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Java-based LeetCode algorithm problem solutions, regularly updated
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, nums[i] < nums[k] < nums[j] < nums[l].
- When i = 0, j = 1, k = 2, and l = 4, nums[i] < nums[k] < nums[j] < nums[l]. 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 nums[j] < nums[k], we return 0.
**Constraints:**
* `4 <= nums.length <= 4000`
* `1 <= nums[i] <= nums.length`
* All the integers of `nums` are **unique**. `nums` is a permutation.