Winnie has fallen in love with the people from the K-pop band group: BTS. In this group, there are ~N~ people. Her love for each person can be modeled as a line of the form ~y = mx + b~, with ~x~ representing time, and ~y~ representing her affection for the person.
You want to know, how many pairs of people will receive the same amount of affection from Winnie at a common point in time (including negative time)?
The first line will contain the integer ~N~ ~(1 \le N \le 10^5)~, the number of people.
The next ~N~ lines will each contain two integers, ~m, b~ ~(|m|, |b| \le 10^9)~.
Output the number of pairs of people that will receive the same amount of affection from Winnie at a common point in time.
Subtask 1 [10%]
~N \le 10^3~
Subtask 2 [90%]
No additional constraints.
4 1 3 2 3 0 2 1 2