Four players are playing a game involving choosing squares on a grid of size . Each player chooses a random square on the grid, then all players reveal their choices and a token is placed in the center of each of these squares. The probability that the tokens form the vertices of a non-degenerate rectangle can be expressed as where and are coprime positive integers. What is the value of
Details and assumptions
Players are allowed to have selected the same squares. There is no restriction on their choices.
A degenerate rectangle has 0 area.
Squares are rectangles.