You are given an integer n representing the size of an n by n binary grid. All cells in the grid are initially set to $1$, except for the coordinates provided in the $2$D array mines, where each element mines[i] = [x_i, y_i] indicates that the cell at (x_i, y_i) contains a $0$.

An axis aligned plus sign of order k centered at cell (r, c) consists of grid[r][c] = 1 along with four extending arms of length $k - 1$ in the up, down, left, and right directions, where every cell along all four arms also contains a $1$. Note that if $k = 1$, the plus sign consists of just a single cell containing $1$.

Return the order of the largest plus sign that can be formed in the grid. If no valid plus sign exists, return $0$.

Constraints:

• $1 \leq$ n $\leq 500$

• $1 \leq$ mines.length $\leq 5000$

• $0 \leq$ x_i, y_i $<$ n

• All the pairs (x_i, y_i) are unique.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.