Given two arrays nums1 and nums2.
Return the maximum dot product between non-empty subsequences of nums1 and nums2 with the same length.
A subsequence of a array is a new array which is formed from the original array by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, [2,3,5] is a subsequence of [1,2,3,4,5] while [1,5,3] is not).
 
Example 1:
Input: nums1 = [2,1,-2,5], nums2 = [3,0,-6]
Output: 18
Explanation: Take subsequence [2,-2] from nums1 and subsequence [3,-6] from nums2.
Their dot product is (2*3 + (-2)*(-6)) = 18.
Example 2:
Input: nums1 = [3,-2], nums2 = [2,-6,7]
Output: 21
Explanation: Take subsequence [3] from nums1 and subsequence [7] from nums2.
Their dot product is (3*7) = 21.
Example 3:
Input: nums1 = [-1,-1], nums2 = [1,1]
Output: -1
Explanation: Take subsequence [-1] from nums1 and subsequence [1] from nums2.
Their dot product is -1.
 
Constraints:

1 <= nums1.length, nums2.length <= 500
-1000 <= nums1[i], nums2[i] <= 1000

```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 maxDotProduct(self, nums1: List[int], nums2: List[int]) -> int:\n#         Target: We want to calculate the maximal dot product for nums1[0:i] and nums2[0:j]\n# Base case\n# When i == 0 or j == 0, we return -inf. (Because this is an empty case, which is intolerable)\n# State Transition, for any i > 0 and j > 0, there are 4 possibilities\n# nums1[i - 1] is not selected, dp[i][j] = dp[i - 1][j]\n# nums2[j - 1] is not selected, dp[i][j] = dp[i][j - 1]\n# Neither nums1[i - 1] or nums2[j - 1] is selected, dp[i][j] = dp[i - 1][j - 1]\n# Both nums1[i - 1] and nums2[j - 1] are selected, dp[i][j] = max(dp[i - 1][j - 1], 0) + nums1[i - 1] * nums2[j - 1]\n# Since we already selected one pair (nums1[i - 1], nums2[j - 1]), we can assume the minimal proceeding value is 0\n        mx, m, n = -math.inf, len(nums1), len(nums2)\n        dp = [[0] * (n + 1) for _ in range(m + 1)]\n        for i, num1 in enumerate(nums1):\n            for j, num2 in enumerate(nums2):\n                p = num1 * num2\n                mx = max(p, mx)\n                p = max(p, 0)\n                dp[i + 1][j + 1] = max(dp[i][j] + p, dp[i + 1][j], dp[i][j + 1])\n                \n        return mx if mx <= 0 else dp[m][n]\n             \n        # n, m = len(nums1), len(nums2)\n        # dp = [-math.inf] * (m + 1)\n        # for i in range(1, n + 1):\n        #     dp, old_dp = [-math.inf], dp\n        #     for j in range(1, m + 1):\n        #         dp += max(\n        #             old_dp[j], # not select i\n        #             dp[-1], # not select j\n        #             old_dp[j - 1], # not select either\n        #             max(old_dp[j - 1], 0) + nums1[i - 1] * nums2[j - 1], # select both\n        #         ),\n        # return dp[-1]     \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'maxDotProduct'
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: 6506