<p>You are given an integer <code>n</code>. You have an <code>n x n</code> binary grid <code>grid</code> with all values initially <code>1</code>&#39;s except for some indices given in the array <code>mines</code>. The <code>i<sup>th</sup></code> element of the array <code>mines</code> is defined as <code>mines[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> where <code>grid[x<sub>i</sub>][y<sub>i</sub>] == 0</code>.</p>

<p>Return <em>the order of the largest <strong>axis-aligned</strong> plus sign of </em>1<em>&#39;s contained in </em><code>grid</code>. If there is none, return <code>0</code>.</p>

<p>An <strong>axis-aligned plus sign</strong> of <code>1</code>&#39;s of order <code>k</code> has some center <code>grid[r][c] == 1</code> along with four arms of length <code>k - 1</code> going up, down, left, and right, and made of <code>1</code>&#39;s. Note that there could be <code>0</code>&#39;s or <code>1</code>&#39;s beyond the arms of the plus sign, only the relevant area of the plus sign is checked for <code>1</code>&#39;s.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/13/plus1-grid.jpg" style="width: 404px; height: 405px;" />
<pre>
<strong>Input:</strong> n = 5, mines = [[4,2]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> In the above grid, the largest plus sign can only be of order 2. One of them is shown.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/13/plus2-grid.jpg" style="width: 84px; height: 85px;" />
<pre>
<strong>Input:</strong> n = 1, mines = [[0,0]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There is no plus sign, so return 0.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>1 &lt;= mines.length &lt;= 5000</code></li>
	<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt; n</code></li>
	<li>All the pairs <code>(x<sub>i</sub>, y<sub>i</sub>)</code> are <strong>unique</strong>.</li>
</ul>

class Solution {
public:
void updateGridsWithMines(vector<vector<int>>& arr, vector<vector<vector<int>>>& grids, const vector<vector<int>>& mines) {
    int n = arr.size();
    
    // Set zeros in arr based on mines
    for (auto i : mines) {
        arr[i[0]][i[1]] = 0;
    }
    
    // Copy arr to all 4 grids
    for (int k = 0; k < 4; ++k) {
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                grids[k][i][j] = arr[i][j];
            }
        }
    }
}
    int orderOfLargestPlusSign(int n, vector<vector<int>>& mines) 
    {
        vector<vector<int>> arr(n,vector<int> (n,1));
        vector<vector<vector<int>>> grid(4,vector<vector<int>>(n, vector<int>(n, 1)));
        updateGridsWithMines(arr, grid, mines);
        for(int i=n-1;i>-1;--i)
        {
            for(int j=1;j<n;++j)
            {
                if(grid[0][i][j]!=0) grid[0][i][j]+=grid[0][i][j-1];
            }
        }
        for(int i=n-1;i>-1;--i)
        {
            for(int j=n-2;j>-1;--j)
            {
                if(grid[1][i][j]!=0) grid[1][i][j]+=grid[1][i][j+1];
            }
        }
        for(int j=0;j<n;++j)
        {
            for(int i=1;i<n;++i)
            {
                if(grid[2][i][j]!=0) grid[2][i][j]+=grid[2][i-1][j];
            }
        }
        for(int j=0;j<n;++j)
        {
            for(int i=n-2;i>-1;--i)
            {
                if(grid[3][i][j]!=0) grid[3][i][j]+=grid[3][i+1][j];
            }
        }int m=0;
        for(int i=0;i<n;++i)
        {
            for(int j=0;j<n;++j)
            {
                int temp=grid[0][i][j];
                for(int k=1;k<4;++k)
                {
                    temp=min(temp,grid[k][i][j]);
                }
                m=max(temp,m);
            }
        }return m;
    }
};
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