Symmetry 2#251
Given a point and a line on the plane, the reflection of with respect to is a point p', such that the segment pp' is perpendicular to and its midpoint lies on . If lies on , then p' = p.
Given a set of points on the plane, an axis of symmetry is a line such that the reflection of any point of the set with respect to this line is also a point from this set. In this problem, you are given a set of points on the plane, and you must determine whether there exists at least one axis of symmetry for this set.
Because real numbers are used, consider a line to be an axis of symmetry if, for any point of the set, the distance from its reflection p' with respect to this line to some point of the set does not exceed 10^{-6}.
The input file contains several test cases. The first line contains the integer (1 \le K \le 10), the number of test cases. The first line of each test case contains the integer , the number of points in the set (1 \le N \le 100\,000). Each of the next lines describes a single point — two real numbers and separated by a space, the coordinates of the point on the plane (-10\,000 \le X, Y \le 10\,000). No two points in the same test coincide. It is guaranteed that the sum of over all test cases does not exceed .
For each test case, output one line: if there exists at least one axis of symmetry for the given set of points, and otherwise.
Example 1