Balance

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_Here's a neat problem I've seen again recently._

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Given A, a set of n points in the plane, each point having integer coordinates. Come up with an algorithm that colors some of the points in the set red and the remaining points white in such a way that for any straight line L parallel to either one of the coordinate axes the difference (in absolute value) between the numbers of white point and red points on L is not greater than 1.

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