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Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.



You are a modern artist and you like drawing random lines on a sheet of paper like François Morellet.
These lines draw a somewhat strange chess board that you fill with only two colours.
You are given the lines and the coordinates of two point A and B and you have to tell if the points have the same colour or not or if one of them is on one line.
You will be given the coefficients of each line (Cartesian style, ie ax+by+c=0, a, b and c given).

Count each line once because sometimes, some lines might have more than one equation in the list.
For example, 2x+4y+6=0 is the same line than x+2y+3=0.
a and b can’t be null at the same time.
Line 1: xA yA xB yB
Line 2: n, the number of straight lines
Next n lines: a b c for each line
If at least A or B is on one line, print ON A LINE
If not, print YES if A and B have the same colour, else NO
1 1 0 0
1 2 3

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