Question 11
Two sets of points in the coordinate plane are given: $\{(-1,1),(-1,2), \ldots,(-1,2000)\}$ and $\{(1,1),(1,2), \ldots,(1,2000)\}$. $2000$ line segments are drawn connecting these points so that each point in the first set is connected to exactly one point in the second set, and vice versa. Find, with proof, the sum of the $y$-intercepts of the segments.