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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '#SELF TRY 9/20/2020\nclass Solution:\n    def longestArithSeqLength(self, A: List[int]) -> int:\n        #Problem asks -> array A \n        #Want -> return the length of longest arithmetic subseq in A \n        \n        #Two cases basically.\n        #When building up to to your table \n        #When looking at previous values i.e from (col, change) we see that there is a PREVIOUS value already there. (With the same change) so you know you can extend that length by 1\n        #This \\"1\\" indicates the CUR number is being added because it\'s change is the same. \n        #If it\'s never been seen that the base case is at most length 2 \n        #i.e some \\"subseq\\" whatever it is with 2 elements would always be \\"valid\\" and so would be length 2 \n        table = dict()\n        longest_subseq = float(\'-inf\')\n        \n        for row in range(len(A)): \n            for col in range(0, row): \n                change = A[row] - A[col]\n                if (col, change) in table: \n                    table[(row, change)] = 1 + table[(col, change)]\n                    \n                \n                \n                else: \n                    table[(row, change)] = 2 \n                    \n                longest_subseq = max(longest_subseq, table[(row, change)])\n                \n                \n                \n        return longest_subseq\n    \n    \n# class Solution:\n#     def longestArithSeqLength(self, A):\n#         d = {}\n#         for i in range(1, len(A)):\n#             for j in range(len(A)):\n#                 delta = A[i] - A[j]\n#                 d[(i, delta)] = d[(j, delta)] + 1 if (j, delta) in d else 2\n#         return max(d.values())\n# class Solution:\n#     def longestArithSeqLength(self, A: List[int]) -> int:\n#         #Array A \n#         #Want return the (Len of longest arithmetic subseq in A)\n#         #Recall that a subseq of A is a list A[i_1], A[i_2]... A[i_k] s.t\n#         # 0 <= i_1 < i_2 < i_k <= A.len() - 1 \n    \n#         #ROW\n#         # [9,4,7,2,10]\n        \n#         #COL\n#         #[\n#         #9\n#         #4\n#         #7 \n#         #2\n#         #10\n#         #]\n#         table = dict()\n#         for row in range(1, len(A)):\n#             for col in range(0, row): \n#                 change = A[row] - A[col]\n                \n#                 if (col, change) in table: \n#                     table[(row, change)] = table[(col, change)] + 1 \n#                 else: \n#                     #table(1, -5) = 2  \n#                     #table(1, 0) = 2 \n#                     #table(1, -3) = 2 + 1 \n#                     #table(1, -2) = 2\n#                     #table(1, -6) = 2\n#                     #table(0, -2) = 2\n#                     #(2, 0) = 2 \n#                     #(3,5) = 2 \n#                     #(2, -3) = 2 \n                    \n#                     table[(row, change)] = 2 \n            \n#         return max(table.values())\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'longestArithSeqLength'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5994