3404 - Count Special Subsequences.

Medium

You are given an array nums consisting of positive integers.

A special subsequence is defined as a subsequence of length 4, represented by indices (p, q, r, s), where p < q < r < s. This subsequence must satisfy the following conditions:

• nums[p] * nums[r] == nums[q] * nums[s]

• There must be at least one element between each pair of indices. In other words, q - p > 1, r - q > 1 and s - r > 1.

A subsequence is a sequence derived from the array by deleting zero or more elements without changing the order of the remaining elements.

Return the number of different special subsequences in nums.

Example 1:

Input: nums = 1,2,3,4,3,6,1

Output: 1

Explanation:

There is one special subsequence in nums.

• (p, q, r, s) = (0, 2, 4, 6):

Example 2:

Input: nums = 3,4,3,4,3,4,3,4

Output: 3

Explanation:

There are three special subsequences in nums.

• (p, q, r, s) = (0, 2, 4, 6):

• (p, q, r, s) = (1, 3, 5, 7):

• (p, q, r, s) = (0, 2, 5, 7):

Constraints:

• 7 <= nums.length <= 1000

• 1 <= nums[i] <= 1000