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