"""
You are given two images, img1 and img2, represented as binary, square matrices of size n x n. A binary matrix has only 0s and 1s as values.

We translate one image however we choose by sliding all the 1 bits left, right, up, and/or down any number of units. We then place it on top of the other image. We can then calculate the overlap by counting the number of positions that have a 1 in both images.
Note also that a translation does not include any kind of rotation. Any 1 bits that are translated outside of the matrix borders are erased.
Return 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 translate 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 == img1[i].length
n == img2.length == img2[i].length
1 <= n <= 30
img1[i][j] is either 0 or 1.
img2[i][j] is either 0 or 1.
"""
import collections
from typing import List


class ImageOverlap:
    def largestOverlap(self, A: List[List[int]], B: List[List[int]]) -> int:
        points_A = [(r, c) for r, row in enumerate(A) for c, val in enumerate(row) if val]
        points_B = [(r, c) for r, row in enumerate(B) for c, val in enumerate(row) if val]
        cnt = collections.Counter((ar - br, ac - bc) for ar, ac in points_A for br, bc in points_B)
        return max(cnt.values() or [0])