In the case of {(0,0),(0,2)}, (0,1) counts as "1 more integer point" - the point has to be not one of the two points generating the line, not a point outside th

In the case of {(0,0),(0,2)}, (0,1) counts as "1 more integer point" - the point has to be not one of the two points generating the line, not a point outside the set of 5 points on the plane.