You are given two images img1 and img2 both of size n x n, represented as binary, square matrices of the same size. (A binary matrix has only 0s and 1s as values.)
We translate one image however we choose (sliding it left, right, up, or down any number of units), and place it on top of the other image.  After, the overlap of this translation is the number of positions that have a 1 in both images.
(Note also that a translation does not include any kind of rotation.)
What is the largest possible overlap?
 
Example 1:

Input: img1 = [[1,1,0],[0,1,0],[0,1,0]], img2 = [[0,0,0],[0,1,1],[0,0,1]]
Output: 3
Explanation: We slide img1 to right by 1 unit and down by 1 unit.

The number of positions that have a 1 in both images is 3. (Shown in red)


Example 2:
Input: img1 = [[1]], img2 = [[1]]
Output: 1

Example 3:
Input: img1 = [[0]], img2 = [[0]]
Output: 0

 
Constraints:

n == img1.length
n == img1[i].length
n == img2.length 
n == img2[i].length
1 <= n <= 30
img1[i][j] is 0 or 1.
img2[i][j] is 0 or 1.

```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 = '#\n# @lc app=leetcode id=835 lang=python3\n#\n# [835] Image Overlap\n#\n\n# @lc code=start\nfrom functools import lru_cache\n\n@lru_cache\ndef countBits(n):\n    if n == 0:\n        return 0\n    return (n & 1) + countBits(n >> 1)\n\nclass Solution:\n    def stateCompress(self, img):\n        n, m = len(img), len(img[0])\n        rows = [0 for _ in range(n)]\n        for i, row in enumerate(img):\n            for j, e in enumerate(row):\n                rows[i] = (rows[i] << 1) + e\n        return n, m, rows\n    \n    \n    def largestOverlap(self, A: List[List[int]], B: List[List[int]]) -> int:\n        n, m, rA = self.stateCompress(A)\n        _, _, rB = self.stateCompress(B)\n\n        @lru_cache\n        def shift(xAs, xAe, xBs, xBe, dy):\n            if dy > 0:\n                ret = list(countBits((e1 << dy) & e2) for e1, e2 in zip(rA[xAs:xAe], rB[xBs:xBe]))\n                return ret\n            else:\n                dy = -dy\n                ret = list(countBits((e1 >> dy) & e2) for e1, e2 in zip(rA[xAs:xAe], rB[xBs:xBe]))\n                return ret\n\n        print((rA, rB))\n        maxOverLap = 0\n        for dr in range(n):\n            for dc in range(m):\n                maxOverLap = max(maxOverLap, sum(shift(dr, n, 0, n - dr, dc)))\n                maxOverLap = max(maxOverLap, sum(shift(0, dr, n - dr, n, dc)))\n                maxOverLap = max(maxOverLap, sum(shift(dr, n, 0, n - dr, -dc)))\n                maxOverLap = max(maxOverLap, sum(shift(0, dr, n - dr, n, -dc)))\n        return maxOverLap\n                \n                \n# @lc code=end\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'largestOverlap'
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: 25043