<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 {
    long long merge(multiset<vector<long long>>& intervals) {
        vector<vector<long long>> ans;
        for(auto it=intervals.begin();it!=intervals.end();it++) {
            vector<long long> vv = (*it);
            long long beg = (vv[0]), end = (vv[1]);
            if(ans.size()==0 || ans.back()[1] < beg) {
                ans.push_back({beg,end});
            } else {
                ans[ans.size()-1][1] = max(ans[ans.size()-1][1], end);
            }
        } 
        long long s = 0;
        for(int i=0;i<ans.size();i++) {
            s += (ans[i][1]-ans[i][0]);
        }
        return s;
    }
public:
    int rectangleArea(vector<vector<int>>& rectangles) {
        vector<vector<long long>> sides;
        for(int i=0;i<rectangles.size();i++) {
            vector<int> r = rectangles[i];
            sides.push_back({r[0],0,r[1],r[3]});
            sides.push_back({r[2],1,r[1],r[3]});
        }
        sort(sides.begin(),sides.end());
        multiset<vector<long long>> intervals;
        long long ans = 0;
        long long prevX = sides[0][0];
        for(int i=0;i<sides.size();i++) {
            vector<long long> r = sides[i];
            long long x = r[0], op_cl = r[1], y1 = r[2], y2 = r[3];
            ans += merge(intervals) * (x - prevX);
            if(op_cl == 0) intervals.insert({y1,y2});
            else intervals.erase(intervals.find({y1,y2}));
            prevX = x;
        }
        return ans % (1000000007);
    }
};
14800