<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
        
        # Initialize lists for storing x and y coordinates
        x_coordinates = set()
        y_coordinates = set()
        
        # Collect all x and y coordinates
        for rect in rectangles:
            x1, y1, x2, y2 = rect
            x_coordinates.add(x1)
            x_coordinates.add(x2)
            y_coordinates.update([y1, y2])
        
        # Sort the x and y coordinates for processing
        x_coordinates = sorted(x_coordinates)
        y_coordinates = sorted(y_coordinates)
        
        # Create a 2D array to represent the grid
        grid = [[0] * len(y_coordinates) for _ in range(len(x_coordinates))]
        
        # Fill the grid based on rectangles
        for rect in rectangles:
            x1, y1, x2, y2 = rect
            x1_index = x_coordinates.index(x1)
            x2_index = x_coordinates.index(x2)
            y1_index = y_coordinates.index(y1)
            y2_index = y_coordinates.index(y2)
            for i in range(x1_index, x2_index):
                for j in range(y1_index, y2_index):
                    grid[i][j] = 1
        
        # Calculate the total area
        total_area = 0
        for i in range(len(x_coordinates) - 1):
            x_dist = x_coordinates[i + 1] - x_coordinates[i]
            for j in range(len(y_coordinates) - 1):
                y_dist = y_coordinates[j + 1] - y_coordinates[j]
                if grid[i][j] == 1:
                    total_area += x_dist * y_dist
                    total_area %= MOD
        
        return total_area

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