<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 rectangleArea(vector<vector<int>>& rectangles) {
        const int MOD = 1e9+7;
        vector<vector<int>> events;
        for(auto& i:rectangles){
            events.push_back({i[0],0,i[1],i[3]});
            events.push_back({i[2],1,i[1],i[3]});
        }
        sort(events.begin(),events.end(),[](const vector<int>& a,const vector<int> &b){
                if(a[0] == b[0]){
                    return a[2] < b[2];
                }
                return a[0] < b[0];
        });
        int ans = 0,prev = INT_MIN;
        multiset<pair<int,int>> mp;
        auto get_area = [&](int x) -> long long int {
            long long int area = 0;
            long long int prev = INT_MIN;
            int sum = 0;
            for(auto i:mp){
                sum += i.second;
                if(sum == i.second){
                    prev = i.first;
                }
                if(sum == 0){
                    area = (area+x*(i.first-prev))%MOD;
                }
            }
            return area;
        };
        for(auto i:events){
            if(prev != INT_MIN){
                ans = (ans+get_area(i[0]-prev))%MOD;
            }
            if(i[1]){
                mp.erase(mp.find({i[2],1}));
                mp.erase(mp.find({i[3],-1}));
            }else{
                mp.insert({i[2],1});
                mp.insert({i[3],-1});
            }
            prev = i[0];
        }
        return ans;
    }
};
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