Valentine's Day '19 J5 - Falling in Love

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Points: 7 (partial)
Time limit: 1.0s
Memory limit: 64M

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Winnie has fallen in love with the people from the kpop 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)?

Input Specification

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 Specification

Output the number of pairs of people that will receive the same amount of affection from Winnie at a common point in time.

Subtasks

Subtask 1 [10%]

N \le 10^3

Subtask 2 [90%]

No further constraints.

Sample Input

4
1 3
2 3
0 2
1 2

Sample Output

5

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