Any integer-sided rectangle can be cut into unit rectangles (
) and rearranged into sets of smaller rectangles. For example the 
rectangle can be broken as follows:
) and rearranged into sets of smaller rectangles. For example the rectangle can be broken as follows:
We call an integer rectangle as "squarable" if it can be can be broken (i.e. cut into unit rectangles and rearranged) into any number of non-unit squares of equal sizes. For example the 
rectangle can be broken into six 
squares. Therefore, the rectangle is squarable.
rectangle can be broken into six squares. Therefore, the rectangle is squarable.Integer rectangles that are not squarable are called "non-squarable". The rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable rectangles with area 
square units are as follows:
rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable rectangles with area square units are as follows:
Create a program that calculates the total area of all non-squarable integer rectangles whose areas are less than or equal to a given area limit A.
For 
, the program should output:
, the program should output:
NOTE: Reflections and rotations are not significant and should be counted only once.
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