<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:
    def orderOfLargestPlusSign(self, n: int, mines: List[List[int]]) -> int:
        def counter_valid(m):
            block = set()
            for mine in mines:
                i = mine[0]
                j = mine[1]
                for d in [[0, 1], [1, 0], [-1, 0], [0, -1]]:
                    i_end = i+d[0]*m
                    j_end = j+d[1]*m
                    #print(i, i_end, j, j_end)
                    if d[0] == 0:
                        for jb in range(j, j_end, d[1]):
                            if i>=m-1 and i<n-(m-1) and jb>=m-1 and jb<n-(m-1):
                                block.add((i, jb))
                    else:
                        for ib in range(i, i_end, d[0]):
                            if ib>=m-1 and ib<n-(m-1) and j>=m-1 and j<n-(m-1):
                                block.add((ib, j))
            #print(block)
            if n-2*(m-1)<=0 or len(block) == (n-2*(m-1))**2:
                return False
            else:
                return True
        l = 1
        r = n+1
        while l<r-1:
            m = (l+r)//2
            f = counter_valid(m)
            print(m, f)
            if f:
                l = m
            else:
                r = m
        if l == 1:
            if counter_valid(1):
                return 1
            else:
                return 0
        else:
            return l
26401