# USACO 2020 December

# Square Pasture

Farmer John's largest pasture can be regarded as a large 2D grid of square "cells" (picture a huge chess board). Currently, there are **n** cows occupying some of these cells.

Farmer John wants to build a fence that will enclose a square region of cells; the square must be oriented so its sides are parallel with the **x** and **y** 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.

#### Input

The first line contains a single integer **n** (**1** ≤ **n** ≤ **200**). Each of the next **n** lines contains two integers, indicating the (**x**, **y**) coordinates of a cow's cell. All **x** coordinates are distinct from each-other, and all **y** coordinates are distinct from each-other. All **x** and **y** values lie in the range **0**...`10`

.^{9}

Note that although the coordinates of cells with cows are nonnegative, the square fenced area might possibly extend into cells with negative coordinates.

#### Output

The number of subsets of cows that FJ can fence off. It can be shown that this quantity fits within a signed 32-bit integer.

#### Example

In this example, there are **24** subsets in total. FJ cannot create a fence enclosing only cows **1** and **3**, or only cows **2** and **4**, so the answer is **24** − **2** = **16** − **2** = **14**.

4 0 2 2 3 3 1 1 0

14

16 17 4 16 13 0 15 1 19 7 11 3 17 6 16 18 9 15 6 11 7 10 8 2 1 12 0 5 18 14 5 13 2

420