<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 Intervals{
public:
    multiset<pair<int,int>>intervals;
    Intervals(){
        
    }
    void add(int left,int right){
        intervals.insert({left,right});
    }
    void remove(int left,int right){
        auto it = intervals.find({left,right});
        if(it!=intervals.end())intervals.erase(it);
    }
    int getLen(){
        int len=0;
        pair<int,int>prev = {-1,-1};
        for(auto &[l,r]:intervals){
            if(prev.first==-1){
                prev = {l,r};
                continue;
            }
            if(prev.second<l){
                len+= (prev.second-prev.first);
                prev = {l,r};
            }else {
                prev.first = min(prev.first,l);
                prev.second = max(prev.second,r);
            }
        }
        if(prev.first!=-1)len+= (prev.second-prev.first);
        return len;
    }
};
class Solution {
public:
    int rectangleArea(vector<vector<int>>& rectangles) {
        map<int,vector<vector<int>>>mp;
        for(auto rectangle:rectangles){
            int x1 = rectangle[0];
            int y1 = rectangle[1];
            int x2 = rectangle[2];
            int y2 = rectangle[3];
            mp[x1].push_back({0,y1,y2});
            mp[x2].push_back({1,y1,y2});
        }
        const int mod = 1e9+7;
        Intervals active;
        int prevX = 0;
        int area = 0;
        for(auto &i:mp){
            int x = i.first;
            int len = active.getLen();
            area = (area + (x-prevX)*1LL*len%mod)%mod;
            prevX = x;
            for(auto &e:i.second){
                if(e[0]==1){
                    active.remove(e[1],e[2]);
                }else active.add(e[1],e[2]);
            }
        }
        
        return area;
    }
};







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