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 $2018$ 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 $2018$ length units apart.

-----Examples-----
Sample Input:
4
20180000 20180000
20180000 20182018
20182018 20180000
20182018 20182018
Sample Output:
4

Source: kattis | Difficulty: MEDIUM


Solutions: