The Cross Covers Everything

A cross-shaped infinite area on the $x$-$y$ plane is specified by two distinct points, as shown in the figure below.

Figure J.1. The cross area specified by points 2 and 4

Given a set of points on the plane, count the ordered pairs $\langle p, q \rangle$ that cover all the points. The pair $\langle p, q \rangle$ covers a point $(x, y)$ if $x_p \le x \le x_q$, or $y_p \le y \le y_q$, or both hold. No two points share an $x$-coordinate or a $y$-coordinate.

The first line contains an integer $n$ ($2 \le n \le 2 \times 10^5$), the number of points. Each of the following $n$ lines contains two integers $x_i$ and $y_i$ ($1 \le x_i \le 10^6$, $1 \le y_i \le 10^6$), the coordinates of the $i$-th point. For all $j \ne k$, $x_j \ne x_k$ and $y_j \ne y_k$. The input is a single test case.

Print the number of ordered pairs of points that cover all the points, on one line.

The cross in the figure is specified by the second and fourth points of the first sample input. It is one of the crosses covering all the points.