Valid Boomerang

easy
Given an array points where points[i] = [xi, yi] represents a point on the X-Y plane, return true if these points are a boomerang.

A boomerang is a set of three points that are all distinct and not in a straight line.

 

Input Format

Integer n 2*n Integers

Output Format

boolean value

Constraints

points.length == 3
points[i].length == 2
0 <= xi, yi <= 100

Notice

NA

Example

Input
3
1 1
2 3
1 2
Output
true
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