<p>Given an array <code>rectangles</code> where <code>rectangles[i] = [x<sub>i</sub>, y<sub>i</sub>, a<sub>i</sub>, b<sub>i</sub>]</code> represents an axis-aligned rectangle. The bottom-left point of the rectangle is <code>(x<sub>i</sub>, y<sub>i</sub>)</code> and the top-right point of it is <code>(a<sub>i</sub>, b<sub>i</sub>)</code>.</p>

<p>Return <code>true</code> <em>if all the rectangles together form an exact cover of a rectangular region</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/27/perectrec1-plane.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> rectangles = [[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]
<strong>Output:</strong> true
<strong>Explanation:</strong> All 5 rectangles together form an exact cover of a rectangular region.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/27/perfectrec2-plane.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> rectangles = [[1,1,2,3],[1,3,2,4],[3,1,4,2],[3,2,4,4]]
<strong>Output:</strong> false
<strong>Explanation:</strong> Because there is a gap between the two rectangular regions.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/27/perfecrrec4-plane.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> rectangles = [[1,1,3,3],[3,1,4,2],[1,3,2,4],[2,2,4,4]]
<strong>Output:</strong> false
<strong>Explanation:</strong> Because two of the rectangles overlap with each other.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= rectangles.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>rectangles[i].length == 4</code></li>
	<li><code>-10<sup>5</sup> &lt;= x<sub>i</sub> &lt; a<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>5</sup> &lt;= y<sub>i</sub> &lt; b<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    bool isRectangleCover(vector<vector<int>>& r) {
        int a = INT_MAX,b = INT_MAX,c = INT_MIN,d = INT_MIN;
        long long int tot = 0,check = 0;

        set<pair<int,int>>corner;
        
        for(auto it : r){

            a = min(a,it[0]);
            b = min(b,it[1]);
            c = max(c,it[2]);
            d = max(d,it[3]);

            check += (long long int)abs(it[0]-it[2])*abs(it[1]-it[3]);

            pair<int,int> p1 = {it[0],it[1]} ,p2 = {it[0],it[3]} ,p3 = {it[2],it[1]} ,p4 = {it[2],it[3]};
            
            // .first returns an iterator for that element and .second return false if that element 
            // already exist and return true if element is inserted

            if(!corner.insert(p1).second) corner.erase(p1);
            if(!corner.insert(p2).second) corner.erase(p2);
            if(!corner.insert(p3).second) corner.erase(p3);
            if(!corner.insert(p4).second) corner.erase(p4);
        }
        if(corner.size() != 4 || corner.count({a,b}) == 0 || corner.count({a,d}) == 0 || corner.count({c,b}) == 0 || corner.count({c,d}) == 0)
            return 0;
        tot = (long long int)abs(a-c)*abs(b-d);
        return tot == check;
    }
};
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