<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 get_grid():
            grid = [[0] * n for _ in range(n)]
            for lamp in lamps:
                x, y = lamp
                m1 = min(x, y)
                x1, y1 = x - m1, y - m1
                m2 = min(n - x - 1, y)
                x2, y2 = x + m2, y - m2
                #print(f"x2: {x2}, y2: {y2}, m2: {m2}")
                for i in range(n):
                    grid[x][i] = 1
                    grid[i][y] = 1
                    if 0 <= x1 < n and 0 <= y1 < n:
                        grid[x1][y1] = 1
                        x1 += 1
                        y1 += 1
                    if 0 <= x2 <= n and 0 <= y2 < n:
                        grid[x2][y2] = 1
                        x2 -= 1
                        y2 += 1
            
            return grid

        def calculate(point):
            x = point[0]
            y = point[1]
            m1 = min(x, y)
            x1, y1 = x - m1, y - m1
            m2 = min(n - x - 1, y)
            x2, y2 = x + m2, y - m2

            return x, y, (x1, y1), (x2, y2)

        def get_counts(lamps):
            rows = {}
            cols = {}
            decd = {}
            incd = {}
            for lamp in lamps:
                row, col, dec, inc = calculate(lamp)
                rows.setdefault(row, 0)
                rows[row] += 1

                cols.setdefault(col, 0)
                cols[col] += 1

                decd.setdefault(dec, 0)
                decd[dec] += 1

                incd.setdefault(inc, 0)
                incd[inc] += 1
            
            return rows, cols, decd, incd


        out = []

        rows, cols, decd, incd = get_counts(lamps)
        lamp_count = {}
        for x, y in lamps:
            lamp = (x, y)
            lamp_count.setdefault(lamp, 0)
            lamp_count[lamp] += 1

        for query in queries:
            row, col, dec, inc = calculate(query)
            if (
                rows.get(row, 0) > 0 or
                cols.get(col, 0) > 0 or
                decd.get(dec, 0) > 0 or
                incd.get(inc, 0) > 0
            ):
                out.append(1)
            else:
                out.append(0)
            
            for i in range(row - 1, row + 2):
                for j in range(col - 1, col + 2):
                    lamp = (i, j)
                    if lamp in lamp_count:
                        lc = lamp_count.pop(lamp)
                        row, col, dec, inc = calculate(lamp)
                        rows[row] -= lc
                        cols[col] -= lc
                        decd[dec] -= lc
                        incd[inc] -= lc
        
        return out

            
                



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