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Rectangle Area

You are given the coordinates of two axis-aligned rectangles in a 2D plane. Your task is to calculate the total area covered by both rectangles.

The first rectangle is specified by the coordinates of its bottom-left corner (ax1, ay1) and top-right corner (ay1, ay2).

Similarly, the second rectangle is defined by its bottom-left corner (bx1, by1) and top-right corner (bx2, by2).

Note: The rectangles may overlap.

Constraints

  1. -10^4 ≤ ax1 ≤ ax2 ≤ 10^4
  2. −10^4 ≤ ay1 ≤ ay2 ≤ 10^4
  3. −10^4 ≤ bx1 ≤ bx2 ≤10^4
  4. −10^4 ≤ by1 ≤ by2 ≤ 10^4

Examples

Example 1 Example 2 Example 3 Example 4