<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:
    unordered_map<long long, long> r, c, nd, pd;
    unordered_map<long long, bool> on;
    inline void ill(int i, int j, int n) {
        r[i]++, c[j]++, nd[i-j]++, pd[i+j]++, on[(long long)i*n+j] = true;
    }
    void help(vector<int> &res, int i, int j, int n, int co) {
        bool x = (r[i] > 0 || c[j] > 0 || nd[i-j] > 0 || pd[i+j] > 0);
        cout << r[i] << " "<< c[j] << " "<< nd[i-j] << " " << pd[i+j] << endl;
        if (x) res.push_back(1);
        else res.push_back(0);
        //if (co == n - 1) return;
        int m[9][2] = {{0,1}, {0,-1}, {1,0}, {-1,0}, {1,1}, {1,-1}, {-1,1}, {-1,-1}, {0,0}};
        for (int k = 0; k < 9; k++) {
            int a = i + m[k][0], b = j + m[k][1];
            if (a >= 0 && b >= 0 && a < n && b < n && on[(long long)a * n + b]) {
                r[a]--, c[b]--, nd[a-b]--, pd[a+b]--;
                on[a * n + b] = false;
            }
        }
    }void print() {
        cout << "r : " ;
        for (auto it:r) cout << "(" << it.first << ", " <<  it.second << ")" << " ";
        cout << endl;
        cout << "c : " ;
        for (auto it:c) cout << "(" << it.first << ", " <<  it.second << ")" << " ";
        cout << endl;
        cout << "nd : " ;
        for (auto it:nd) cout << "(" << it.first << ", " <<  it.second << ")" << " ";
        cout << endl;
        cout << "pd : " ;
        for (auto it:pd) cout << "(" << it.first << ", " <<  it.second << ")" << " ";
        cout << endl;
        cout << "on : " ;
        for (auto it:on) cout << "(" << it.first << ", " <<  it.second << ")" << " ";
        cout << endl;
    }
    vector<int> gridIllumination(int n, vector<vector<int>>& lamps, vector<vector<int>>& queries) {
        if (!queries.size() || n==0 || !lamps.size()) return {};
        vector<int> res;
        int co=0;
        for (auto it:lamps) {
            if (!on[(long long)it[0]*n+it[1]])
            ill(it[0], it[1], n);
        }
        for (auto it:queries) {
            help(res, it[0], it[1], n, co);
            //print
            co++;
        }
        return res;
    }
};

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