<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
{
public:

    void turnOffAdjacent(int i,
                         int j,
                         int n,
                         std::unordered_multiset<int> &includeRows,
                         std::unordered_multiset<int> &includeColumns,
                         std::unordered_multiset<int> &includeAntiDiagonals,
                         std::unordered_multiset<int> &includeDiagonals,
                         std::set<std::pair<int, int>> &lampMap)
    {
        long long dx[] = { -1, 0, 1 };
        long long dy[] = { -1, 0, 1 };
        for (long long x : dx)
        {
            for (long long y : dy)
            {
                auto u = x + i;
                auto v = y + j;
                auto thisIsA_ShittyAssProblem = lampMap.find({ u, v });
                if (thisIsA_ShittyAssProblem != std::end(lampMap))
                {
                    lampMap.erase(thisIsA_ShittyAssProblem);
                    auto it = includeRows.find(u);
                    if (it != std::end(includeRows))
                    {
                        includeRows.erase(it);
                    }

                    it = includeColumns.find(v);
                    if (it != std::end(includeColumns))
                    {
                        includeColumns.erase(it);
                    }
                    
                    it = includeAntiDiagonals.find(u + v);
                    if (it != std::end(includeAntiDiagonals))
                    {
                        includeAntiDiagonals.erase(it);
                    }

                    it = includeDiagonals.find(u - v);
                    if (it != std::end(includeDiagonals))
                    {
                        includeDiagonals.erase(it);
                    }
                }
            }
        }
    }


    std::vector<int> gridIllumination(int n, std::vector<std::vector<int>> &lamps, std::vector<std::vector<int>> &queries)
    {
        std::unordered_multiset<int> includeRows;
        std::unordered_multiset<int> includeAntiDiagonals;
        std::unordered_multiset<int> includeDiagonals;
        std::unordered_multiset<int> includeColumns;
        std::set<std::pair<int, int>> lampMap;
        for (int i = 0; i < lamps.size(); ++i)
        {
             auto x = lamps[i][0];
             auto y = lamps[i][1];
             if (lampMap.count({ x, y }) != 0)
             {
                continue;
             }
             includeRows.insert(x);
             includeColumns.insert(y);
             includeAntiDiagonals.insert(x + y);
             includeDiagonals.insert(x - y);
             lampMap.insert({ x, y });
        }

        std::vector<int> answer;
        for (auto query : queries)
        {
            auto x = query[0];
            auto y = query[1];
            auto index = static_cast<long long>(x) * n + y;
            if (  includeRows.count(x) != 0
               || includeColumns.count(y) != 0
               || includeAntiDiagonals.count(x + y) != 0
               || includeDiagonals.count(x - y) != 0)
            {
                answer.push_back(1);
            }
            else
            {
                answer.push_back(0);
            }
            turnOffAdjacent(x,
                            y,
                            n,
                            includeRows,
                            includeColumns,
                            includeAntiDiagonals,
                            includeDiagonals,
                            lampMap);
        }
        return answer;
    }
};

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