2972 - Count the Number of Incremovable Subarrays II\.

Hard

You are given a 0-indexed array of positive integers nums.

A subarray of nums is called incremovable if nums becomes strictly increasing on removing the subarray. For example, the subarray [3, 4] is an incremovable subarray of [5, 3, 4, 6, 7] because removing this subarray changes the array [5, 3, 4, 6, 7] to [5, 6, 7] which is strictly increasing.

Return the total number of incremovable subarrays of nums.

Note that an empty array is considered strictly increasing.

A subarray is a contiguous non-empty sequence of elements within an array.

Example 1:

Input: nums = 1,2,3,4

Output: 10

Explanation: The 10 incremovable subarrays are: 1, 2, 3, 4, 1,2, 2,3, 3,4, 1,2,3, 2,3,4, and 1,2,3,4, because on removing any one of these subarrays nums becomes strictly increasing. Note that you cannot select an empty subarray.

Example 2:

Input: nums = 6,5,7,8

Output: 7

Explanation: The 7 incremovable subarrays are: 5, 6, 5,7, 6,5, 5,7,8, 6,5,7 and 6,5,7,8. It can be shown that there are only 7 incremovable subarrays in nums.

Example 3:

Input: nums = 8,7,6,6

Output: 3

Explanation: The 3 incremovable subarrays are: 8,7,6, 7,6,6, and 8,7,6,6. Note that 8,7 is not an incremovable subarray because after removing 8,7 nums becomes 6,6, which is sorted in ascending order but not strictly increasing.

Constraints:

• <code>1 <= nums.length <= 10⁵</code>

• <code>1 <= numsi<= 10⁹</code>