<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:
    static constexpr int M = 1e9 + 7;
    long long add(const vector<vector<int>>& recs, int begin, int end, int x1, int y1,
            int x2, int y2) {
        if (x1 >= x2 || y1 >= y2)
            return 0;
        for (int i = begin; i < end; ++i) {
            int b_x1 = recs[i][0], b_y1 = recs[i][1], b_x2 = recs[i][2],
                b_y2 = recs[i][3];
            int i_x1 = max(x1, b_x1), i_y1 = max(y1, b_y1),
                i_x2 = min(x2, b_x2), i_y2 = min(y2, b_y2);
            if (i_x2 > i_x1 && i_y2 > i_y1) {
                long long ret = 0;
                return (add(recs, begin + 1, end, x1, y1, i_x1, y2) +
                        add(recs, begin + 1, end, i_x1, i_y2, i_x2, y2) +
                        add(recs, begin + 1, end, i_x1, y1, i_x2, i_y1) +
                        add(recs, begin + 1, end, i_x2, y1, x2, y2)) %
                       M;
            }
        }
        long long w = x2 - x1;
        long long h = y2 - y1;
        return (w * h) % M;
    }
    int rectangleArea(vector<vector<int>>& rectangles) {
        long long ret = 0;
        for (int i = 0, n = rectangles.size(); i < n; ++i) {
            ret =
                (ret + add(rectangles, 0, i, rectangles[i][0], rectangles[i][1],
                           rectangles[i][2], rectangles[i][3])) %
                M;
        }
        return ret;
    }
};
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