Steady Speed

You are given a list of integers positions representing the position of a car at equally spaced intervals of time. Return the length of the longest sublist where the car was traveling at a constant speed.

Constraints

• n ≤ 100,000 where n is length of positions.

https://binarysearch.com/problems/Steady-Speed

Examples

Example 1

Input

• positions = [0, 3, 6, 3, 0]

Output

• answer = 5

Explanation

The car is always traveling at 3 units of distance per time

Example 2

Input

• positions = [0, 3, 6, 5, 4, 3, 1, 7, 10, 13]

Output

• answer = 4

Explanation

The longest period the car was traveling at a constant speed was in the sublist [6, 5, 4, 3]

Solution