Largest Square

Given $N$ points on a plane, find the area of the largest square whose four vertices are all among the given points. The sides of the square need not be parallel to the coordinate axes; tilted squares are also allowed.

The first line contains the number of test cases $T$.

For each test case, the first line contains the number of points $N$ ($4 \le N \le 3000$). Each of the next $N$ lines contains the $x$ and $y$ coordinates of a point, separated by a space. All coordinates are integers between $-10000$ and $10000$ inclusive, and no two points share the same position.

For each test case, print the area of the largest square that can be formed, one per line. If no square can be formed, print $0$.