<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 {
    struct side{
        int x;
        bool start;
        pair<int,int> y;
    };

    int get_length(multiset<pair<int,int>>& ycords){
        int len = 0;

        int start = ycords.begin()->first;
        int end = ycords.begin()->second;

        for(auto& p: ycords){
            if(p.first <= end){
                end = max(end, p.second);
            }
            else{
                len += (end-start);
                start = p.first, end = p.second;
            }
        }

        len += (end-start);

        return len;
    }

public:
    int rectangleArea(vector<vector<int>>& rectangles) {
        vector<side> sides;

        for(auto& v: rectangles){
            side start{v[0], true, {v[1], v[3]}};
            side end{v[2], false, {v[1], v[3]}};

            sides.push_back(start);
            sides.push_back(end);
        }

        sort(begin(sides), end(sides), [](const auto& a, const auto& b){
            return a.x < b.x;
        });

        int i = 0, prev;

        long long area = 0;

        const int MOD = 1e9+7;

        bool has_open = false;

        multiset<pair<int,int>> ycords;

        while(i<sides.size()){
            int curr = sides[i].x;

            if(has_open){
                int y_len = get_length(ycords);

                area += 1ll*(curr-prev)*y_len;

                area%=MOD;
            }

            while(i<sides.size() && sides[i].x == curr){
                if(sides[i].start){
                    ycords.insert(sides[i].y);
                }
                else{
                    ycords.erase(ycords.find(sides[i].y));
                }

                i++;
            }

            if(ycords.size() > 0 && !has_open){
                has_open = true;
            }
            else if(ycords.size() == 0){
                has_open = false;
            }

            prev = curr;
        }

        return area;
    }
};
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