Given an array A of integers, return the length of the longest arithmetic subsequence in A.
Recall that a subsequence of A is a list A[i_1], A[i_2], ..., A[i_k] with 0 <= i_1 < i_2 < ... < i_k <= A.length - 1, and that a sequence B is arithmetic if B[i+1] - B[i] are all the same value (for 0 <= i < B.length - 1).
Example 1:
Input: A = [3,6,9,12]
Output: 4
Explanation: 
The whole array is an arithmetic sequence with steps of length = 3.
Example 2:
Input: A = [9,4,7,2,10]
Output: 3
Explanation: 
The longest arithmetic subsequence is [4,7,10].
Example 3:
Input: A = [20,1,15,3,10,5,8]
Output: 4
Explanation: 
The longest arithmetic subsequence is [20,15,10,5].
Constraints:
2 <= A.length <= 1000
0 <= A[i] <= 500
class Solution:
    def longestArithSeqLength(self, A: List[int]) -> int:
        dp = [collections.defaultdict(int) for _ in range(len(A))]
        res = 0
        for i in range(1, len(A)):
            for j in range(i):
                dp[i][A[i]-A[j]] = max(dp[i][A[i]-A[j]], dp[j].get(A[i]-A[j], 1)+1)
                res = max(res, dp[i][A[i]-A[j]])
        return res
class Solution:
    def longestArithSeqLength(self, A: List[int]) -> int:
        dp = [collections.defaultdict(int) for _ in range(len(A))]
        res = 0
        for i in range(1, len(A)):
            for j in range(i):
                dp[i][A[i]-A[j]] = max(dp[i][A[i]-A[j]], dp[j].get(A[i]-A[j], 1)+1)
                res = max(res, dp[i][A[i]-A[j]])
        return res