Kattis

# Greeting Card

Image by Varou.d

Quido plans to send a New Year greeting to his friend Hugo. He has recently acquired access to an advanced high-precision plotter and he is planning to print the greeting card on the plotter.

Here’s how the plotter operates. In step one, the plotter plots an intricate pattern of $n$ dots on the paper. In step two, the picture in the greeting emerges when the plotter connects by a straight segment each pair of dots that are exactly $2\, 018$ length units apart.

The plotter uses a special holographic ink, which has a limited supply. Quido wants to know the number of all plotted segments in the picture to be sure that there is enough ink to complete the job.

## Input

The first line of input contains a positive integer $n$ specifying the number of plotted points. The following $n$ lines each contain a pair of space-separated integer coordinates indicating one plotted point. Each coordinate is non-negative and less than $2^{31}$. There are at most $10^{5}$ points, all of them are distinct.

In this problem, all coordinates and distances are expressed in plotter length units, the length of the unit in the x-direction and in the y-direction is the same.

## Output

The output contains a single integer equal to the number of pairs of points which are exactly $2\, 018$ length units apart.

Sample Input 1 Sample Output 1
4
20180000 20180000
20180000 20182018
20182018 20180000
20182018 20182018

4

Sample Input 2 Sample Output 2
6
0 0
1680 1118
3360 0
5040 1118
6720 0
8400 1118

5