KZ-MO 2016 Problem 5

$101$ blue and $101$ red points are selected on the plane, and no three lie on one straight line. The sum of the pairwise distances between the red points is $1$ (that is, the sum of the lengths of the segments with ends at red points), the sum of the pairwise distances between the blue ones is also $1$ , and the sum of the lengths of the segments with the ends of different colors is $400$ . Prove that you can draw a straight line separating everything red dots from all blue ones.