<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 mod = 1000000007;
    long calculate(multiset<pair<int,int>>&st, long x) {
        long ans = 0;
        long prev=-1, tt=0;
        for(auto it: st) {
            // cout<<it<<"\n";
            tt+=it.second;
            if(tt==0) {
                ans = (ans +((x%mod) * ((it.first-prev)%mod))%mod)%mod;
            }
            if(it.second==tt)
            prev = it.first;
        }
        return ans;
    }
    int rectangleArea(vector<vector<int>>& rectangles) {
        map<int, vector<pair<int,int>>>mp;
        for(int i=0;i<rectangles.size();i++) {
            mp[rectangles[i][0]].push_back({1, i});
            mp[rectangles[i][2]].push_back({0, i});
        }
        long ans=0;
        
        multiset<pair<int,int>>st;
        long cnt=-1;
        for(auto it: mp){
            if(cnt!=-1) {
                ans = (ans + calculate(st, it.first-cnt))%mod;
                // cout<<it.first<<" "<<ans<<"\n";
            }
            for(auto it1: it.second) {
                
                if(it1.first){
                    st.insert({rectangles[it1.second][1],1});
                    st.insert({rectangles[it1.second][3], -1});
                } else {
                    st.erase(st.find({rectangles[it1.second][1], 1}));
                    st.erase(st.find({rectangles[it1.second][3], -1}));
                }
            
            }
            cnt=it.first;
            
        }
        return ans;
    }
};
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