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Find all possible values for the area [Slovenia 2010]

Source:

November 14, 2010
geometryrectanglecombinatorics proposedcombinatorics

Problem Statement

Let ABCDABCD be a square with the side of 2020 units. Amir divides this square into 400400 unit squares. Reza then picks 44 of the vertices of these unit squares. These vertices lie inside the square ABCDABCD and define a rectangle with the sides parallel to the sides of the square ABCD.ABCD. There are exactly 2424 unit squares which have at least one point in common with the sides of this rectangle. Find all possible values for the area of a rectangle with these properties.
[hide="Note"]Note: Vid changed to Amir, and Eva change to Reza!