Square 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 $N$ cows occupying some of these cells ($1 \leq N \leq 200$).

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.

입력

The first line contains a single integer $N$. Each of the next $N$ lines Each of the next $N$ lines contains two space-separated 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 $0 \ldots 10^9$.

출력

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

예제 입력 1

4
0 2
2 3
3 1
1 0

예제 출력 1

14

예제 입력 2

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

예제 출력 2

420

점수

In test cases 1-5, all coordinates of cells containing cows are less than $20$.In test cases 6-10, $N\le 20$.In test cases 11-20, there are no additional constraints.