Most Frequent Square

You are given a set of grid points in the plane. Consider every axis-parallel square whose four corners all belong to the given set — a square whose sides are horizontal and vertical and are never tilted. Determine which side length occurs in the greatest number of such squares, and how many squares have that side length.

For example, in the figure above there are $3$ squares with side length $2$ and $3$ squares with side length $4$.

The first line contains the number of test cases $T$ ($T \le 50$).

Each of the next $T$ lines describes one test case. A line starts with the number of points $k$ ($k \le 30$), followed by $k$ coordinate pairs (that is, $2k$ integers in total). Every coordinate is an integer with $0 \le x, y \le 30$.

For each test case, print one line.

If the points form at least one axis-parallel square, output

LENGTH = L, COUNT = C

where $L$ is the side length that appears in the greatest number of squares and $C$ is the number of squares with that side length. If several side lengths tie for the greatest count, use the largest such side length $L$.

If the points form no axis-parallel square at all, output

No squares among the points.