Changing Directions

Given a list of integers nums, return the number of times that the list changes from positive-to-negative or negative-to-positive slope.

Constraints

• n ≤ 100,000 where n is the length of nums

https://binarysearch.com/problems/Changing-Directions

Examples

Example 1

Input

• nums = [1, 3, 9, 7, 5, 10, 12]

Output

• answer = 2

Explanation

Change of direction happens at 9 (positive-to-negative slope), and then at 5 (negative-to-positive slope).

Example 2

Input

• nums = [1, 2, 3, 3, 2, 1]

Output

• answer = 0

Explanation

The slope is 0 between [3, 3]. So there are no positive-to-negative or negative-to-positive changes in slope since 0 is neither positive nor negative.

Solution