<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:
    def rectangleArea(self, rectangles):
        # Define the modulo value
        MOD = 10**9 + 7
        
        # Separate x and y coordinates
        xs = sorted(set([x for rectangle in rectangles for x in rectangle[::2]]))
        ys = sorted(set([y for rectangle in rectangles for y in rectangle[1::2]]))
        
        # Map x and y coordinates to indices
        x_index = {x: i for i, x in enumerate(xs)}
        y_index = {y: i for i, y in enumerate(ys)}
        
        # Initialize the grid
        grid = [[0] * len(ys) for _ in range(len(xs))]
        
        # Fill the grid with rectangles
        for x1, y1, x2, y2 in rectangles:
            for i in range(x_index[x1], x_index[x2]):
                for j in range(y_index[y1], y_index[y2]):
                    grid[i][j] = 1
        
        # Calculate the total area
        total_area = 0
        for i in range(len(xs) - 1):
            for j in range(len(ys) - 1):
                if grid[i][j]:
                    total_area += (xs[i+1] - xs[i]) * (ys[j+1] - ys[j])
        
        return total_area % MOD

# Example usage:
solution = Solution()
rectangles = [[0,0,2,2],[1,0,2,3],[1,0,3,1]]
print(solution.rectangleArea(rectangles))  # Output: 6
16900