Given a collection of points P in the plane, a 1-set is a point in P that can

Given a collection of points P in the plane, a 1-set is a
point in P that can be separated from the rest by a line;
i.e. the point lies on one side of the line while the
others lie on the other side. The number of 1-sets of P is
denoted by n1(P). The maximum value of n1(P) over all
configurations P of 19 points in the plane is

18

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