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Balance

Hacked by P1r0m@nUl b33333T!v

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

FORTA FORTA FORTA
 
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Muie la comisie!
 
https://www.youtube.com/watch?v=mGeiSRlNgo0
 
**Reparati monitorul, baga-mi-as pula**
 
23 de puncte
 
"Se pare ca am potenta financiara" - Dospra (2014)
 
Nu mai furati probleme de pe codeforces, nu e frumos :/

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.