Count Arithmetic Subsequences

# Count Arithmetic Subsequences Given an integer array `nums`, return the number of subsequences of length at least three whose consecutive values have the same difference. A subsequence keeps the original order but may skip elements. Choices of different indices count separately, even when they produce the same values. The answer is guaranteed to fit in a signed 32-bit integer. ### Function `int numberOfArithmeticSlices(vector<int>& nums)` ### Example 1 ```text Input: nums = [1,3,5,7] Output: 3 ``` The three subsequences are `[1,3,5]`, `[3,5,7]`, and `[1,3,5,7]`. ### Example 2 ```text Input: nums = [4,4,4,4] Output: 5 ``` There are four ways to choose three indices and one way to choose all four. Every such choice has difference zero. ### Constraints - `1 <= nums.length <= 1000`. - `-2147483648 <= nums[i] <= 2147483647`. - The required count fits in a signed 32-bit integer. ### Clarifications Two elements alone do not count. Subsequence elements need not be adjacent. Negative and zero differences are allowed, and equal values at different positions remain distinct index choices. ### What a Strong Answer Covers - Counting every eligible index sequence exactly once. - Repeated values, short arrays, and decreasing subsequences. - Arithmetic across the full signed 32-bit value range. - Correctness and time and space bounds for one thousand elements.