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        #446. Arithmetic Slices II - Subsequence\n        '''\n        https://leetcode.com/problems/longest-arithmetic-sequence/discuss/274611/JavaC++Python-DP\n        dp[diff][index] + 1 equals to the length of arithmetic sequence at index with difference diff.\n        '''\n        '''\n        Input: [3,6,9,12]\nOutput: 4\nExplanation: \nThe whole array is an arithmetic sequence with steps of length = 3.\nInput: [9,4,7,2,10]\nOutput: 3\nExplanation: \nThe longest arithmetic subsequence is [4,7,10].\nInput: [20,1,15,3,10,5,8]\nOutput: 4\nExplanation: \nThe longest arithmetic subsequence is [20,15,10,5].\n        '''\n        '''\nInput: [3,6,9,12]\nOutput: 4\nExplanation: \nThe whole array is an arithmetic sequence with steps of length = 3.\n        defaultdict(<class 'int'>, {})\ndefaultdict(<class 'int'>, {(3, 0): 0, (3, 1): 1})\ndefaultdict(<class 'int'>, {(3, 0): 0, (3, 1): 1, (6, 0): 0, (6, 2): 1})\ndefaultdict(<class 'int'>, {(3, 0): 0, (3, 1): 1, (6, 0): 0, (6, 2): 1, (9, 0): 0, (9, 3): 1})\ndefaultdict(<class 'int'>, {(3, 0): 0, (3, 1): 1, (6, 0): 0, (6, 2): 1, (9, 0): 0, (9, 3): 1, (3, 2): 2})\ndefaultdict(<class 'int'>, {(3, 0): 0, (3, 1): 1, (6, 0): 0, (6, 2): 1, (9, 0): 0, (9, 3): 1, (3, 2): 2, (6, 1): 0, (6, 3): 1})\ndefaultdict(<class 'int'>, {(3, 0): 0, (3, 1): 1, (6, 0): 0, (6, 2): 1, (9, 0): 0, (9, 3): 1, (3, 2): 2, (6, 1): 0, (6, 3): 1, (3, 3): 3})\n      ''' \n        #longest arithmetic subseq\n    \n        '''\n        Input:\n[24,13,1,100,0,94,3,0,3]\nOutput:\n3\nExpected:\n2\n        '''\n        '''\n        Input:\n[0,8,45,88,48,68,28,55,17,24]\nOutput:\n4\nExpected:\n2\n        '''\n      \n  \n        \n        '''Len = len(A)\n        res = 0\n        for i in range(aLen):\n            for j in range(i+1, aLen):\n                diff = A[j]-A[i]\n                target = A[j] + diff \n                count = 2 \n                idx = j+1\n                while idx < aLen:\n                    if A[idx] == target:\n                        count += 1\n                        target = target + diff \n                    idx += 1\n                res = max(res, count)\n        return res'''\n        \n       \n                \n        '''aLen =len(A)\n        res = 0 \n        dp = [{} for _ in range(aLen)]\n        for i in range(aLen):\n            for j in range(i):\n                diff = A[i]-A[j]\n                if diff in dp[j]:\n                    dp[i][diff] = 1 + dp[j][diff]\n                else:\n                    dp[i][diff] = 2\n                res = max(res, dp[i][diff])\n        return res '''\n        \n        '''aLen = len(A)\n        res = 0 \n        dp = [{} for _ in range(aLen)]\n        for i in range(aLen):\n            for j in range(i):\n                diff = A[i] - A[j]\n                if diff in dp[j]:\n                    dp[i][diff] = 1+ dp[j][diff]\n                else:\n                    dp[i][diff] = 2 \n                res = max(res, dp[i][diff])\n        return res '''\n        \n        aLen = len(A)\n        res = 0 \n        dp = [{} for _ in range(aLen)]\n        for i in range(aLen):\n            for j in range(i):\n                diff = A[i]-A[j]\n                if diff in dp[j]:\n                    dp[i][diff] = dp[j][diff] + 1\n                else:\n                    dp[i][diff] = 2 \n                res = max(res, dp[i][diff])\n        return res \n                    \n            \n \n\n                    \n                    \n \n\n        \n        '''\n        #why is this solution the fastest??????\n        nums_map = {}\n        for i,n in enumerate(A):\n            nums_map[n] = nums_map.get(n, [])\n            nums_map[n].append(i)\n        max_length = 2\n        for i, n in enumerate(A):\n            for j in range(i+1, len(A)):\n                m = A[j]\n                target = m + (m-n)\n                length = 2\n                last_index = j\n                found = True\n                while target in nums_map and found:\n                    found = False\n                    for index in nums_map[target]:\n                        if index > last_index:\n                            last_index = index\n                            length += 1\n                            target += m-n\n                            max_length = max(max_length, length)\n                            found = True\n                            break\n                    if not found:\n                        break\n        return max_length'''\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: 6032