. 41
E. 36