<p>There is a 2D <code>grid</code> of size <code>n x n</code> where each cell of this grid has a lamp that is initially <strong>turned off</strong>.</p>

<p>You are given a 2D array of lamp positions <code>lamps</code>, where <code>lamps[i] = [row<sub>i</sub>, col<sub>i</sub>]</code> indicates that the lamp at <code>grid[row<sub>i</sub>][col<sub>i</sub>]</code> is <strong>turned on</strong>. Even if the same lamp is listed more than once, it is turned on.</p>

<p>When a lamp is turned on, it <strong>illuminates its cell</strong> and <strong>all other cells</strong> in the same <strong>row, column, or diagonal</strong>.</p>

<p>You are also given another 2D array <code>queries</code>, where <code>queries[j] = [row<sub>j</sub>, col<sub>j</sub>]</code>. For the <code>j<sup>th</sup></code> query, determine whether <code>grid[row<sub>j</sub>][col<sub>j</sub>]</code> is illuminated or not. After answering the <code>j<sup>th</sup></code> query, <strong>turn off</strong> the lamp at <code>grid[row<sub>j</sub>][col<sub>j</sub>]</code> and its <strong>8 adjacent lamps</strong> if they exist. A lamp is adjacent if its cell shares either a side or corner with <code>grid[row<sub>j</sub>][col<sub>j</sub>]</code>.</p>

<p>Return <em>an array of integers </em><code>ans</code><em>,</em><em> where </em><code>ans[j]</code><em> should be </em><code>1</code><em> if the cell in the </em><code>j<sup>th</sup></code><em> query was illuminated, or </em><code>0</code><em> if the lamp was not.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/illu_1.jpg" style="width: 750px; height: 209px;" />
<pre>
<strong>Input:</strong> n = 5, lamps = [[0,0],[4,4]], queries = [[1,1],[1,0]]
<strong>Output:</strong> [1,0]
<strong>Explanation:</strong> We have the initial grid with all lamps turned off. In the above picture we see the grid after turning on the lamp at grid[0][0] then turning on the lamp at grid[4][4].
The 0<sup>th</sup>&nbsp;query asks if the lamp at grid[1][1] is illuminated or not (the blue square). It is illuminated, so set ans[0] = 1. Then, we turn off all lamps in the red square.
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/illu_step1.jpg" style="width: 500px; height: 218px;" />
The 1<sup>st</sup>&nbsp;query asks if the lamp at grid[1][0] is illuminated or not (the blue square). It is not illuminated, so set ans[1] = 0. Then, we turn off all lamps in the red rectangle.
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/illu_step2.jpg" style="width: 500px; height: 219px;" />
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 5, lamps = [[0,0],[4,4]], queries = [[1,1],[1,1]]
<strong>Output:</strong> [1,1]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 5, lamps = [[0,0],[0,4]], queries = [[0,4],[0,1],[1,4]]
<strong>Output:</strong> [1,1,0]
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>9</sup></code></li>
	<li><code>0 &lt;= lamps.length &lt;= 20000</code></li>
	<li><code>0 &lt;= queries.length &lt;= 20000</code></li>
	<li><code>lamps[i].length == 2</code></li>
	<li><code>0 &lt;= row<sub>i</sub>, col<sub>i</sub> &lt; n</code></li>
	<li><code>queries[j].length == 2</code></li>
	<li><code>0 &lt;= row<sub>j</sub>, col<sub>j</sub> &lt; n</code></li>
</ul>

class Solution:
    def gridIllumination(self, n: int, lamps: List[List[int]], queries: List[List[int]]) -> List[int]:
        def check(i, j, dRow, dCol, dDiagS, dDiagP):
            if (i in dRow and dRow[i] > 0) or (j in dCol and dCol[j] > 0) or (
                    i + j in dDiagS and dDiagS[i + j] > 0) or (
                    i - j in dDiagP and dDiagP[i - j] > 0):
                return True
            return False
        
        def decrement(i, j, dRow, dCol, dDiagS, dDiagP):
            dRow[i] -= 1
            dCol[j] -= 1
            dDiagS[i + j] -= 1
            dDiagP[i - j] -= 1
        
        my_set = set()
        dRow, dCol, dDiagS, dDiagP = {}, {}, {}, {} 
        for i in range(len(lamps)):
            if (lamps[i][0], lamps[i][1]) not in my_set:
                if lamps[i][0] not in dRow:
                    dRow[lamps[i][0]] = 1
                else:
                    dRow[lamps[i][0]] += 1
                if lamps[i][1] not in dCol:
                    dCol[lamps[i][1]] = 1
                else:
                    dCol[lamps[i][1]] += 1
                if sum(lamps[i]) not in dDiagS:
                    dDiagS[sum(lamps[i])] = 1
                else:
                    dDiagS[sum(lamps[i])] += 1
                if lamps[i][0] - lamps[i][1] not in dDiagP:
                    dDiagP[lamps[i][0] - lamps[i][1]] = 1
                else:
                    dDiagP[lamps[i][0] - lamps[i][1]] += 1
                my_set.add((lamps[i][0], lamps[i][1]))
        ans = []
        directions = [(-1, -1), (-1, 0), (0, -1), (0, 0), (0, 1), (1, 0), (1, 1), (1, -1), (-1, 1)]
        for i in range(len(queries)):
            # check if it's lighted up
            if check(queries[i][0], queries[i][1], dRow, dCol, dDiagS, dDiagP):
                ans.append(1)
                # check for lamp at 9 blocks
                for x in directions:
                    if (queries[i][0]+x[0], queries[i][1]+x[1]) in my_set:
                        decrement(queries[i][0]+x[0], queries[i][1]+x[1], dRow, dCol, dDiagS, dDiagP)
                        my_set.remove((queries[i][0]+x[0], queries[i][1]+x[1]))
            else:
                ans.append(0)
        return ans
33800