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)?

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.

Constraints

Subtask 1 [10%]

~N \le 10^3~

Subtask 2 [90%]

No additional constraints.

Sample Input

4
1 3
2 3
0 2
1 2

Sample Output

5