2552 - Count Increasing Quadruplets\.

Hard

Given a 0-indexed integer array nums of size n containing all numbers from 1 to n, return the number of increasing quadruplets.

A quadruplet (i, j, k, l) is increasing if:

• 0 <= i < j < k < l < n, and

• nums[i] < nums[k] < nums[j] < nums[l].

Example 1:

Input: nums = 1,3,2,4,5

Output: 2

Explanation:

• When i = 0, j = 1, k = 2, and l = 3, numsi< numsk< numsj< numsl.

• When i = 0, j = 1, k = 2, and l = 4, numsi< numsk< numsj< numsl. There are no other quadruplets, so we return 2.

Example 2:

Input: nums = 1,2,3,4

Output: 0

Explanation:

There exists only one quadruplet with i = 0, j = 1, k = 2, l = 3, but since numsj< numsk, we return 0.

Constraints:

• 4 <= nums.length <= 4000

• 1 <= nums[i] <= nums.length

• All the integers of nums are unique. nums is a permutation.