Dividing a Square into Unique Rectangles

For 1<=N<=8,
divide an NxN square into the maximum number of
nonoverlapping rectangles with integral sides,
such that each rectangle is unique in dimensions from any other. That
is, between any two rectangles, the length or width or both must be
different.

Same as number 1, with the added constraint that no rectangle can be
a square.

Divide a checkerboard into the maximum number of unique rectangles.
Here you have the added variable of color, so two rectangles of equal
size can still vary by pattern.
Source: Original.
Solution
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