Longest Strictly Increasing Then Decreasing Sublist

You are given a list of integers nums. Return the length of the longest sublist such that its length is at least 3 and its values are strictly increasing and then decreasing. Both the increasing part and the decreasing part must be non-empty.

Constraints

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

https://binarysearch.com/problems/Longest-Strictly-Increasing-Then-Decreasing-Sublist

Examples

Example 1

Input

• nums = [7, 1, 3, 5, 2, 0]

Output

• answer = 5

Explanation

The sublist [1, 3, 5, 2, 0] is strictly increasing then decreasing.

Example 2

Input

• nums = [1, 2, 3]

Output

• answer = 0

Example 3

Input

• nums = [3, 2, 1]

Output

• answer = 0

Example 4

Input

• nums = [1, 2, 1, 1]

Output

• answer = 3

Solution