<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:
    struct hashFunction 
    { 
    size_t operator()(const pair<int ,  
                        int> &x) const
    { 
        return x.first ^ x.second; 
    } 
    }; 
    bool isRectangleCover(vector<vector<int>>& rectangles) {
        unordered_set<pair<int,int>, hashFunction> s;
        pair<int,int>key;
        for(int i=0;i<rectangles.size();i++)
        {
            for(int j=0;j<4;j+=2)
            {
                for(int k=1;k<4;k+=2)
                {
                    key.first = rectangles[i][j];
                    key.second = rectangles[i][k];
                    if (s.find(key) == s.end())
                        s.insert(key);
                    else
                        s.erase(key);
                }
            }            
        }
        int count = 0;
        for (unordered_set<pair<int,int>>::iterator itr = s.begin(); itr != s.end();itr++)
        {
            count++;
        }
        if(count != 4)
            return false;
        int maxx = INT_MIN, maxy = INT_MIN, minx = INT_MAX, miny = INT_MAX;
        for (unordered_set<pair<int,int>>::iterator itr = s.begin(); itr != s.end();itr++)
        {
            //cout<<itr -> first<<" "<<itr -> second<<endl;
            maxx = max(maxx, itr -> first);
            maxy = max(maxy, itr -> second);
            minx = min(minx, itr -> first);
            miny = min(miny, itr -> second);
        }
        long long area = (long long)(maxx-minx) * (maxy-miny);
        for(int i=0;i<rectangles.size();i++)
        {
            //cout<<area<<endl;
            area -= (long long)(rectangles[i][2]-rectangles[i][0]) * (rectangles[i][3]-rectangles[i][1]);
        }
        //cout<<area;
        return area == 0;
    }
};
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