<p>You are given a 2D array of axis-aligned <code>rectangles</code>. Each <code>rectangle[i] = [x<sub>i1</sub>, y<sub>i1</sub>, x<sub>i2</sub>, y<sub>i2</sub>]</code> denotes the <code>i<sup>th</sup></code> rectangle where <code>(x<sub>i1</sub>, y<sub>i1</sub>)</code> are the coordinates of the <strong>bottom-left corner</strong>, and <code>(x<sub>i2</sub>, y<sub>i2</sub>)</code> are the coordinates of the <strong>top-right corner</strong>.</p>

<p>Calculate the <strong>total area</strong> covered by all <code>rectangles</code> in the plane. Any area covered by two or more rectangles should only be counted <strong>once</strong>.</p>

<p>Return <em>the <strong>total area</strong></em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/06/06/rectangle_area_ii_pic.png" style="width: 600px; height: 450px;" />
<pre>
<strong>Input:</strong> rectangles = [[0,0,2,2],[1,0,2,3],[1,0,3,1]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> A total area of 6 is covered by all three rectangles, as illustrated in the picture.
From (1,1) to (2,2), the green and red rectangles overlap.
From (1,0) to (2,3), all three rectangles overlap.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> rectangles = [[0,0,1000000000,1000000000]]
<strong>Output:</strong> 49
<strong>Explanation:</strong> The answer is 10<sup>18</sup> modulo (10<sup>9</sup> + 7), which is 49.
</pre>

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

<ul>
	<li><code>1 &lt;= rectangles.length &lt;= 200</code></li>
	<li><code>rectanges[i].length == 4</code></li>
	<li><code>0 &lt;= x<sub>i1</sub>, y<sub>i1</sub>, x<sub>i2</sub>, y<sub>i2</sub> &lt;= 10<sup>9</sup></code></li>
	<li><code>x<sub>i1 &lt;= </sub>x<sub>i2</sub></code></li>
	<li><code>y<sub>i1 &lt;=</sub> y<sub>i2</sub></code></li>
</ul>

class Solution {
public:
    int rectangleArea(vector<vector<int>>& rectangles) {
        vector<vector<int>> line; 
        for (auto& rectangle : rectangles) {
            int x1 = rectangle[0], y1 = rectangle[1], x2 = rectangle[2], y2 = rectangle[3]; 
            line.push_back({y1, x1, x2, 1}); 
            line.push_back({y2, x1, x2, 0}); 
        }
        
        sort(line.begin(), line.end()); 
        
        long ans = 0, val = 0; 
        int yy = 0, prev = 0; 
        multiset<vector<int>> segments; 
        for (auto& elem : line) {
            int y = elem[0], x1 = elem[1], x2 = elem[2], tf = elem[3]; 
            ans = (ans + val * (y - yy)) % 1'000'000'007;
            yy = y; 
            if (tf) segments.insert({x1, x2}); 
            else segments.erase(segments.find({x1, x2})); 
            val = prev = 0;
            for (auto& seg : segments) {
                x1 = seg[0];
                x2 = seg[1]; 
                val += max(0, x2 - max(x1, prev)); 
                prev = max(prev, x2); 
            }
        }
        return ans; 
    }
};
11500