<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 {
    unordered_map<int, int> row, col, positiveDiag, negativeDiag;
    set<pair<int, int>> litLamps;
public:
    
    bool isLit(int i, int j){
        
        if(row[i] != 0 || col[j] != 0 || positiveDiag[i + j] != 0 || negativeDiag[i - j] != 0) return true;
        
        return false;
        
    }
    
    void switchOFF(int i, int j, int n){
        if(i < 0 || j < 0 || i >= n || j >= n) return;
        
        if(litLamps.find({i, j}) == litLamps.end()) return;
        
        litLamps.erase({i, j});
        
        row[i]--;
        col[j]--;
        positiveDiag[i + j]--;
        negativeDiag[i - j]--;
        
        return ;
    }
    
    vector<int> gridIllumination(int n, vector<vector<int>>& lamps, vector<vector<int>>& queries) {
                
        int N = lamps.size(), M = queries.size();
        vector<int> ans(M, 0);
        
        for(int i = 0; i < N; i++){
            if(litLamps.find({lamps[i][0], lamps[i][1]}) != litLamps.end()) continue;            
            litLamps.insert({lamps[i][0], lamps[i][1]});
            row[lamps[i][0]]++;
            col[lamps[i][1]]++;
            positiveDiag[lamps[i][0] + lamps[i][1]]++;
            negativeDiag[lamps[i][0] - lamps[i][1]]++;
        }
        
        for(int i = 0; i < M; i++){
            
            int a = queries[i][0], b = queries[i][1];
            
            if(isLit(a, b)){
                ans[i] = 1;
            }
            
            switchOFF(a, b, n);
            switchOFF(a, b + 1, n);
            switchOFF(a + 1, b + 1, n);
            switchOFF(a + 1, b, n);
            switchOFF(a, b - 1, n);
            switchOFF(a - 1, b - 1, n);
            switchOFF(a - 1, b, n);
            switchOFF(a - 1, b + 1, n);
            switchOFF(a + 1, b - 1, n);
            
        }
        
        return ans;
        
    }
};
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