<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:
    vector<int> gridIllumination(int n, vector<vector<int>>& l, vector<vector<int>>& q) {
                vector<int> res;
        unordered_map<int, int> h;
        unordered_map<int, int> v;

        unordered_map<int, int> sp;
        unordered_map<int, int> sn;
        unordered_set<long long> ls;

        for(vector<int>& row : l) {
            if(ls.find((long long) row[0] * (long long)1e9 + row[1]) != ls.end())
            {
                continue;
            }

            ls.insert((long long) row[0] * (long long)1e9 + row[1]);
            h[row[0]]++;
            v[row[1]]++;

            sp[row[0] - row[1]]++;
            sn[row[0] + row[1]]++;
        }

        for(vector<int>& row : q) {
            bool have_light = false;
            bool hh = h.find(row[0]) != h.end();
            bool vv = v.find(row[1]) != v.end();
            bool spp = sp.find(row[0] - row[1]) != sp.end();
            bool snn = sn.find(row[0] + row[1]) != sn.end();
            if(hh || vv || spp || snn ) {
                have_light = true;
            }
            res.push_back(have_light);

            int ii = row[0];
            int jj = row[1];
            for(int i = ii - 1; i < ii + 2; i++) {

                for(int j = jj - 1; j < jj + 2; j++) {
                    if(i < 0 || j < 0 || i >= n || j >= n) {
                        continue;
                    }
                    if(ls.find((long long) i * (long long)1e9 + j) == ls.end()) {
                        continue;
                    }
                    ls.erase((long long) i * (long long)1e9 + j);
                    h[i]--;
                    if(h[i] == 0) {
                        h.erase(i);
                    }
                    v[j]--;

                    if(v[j] == 0) {
                        v.erase(j);
                    }

                    sp[i - j]--;

                    if(sp[i - j] <= 0) {
                        sp.erase(i - j);
                    }

                    sn[j + i]--;
                    if(sn[j + i] <= 0) {
                        sn.erase(j + i);
                    }
                }
            }

        }
        return res;
    }
};;

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