Center of Symmetry
InterviewTime limit1sMemory limit128 MB
Decide whether a set of up to 10000 integer points has a center point such that every point's mirror image is also in the set.
Problem
You are given a set of n distinct points with integer coordinates. Determine whether the set is centrally symmetric around some point.
The center does not have to be one of the given points. A point s is a center of symmetry if, for every point p in the set, there is also a point q in the same set such that p + q = 2s.
Input
The first line contains the number of test cases c.
For each test case, the first line contains the number of points n. (1 <= n <= 10000)
The next n lines each contain two integers x and y, the coordinates of one point. All points are distinct, and -10000000 <= x, y <= 10000000.
Output
For each test case, print yes if the given point set has a center of symmetry, and no otherwise.