<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>> const& rectangles) const {
        vector<int> xs, ys;
        for (auto const& r : rectangles) {
            xs.push_back(r[0]);
            xs.push_back(r[2]);
            ys.push_back(r[1]);
            ys.push_back(r[3]);
        }
        sort(xs.begin(), xs.end());
        sort(ys.begin(), ys.end());
        xs.erase(unique(xs.begin(), xs.end()), xs.end());
        ys.erase(unique(ys.begin(), ys.end()), ys.end());
        unordered_map<int, int> xm, ym;
        for (int i{}; i < xs.size(); ++i) {
            xm[xs[i]] = i;
        }
        for (int i{}; i < ys.size(); ++i) {
            ym[ys[i]] = i;
        }
        vector<vector<bool>> grid(ys.size(), vector<bool>(xs.size()));
        for (auto const& r : rectangles) {
            int x0{xm[r[0]]}, x1{xm[r[2]]}, y0{ym[r[1]]}, y1{ym[r[3]]};
            for (int x{x0}; x < x1; ++x) {
                for (int y{y0}; y < y1; ++y) {
                    grid[y][x] = true;
                }
            }
        }
        int ans{};
        int const mod{1000000007};
        for (int y{}; y < ys.size(); ++y) {
            for (int x{}; x < xs.size(); ++x) {
                if (grid[y][x]) {
                    ans = (ans + (long long)(ys[y+1] - ys[y]) *
                           (xs[x+1] - xs[x])) % mod;
                }
            }
        }
        return ans;
    }
};
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