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 = "class Solution:\n    def longestArithSeqLength(self, A: List[int]) -> int:\n        \n        def dp_matrix_based():\n            item_dict = collections.defaultdict(list)\n            for i, x in enumerate(A):\n                item_dict[x].append(i)\n\n            C = max(A) - min(A)\n            n = len(A)\n            maxlen = -math.inf\n            dp =[[-math.inf]*(2*C+1) for _ in range(n)]\n\n            for i in range(n):\n                dp[i][0 + C] = 1\n\n            for i in range(n):\n                for j in range(i+1, n):\n                    g = A[j] - A[i] + C \n                    dp[j][g] = 2\n\n            for i in range(1,n):\n                for gap in range(2*C+1):\n                    candidate = A[i] - gap + C\n                    if candidate in item_dict:\n                        for t in item_dict[candidate]:\n                            if t < i:\n                                dp[i][gap] = max(dp[i][gap], dp[t][gap] + 1)\n                                maxlen = max(maxlen, dp[i][gap])\n\n            return maxlen\n        \n        # return dp_matrix_based()\n        \n        def dict_based():\n            '''\n            Less space and simpler\n            '''\n            \n            dp = defaultdict(defaultdict)\n            for i in range(len(A)):\n                for j in range(i):\n                    diff = A[i] - A[j]\n                    if diff not in dp:\n                        #save an inner dictionary with the higher index\n                        dp[diff] = { i: 2 }\n                    else:\n                        dic = dp[diff]\n                        if j not in dic:\n                            dic[i] = 2\n                        else:\n                            dic[i] = dic[j] + 1\n            maxlen = 0\n            for k,v in list(dp.items()):\n                for k1, v1 in list(v.items()):\n                    maxlen = max(maxlen, v1)\n            return maxlen\n        return dict_based()\n            \n            \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: 7500