<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 __init__(self):
        self.grid_size = 0
        self.active_lamps = set()
        self.rows = {}
        self.columns = {}
        self.diagonal1 = {}
        self.diagonal2 = {}
    def gridIllumination(self, n, lamps, queries):
        self.grid_size = n  
        self.active_lamps.clear()
        self.rows.clear()
        self.columns.clear()
        self.diagonal1.clear()
        self.diagonal2.clear()
        for lamp in lamps:
            row, column = lamp
            if (row, column) not in self.active_lamps:
                self.active_lamps.add((row, column))
                self._increment_map(self.rows, row)
                self._increment_map(self.columns, column)
                self._increment_map(self.diagonal1, row - column)
                self._increment_map(self.diagonal2, row + column)
        results = []
        for query in queries:
            row, column = query
            if (self._has_illumination(self.rows, row) or
                self._has_illumination(self.columns, column) or
                self._has_illumination(self.diagonal1, row - column) or
                self._has_illumination(self.diagonal2, row + column)):
                results.append(1)
            else:
                results.append(0)
            for x in range(row - 1, row + 2):
                for y in range(column - 1, column + 2):
                    if 0 <= x < self.grid_size and 0 <= y < self.grid_size:
                        if (x, y) in self.active_lamps:
                            self.active_lamps.remove((x, y))
                            self._decrement_map(self.rows, x)
                            self._decrement_map(self.columns, y)
                            self._decrement_map(self.diagonal1, x - y)
                            self._decrement_map(self.diagonal2, x + y)
        return results
    def _increment_map(self, count_map, key):
        if key in count_map:
            count_map[key] += 1
        else:
            count_map[key] = 1
    def _decrement_map(self, count_map, key):
        if key in count_map:
            count_map[key] -= 1
            if count_map[key] == 0:
                del count_map[key]
    def _has_illumination(self, count_map, key):
        return count_map.get(key, 0) > 0

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