## Editorial for An Animal Contest 4 P3 - Snowy Slopes

Remember to use this editorial

**only**when stuck, and**not to copy-paste code from it**. Please be respectful to the problem author and editorialist.**Submitting an official solution before solving the problem yourself is a bannable offence.**Author:

Consider all steepnesses (with taking into account duplicate steepnesses) separately. If some arbitrary point and point form a line with gradient :

By manipulating the equation:

Let of a point with coordinate be . In other words, for two points and to form a line with gradient , must be equal to .

Implementation details are left to the reader as an exercise.

**Time Complexity**:

## Comments

How would you count the amount of same values inside the id array?

When solving for a particular slope , we can maintain the id's in a map

`<id value, frequency (# of points with that id value)>`

. For a id value with frequency you can form distinct pairs of points with slope .For further help, ask in the DMOJ Discord.

ah, ok, thanks a lot, for some reason I was thinking f frequency would form f! pairs, thanks a lot