<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:
    const int MOD = 1e9 + 7;

    int rectangleArea(vector<vector<int>>& rectangles) {
        vector<vector<int>> events;
        
        // Populate events array with all x-coordinate events (start and end)
        for (auto& rect : rectangles) {
            events.push_back({rect[1], 1, rect[0], rect[2]}); // Start event
            events.push_back({rect[3], -1, rect[0], rect[2]}); // End event
        }
        
        // Sort events array based on y-coordinate
        sort(events.begin(), events.end());
        
        long long result = 0;
        long long prev_y = 0;
        multiset<vector<int>> active_rects;
        
        for (auto& event : events) {
            int y = event[0];
            int type = event[1];
            int x1 = event[2];
            int x2 = event[3];
            
            result = (result + (y - prev_y) * calculateActiveArea(active_rects)) % MOD;
            
            if (type == 1) {
                active_rects.insert({x1, x2});
            } else {
                active_rects.erase(active_rects.find({x1, x2}));
            }
            
            prev_y = y;
        }
        
        return result;
    }
    
    long long calculateActiveArea(multiset<vector<int>>& active_rects) {
        long long result = 0;
        int cur_x = -1;
        
        for (auto& rect : active_rects) {
            int x1 = rect[0];
            int x2 = rect[1];
            cur_x = max(cur_x, x1);
            result = (result + max(0, x2 - cur_x)) % MOD;
            cur_x = max(cur_x, x2);
        }
        
        return result;
    }
};

11600