Rectangular Pasture

문제

Farmer John's largest pasture can be regarded as a large 2D grid of square "cells" (picture a huge chess board). Currently, there are $NN$ cows occupying some of these cells ($1\le N\le 25001\; \backslash leq\; N\; \backslash leq\; 2500$).

Farmer John wants to build a fence that will enclose a rectangular region of cells; the rectangle must be oriented so its sides are parallel with the $xx$ and $yy$ axes, and it could be as small as a single cell. Please help him count the number of distinct subsets of cows that he can enclose in such a region. Note that the empty subset should be counted as one of these.

입력

The first line contains a single integer $NN$. Each of the next $NN$ lines Each of the next $NN$ lines contains two space-separated integers, indicating the $(x,y)(x,y)$ coordinates of a cow's cell. All $xx$ coordinates are distinct from each-other, and all $yy$ coordinates are distinct from each-other. All $xx$ and $yy$ values lie in the range $0\dots {10}^{9}0\; \backslash ldots\; 10^9$.

출력

The number of subsets of cows that FJ can fence off. It can be shown that this quantity fits within a signed 64-bit integer (e.g., a "long long" in C/C++).