Recently i found a problem about geometric, that ask for how many pair of points of the set of points, are good pair, and a good pair is a pair (a,b) of points where the max distance between both points to any other c point it is greater or equals at the distance between the firsts two points ( a and b).

as a formula: distance(a,b)<=max(distance(a,c),distance(b,c))

Can be at most 2000 points.

Is ease see, that can be solve for some O(n^2) whit some factor logn for search a point that invalidate a pair of points, but right now i don't see how search this point. If some one can help me, thank in advance???

UPD: here is the problem: link