<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) {
        int mod = 1000000000 + 7;
        vector<int> x;
        for (auto r : rectangles) {
            x.push_back(r[0]);
            x.push_back(r[2]);
        }
        sort(x.begin(), x.end());
        vector<int>::iterator end_unique = unique(x.begin(), x.end());
        x.erase(end_unique, x.end());
        unordered_map<int, int> x_i;
        for (int i = 0; i < x.size(); ++i) {
            x_i[x[i]] = i;
        }
        vector<int> count(x.size(), 0);
        vector<vector<int>> L;
        for (auto r : rectangles) {
            int x1 = r[0], y1 = r[1], x2 = r[2], y2 = r[3];
            L.push_back({y1, x1, x2, 1});
            L.push_back({y2, x1, x2, -1});
        }
        sort(L.begin(), L.end());
        long long cur_y = 0, cur_x_sum = 0, area = 0;
        for (auto l : L) {
            long long  y = l[0], x1 = l[1], x2 = l[2], sig = l[3];
            area = (area + (y - cur_y) * cur_x_sum) % mod;
            cur_y = y;
            for (int i = x_i[x1]; i < x_i[x2]; i++)
                count[i] += sig;
            cur_x_sum = 0;
            for (int i = 0; i < x.size(); ++i) {
                if (count[i] > 0)
                    cur_x_sum += x[i + 1] - x[i];
            }
        }
        return area;
    }
};
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