<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>

#define MAKE_MASK(a, b) (((long)(a) << 32) | b)

class Solution {
public:

    static constexpr int RO[]{1, 0, -1, -1, -1,  0,  1, 1};
    static constexpr int CO[]{1, 1,  1,  0, -1, -1, -1, 0};

    vector<int> gridIllumination(int n, vector<vector<int>>& lamps, vector<vector<int>>& queries) {
        // vector<int> C(n), R(n), D(2*n-1), AD(2*n-1);
        unordered_map<int, int> C, R, D, AD;
        unordered_set<long> L;

        for (auto &lamp : lamps) {
            if (!L.insert(MAKE_MASK(lamp[0], lamp[1])).second)
                continue;
            R[lamp[0]]++;
            C[lamp[1]]++;
            D[lamp[0]+lamp[1]]++;
            AD[lamp[0]-lamp[1]]++;
        }
        vector<int> ans;
        ans.reserve(queries.size());
        for (auto &Q : queries) {
            // printf("%i %i %i %i\n", R[Q[0]],
            //     C[Q[1]],
            //     D[Q[0]+Q[1]],
            //     AD[Q[0]-Q[1]]);
            ans.push_back(
                R[Q[0]] > 0 ||
                C[Q[1]] > 0 ||
                D[Q[0]+Q[1]] > 0 ||
                AD[Q[0]-Q[1]] > 0);
            
            if (L.count(MAKE_MASK(Q[0], Q[1]))) {
                R[Q[0]]--;
                C[Q[1]]--;
                D[Q[0]+Q[1]]--;
                AD[Q[0]-Q[1]]--;
                L.erase(MAKE_MASK(Q[0], Q[1]));
            }
            for (int i = 0; i < 8; ++i) {
                int r = Q[0] + RO[i], c = Q[1] + CO[i];
                // printf("erasing %i %i %i\n", r, c, L.count(MAKE_MASK(r, c)));
                if (r < 0 || r >= n || c < 0 || c >= n || !L.count(MAKE_MASK(r, c))) continue;
                R[r]--;
                C[c]--;
                D[r+c]--;
                AD[r-c]--;
                L.erase(MAKE_MASK(r, c));
            }
        }
        return ans;
    }
};
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