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]q - p > 1, r - q > 1 and s - r > 1.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):
(1, 3, 3, 1).nums[p] * nums[r] = nums[0] * nums[4] = 1 * 3 = 3nums[q] * nums[s] = nums[2] * nums[6] = 3 * 1 = 3Example 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):
(3, 3, 3, 3).nums[p] * nums[r] = nums[0] * nums[4] = 3 * 3 = 9nums[q] * nums[s] = nums[2] * nums[6] = 3 * 3 = 9(p, q, r, s) = (1, 3, 5, 7):
(4, 4, 4, 4).nums[p] * nums[r] = nums[1] * nums[5] = 4 * 4 = 16nums[q] * nums[s] = nums[3] * nums[7] = 4 * 4 = 16(p, q, r, s) = (0, 2, 5, 7):
(3, 3, 4, 4).nums[p] * nums[r] = nums[0] * nums[5] = 3 * 4 = 12nums[q] * nums[s] = nums[2] * nums[7] = 3 * 4 = 12
Constraints:
7 <= nums.length <= 10001 <= nums[i] <= 1000