<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>

map<int,int> mergeIntervals(vector<vector<int>>& meetings)
{
    sort(begin(meetings),end(meetings));
    map<int, int> m;
    for(auto i : meetings)
    {
        int left = i[0];
        int right = i[1];
        auto it = m.lower_bound(left);
        if (it != begin(m) && prev(it)->second >= left)
        {
            it = prev(it);
            left = it->first;
        }
        for (; it != m.end() && it->first <= right; m.erase(it++))
        {
            right = max(right, it->second);
        }
        m[left] = right;
    }
    return m;
}

class Solution {
public:
    int rectangleArea(vector<vector<int>>& rec) {
        map<long long,vector<pair<int,int>>> m;
        for(int i=0;i<rec.size();i++)
        {
            m[rec[i][0]].push_back({0,i});
            m[rec[i][2]].push_back({1,i});
        }
        set<int> active;
        long long start = m.begin()->first;
        long long r = 0;
        int mod = 1e9+7;
        for(auto [k,v] : m)
        {
            long long dist = k-start;
            start = k;
            vector<vector<int>> inter;
            for(auto e : active) inter.push_back({rec[e][1],rec[e][3]});
            map<int,int> fin = mergeIntervals(inter);
            long long y = 0;
            for(auto [k1,v1] : fin) y+=(long long)(v1-k1);
            r+=dist*y;
            for(auto el : v)
            {
                if(el.first==0) active.insert(el.second);
                else active.erase(el.second);
            }
        }
        return r%mod;
    }
};
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