Distance Between the Closest Pair of Points

There are $n$ points $P_1, P_2, \dots, P_n$ on a plane. Among these points, find the two that are closest to each other and determine the distance between them.

The first line contains the number of points $n$.

Each of the next lines, from the 2nd line through the $(n+1)$-th line, contains the coordinates $x$ and $y$ of a single point separated by a space. The values on the $(i+1)$-th line are the $x$- and $y$-coordinates of point $P_i$.

Constraints: $2 \le n \le 500000$ and $-10000 \le x, y \le 10000$. All points have distinct coordinates (no two points share the same coordinates).

Print the square of the distance between the closest pair of points.