Given an array nums of integers, return the length of the longest arithmetic subsequence in nums.

Note that:

• A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.
• A sequence seq is arithmetic if seq[i + 1] - seq[i] are all the same value (for 0 <= i < seq.length - 1).

 

Example 1:

Input: nums = [3,6,9,12]
Output: 4
Explanation:  The whole array is an arithmetic sequence with steps of length = 3.

Example 2:

Input: nums = [9,4,7,2,10]
Output: 3
Explanation:  The longest arithmetic subsequence is [4,7,10].

Example 3:

Input: nums = [20,1,15,3,10,5,8]
Output: 4
Explanation:  The longest arithmetic subsequence is [20,15,10,5].

 

Constraints:

• 2 <= nums.length <= 1000
• 0 <= nums[i] <= 500