Maximum mutually equidistant collinear points.

Given a grid with R (Rows) and C (Coloumns) and N points (R,C) within the grid. I need to find the count of maximum mutually equidistant collinear points.

  • Mutually equidistant points here
    means, Every point on that line
    should be at equal distance with its
    neighbouring point on that line only
    (1,1 -> 3,3 -> 5,5 -> 7,7).

  • A line would be discarded if it
    contains non-mutually equidistant
    points(or point). (1-1 -> 3,3 ->5,5 ->6,6 is an invalid line).

I came up with N^3 complexity approach, but it’s too slow to work.
Is there any better approach?

Thank you.

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