Three Points

There are N points on an infinite two-dimensional plane. The points are numbered 0 through N-1, and point i lies at $(x_i, y_i)$. No two points share an x coordinate, and no two points share a y coordinate.

Pick three of the points and color one red, one green, and one blue. Let $r$ be the number of the red point, $g$ the number of the green point, and $b$ the number of the blue point. The coloring must satisfy $x_r < x_g < x_b$ and $y_r < y_b < y_g$ at the same time.

Given the coordinates of the points, write a program that counts the colorings satisfying both conditions.

The first line contains N. Each of the next N lines contains the coordinates $x$ and $y$ of one point, separated by a space. ($1 \le N \le 300{,}000$, $0 \le x, y < 1{,}000{,}000{,}000$)

Print the number of colorings that satisfy the conditions. This value can exceed the range of a 32-bit integer.