Largest Plus Sign

In an n x n binary grid, each cell is either 1 or 0. A plus sign of order k (k >= 1) is centered at some cell and consists of four arms of equal length extending up, down, left, and right. More precisely, a plus sign of order k on cell (r, c) exists if and only if all cells (r, c), (r - d, c), (r + d, c), (r, c - d), (r, c + d) are all 1 for every d from 0 to k-1. In other words, the arms extend k-1 cells away from the center, so the total length of each arm is k cells (including the center). You are given an integer n and a list of mine coordinates where the cell is 0; all other cells are 1. Implement the function `largest_plus_sign(n: int, mines: list[tuple[int, int]]) -> int` that returns the order of the largest plus sign that can be found in the grid. If no plus sign of order 1 exists (i.e., no cell is 1), return 0. Note: Coordinates are zero-indexed (0 <= row, col < n). Mines are given as a list of (row, col) tuples, and they are guaranteed to be distinct and within bounds.

>>> largest_plus_sign(5, [(4, 2)])
2
>>> largest_plus_sign(1, [])
1
>>> largest_plus_sign(1, [(0, 0)])
0
>>> largest_plus_sign(2, [])
1