# Largest Square of Ones Implement `largest_square_area(matrix: list[list[int]]) -> int`. Given a rectangular binary matrix, return the area of the largest axis-aligned square whose cells are all `1`. ### Input Domain - `0 <= len(matrix) <= 2,000`. - If the matrix is nonempty, every row has the same length between `0` and `2,000`. - The matrix contains at most `1,000,000` cells. - Every cell is exactly `0` or `1`. ### Output Rules - Return the square's area, not its side length. - Return `0` for an empty matrix, a matrix with empty rows, or a matrix containing no `1`. - If several largest squares exist, return their shared area. ### Constraints - Target time is `O(rows * columns)`. - Additional space may be reduced to `O(columns)`. ### Examples #### Example 1 Input: `matrix = [[1,0,1,0,0],[1,0,1,1,1],[1,1,1,1,1],[1,0,0,1,0]]` Output: `4` #### Example 2 Input: `matrix = [[0,0],[0,0]]` Output: `0` ```hint Describe squares by their lower-right corner For a cell containing one, consider what the neighboring partial answers imply about a square ending at that cell. ```