<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>>& rectangles) {
        long x1, y1, x2, y2;
        map<pair<int,int>,int> mp;
        x1 = y1 = INT_MAX;
        x2 = y2 = INT_MIN;
        int n = rectangles.size();
        long long individial_area = 0;
        for(int i=0;i<n;i++){
            mp[make_pair(rectangles[i][0], rectangles[i][1])]++;
            mp[make_pair(rectangles[i][0], rectangles[i][3])]++;
            mp[make_pair(rectangles[i][2], rectangles[i][1])]++;
            mp[make_pair(rectangles[i][2], rectangles[i][3])]++;

            individial_area += (long(rectangles[i][2]) - rectangles[i][0])*(long(rectangles[i][3]) - rectangles[i][1]);
            cout<<individial_area<<"\n";
            if(rectangles[i][0] < x1){
                x1 = rectangles[i][0];
                y1 = rectangles[i][1];
            }else if(rectangles[i][0] == x1 && rectangles[i][1] < y1){
                x1 = rectangles[i][0];
                y1 = rectangles[i][1];
            }
            if(rectangles[i][2] > x2){
                x2 = rectangles[i][2];
                y2 = rectangles[i][3];
            }else if(rectangles[i][2] == x2 && rectangles[i][3] > y2){
                x2 = rectangles[i][2];
                y2 = rectangles[i][3];
            }
        }
        long long area = long(x2 - x1) * (y2 - y1);

        cout<<x1<<" "<<y1<<"\n";
        cout<<x2<<" "<<y2<<"\n";
        cout<<individial_area<<" "<<area<<"\n";
        if(area != individial_area){
            return false;
        }
        int x3 = x1, y3 = y2;
        int x4 = x2, y4 = y1;
        int ones = 0;
        for(auto m: mp){
            if(m.second == 1){
                ones++;
            }
            if(m.second != 2 && m.second != 4 && m.second != 1){
                return false;
            }
        }
        return mp[make_pair(x1, y1)] == 1 && mp[make_pair(x2, y2)] == 1 && mp[make_pair(x3, y3)] == 1 && mp[make_pair(x4, y4)] == 1 && ones == 4;
    }
};
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