<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>

#define ll long long
const ll M=1e9+7;
class Solution {
public:
    ll sum(multiset<pair<int,int>> &s){
        if(s.size()==0) return 0;
        auto it=s.begin();
        int l=(*it).first,r=(*it).second;
        it++;
        ll ss=0;
        while(it!=s.end()){
            if((*it).first>r){
                ss+=(r-l)%M;ss%=M;
                l=(*it).first,r=(*it).second;
            }else{
                r=max(r,(*it).second);
            }
            it++;
        }
        ss+=(r-l)%M;
        ss%=M;
        return ss;
    }
    int rectangleArea(vector<vector<int>>& rect) {
        // we have to calculate the area of rectangles 

        vector<vector<int>> st,en;
        set<int> pts;
        
        for(auto v:rect){
            st.push_back({v[0],v[1],v[3]});
            en.push_back({v[2],v[1],v[3]});
            pts.insert(v[0]);
            pts.insert(v[2]);
        }

        sort(st.begin(),st.end());
        sort(en.begin(),en.end());

        multiset<pair<int,int>> active;
        int n=st.size(),i=0,j=0;
        auto it=pts.begin();
        ll ans=0;
        while(it!=pts.end()){
            ll x1=(*it);
            while(i<n&&st[i][0]==x1){
                active.insert({st[i][1],st[i][2]});
                i++;
            }
            while(j<n&&en[j][0]==x1){
                auto it=active.find({en[j][1],en[j][2]});
                active.erase(it);
                j++;
            }
            
            it++;
            if(it==pts.end()) break;
            ll x2=(*it);
            // active is the pair of y coordinates active between x1 and x2 so we have to just merge them and calculate

            ll ss=sum(active);
            ans+=((x2-x1)*ss)%M;
            // cout<<x1<<" "<<x2<<" "<<ss<<"\n";
            ans%=M;
        }

        return ans;

    }
};
11800