<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) {
        const int MOD = 1e9 + 7;
        set<int> xSet, ySet;

        // Collect all unique x and y coordinates
        for (const auto& r : rectangles) {
            xSet.insert(r[0]);
            xSet.insert(r[2]);
            ySet.insert(r[1]);
            ySet.insert(r[3]);
        }

        // Convert sets to sorted vectors for easier indexing
        vector<int> xCoords(xSet.begin(), xSet.end());
        vector<int> yCoords(ySet.begin(), ySet.end());

        // Create a map for fast look-up of index in the coordinate arrays
        unordered_map<int, int> xMap, yMap;
        for (int i = 0; i < xCoords.size(); ++i) xMap[xCoords[i]] = i;
        for (int i = 0; i < yCoords.size(); ++i) yMap[yCoords[i]] = i;

        // Create a 2D grid to mark covered areas
        vector<vector<bool>> grid(xCoords.size(), vector<bool>(yCoords.size(), false));

        // Mark the grid based on the rectangles
        for (const auto& r : rectangles) {
            int x1 = xMap[r[0]], x2 = xMap[r[2]];
            int y1 = yMap[r[1]], y2 = yMap[r[3]];

            for (int i = x1; i < x2; ++i) {
                for (int j = y1; j < y2; ++j) {
                    grid[i][j] = true;
                }
            }
        }

        // Calculate the total area by iterating over the grid
        long long totalArea = 0;
        for (int i = 0; i < xCoords.size() - 1; ++i) {
            for (int j = 0; j < yCoords.size() - 1; ++j) {
                if (grid[i][j]) {
                    long long width = xCoords[i + 1] - xCoords[i];
                    long long height = yCoords[j + 1] - yCoords[j];
                    totalArea = (totalArea + width * height) % MOD;
                }
            }
        }

        return totalArea;
    }
};

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