Given two arrays of integers with equal lengths, return the maximum value of:
|arr1[i] - arr1[j]| + |arr2[i] - arr2[j]| + |i - j|
where the maximum is taken over all 0 <= i, j < arr1.length.
 
Example 1:
Input: arr1 = [1,2,3,4], arr2 = [-1,4,5,6]
Output: 13

Example 2:
Input: arr1 = [1,-2,-5,0,10], arr2 = [0,-2,-1,-7,-4]
Output: 20

 
Constraints:

2 <= arr1.length == arr2.length <= 40000
-10^6 <= arr1[i], arr2[i] <= 10^6

```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 join(self, a: List[int], b: List[int], add=True, ascend=True):\n        arr = []\n        for i in range(len(a)):\n            if add:\n                arr.append(a[i] + b[i])\n            else:\n                arr.append(a[i] - b[i])\n            if ascend:\n                arr[i] += i\n            else:\n                arr[i] -= i\n        return arr\n        \n    def maxAbsValExpr(self, arr1: List[int], arr2: List[int]) -> int:\n        if not len(arr1):\n            return 0\n        mins, maxes = [], []\n        idx = []\n        for i, arr in enumerate([self.join(arr1, arr2, add, asc) for add, asc in [(True, True), (True, False), (False, True), (False, False)]]):\n            mins.append(arr[0])\n            maxes.append(arr[0])\n            idx.append((0, 0))\n            for j in range(1, len(arr)):\n                if arr[j] < mins[i]:\n                    mins[i] = arr[j]\n                    idx[i] = j, idx[i][1]\n                if arr[j] > maxes[i]:\n                    maxes[i] = arr[j]\n                    idx[i] = idx[i][0], j\n        largest_diff = float('-inf')\n        if (arr1[idx[0][0]] > arr1[idx[0][1]]) == (arr2[idx[0][0]] > arr2[idx[0][1]]) and idx[0][0] <= idx[0][1]:\n            largest_diff = maxes[0] - mins[0]\n        if (arr1[idx[1][0]] > arr1[idx[1][1]]) == (arr2[idx[1][0]] > arr2[idx[1][1]]) and idx[1][0] >= idx[1][1]:\n            largest_diff = max(largest_diff, maxes[1] - mins[1])\n        if (arr1[idx[2][0]] > arr1[idx[2][1]]) != (arr2[idx[2][0]] > arr2[idx[2][1]]) and idx[2][0] <= idx[2][1]:\n            largest_diff = max(largest_diff, maxes[2] - mins[2])\n        if (arr1[idx[3][0]] > arr1[idx[3][1]]) != (arr2[idx[3][0]] > arr2[idx[3][1]]) and idx[3][0] >= idx[3][1]:\n            largest_diff = max(largest_diff, maxes[3] - mins[3])\n        return largest_diff"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'maxAbsValExpr'
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: 8374