Quido plans to send a New Year greeting to his friend Hugo.
He has recently acquired access to an advanced highprecision
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
spaceseparated integer coordinates indicating one plotted
point. Each coordinate is nonnegative 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
xdirection and in the ydirection 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
