Strictly Alternating List

You are given a list of integers nums. Return whether the list alternates from first strictly increasing to strictly decreasing and then strictly increasing etc. If a list is only strictly increasing, return true.

Constraints

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

https://binarysearch.com/problems/Strictly-Alternating-List

Examples

Example 1

Input

• nums = [1, 2, 5, 7, 4, 1, 6, 8, 3, 2]

Output

• answer = True

Explanation

This list strictly increases, strictly decreases, strictly increases, then strictly decreases.

Example 2

Input

• nums = [1, 1, 2, 3, 2, 1]

Output

• answer = False

Explanation

This list increases and then decreases, but is not strictly increasing at first.

Example 3

Input

• nums = [1, 3, 5, 7]

Output

• answer = True

Explanation

This list is strictly increasing.

Example 4

Input

• nums = [5, 3, 1, 5, 7]

Output

• answer = False

Explanation

This list is not strictly increasing at first.

Solution