Area Under Two Rectangles

Medium

Two rectangles with sides parallel to the axes lie on a plane. The first is given by its lower-left corner (a_left, a_bottom) and its upper-right corner (a_right, a_top); the second by its corners (b_left, b_bottom) and (b_right, b_top). Return the area they cover together, counting any overlap only once.

Example 1

a_left=0, a_bottom=0, a_right=4, a_top=3, b_left=2, b_bottom=1, b_right=6, b_top=5 → 24

The areas are 12 and 16, and they share the square from (2, 1) to (4, 3) of area 4. In total 12 + 16 - 4 = 24.

Example 2

a_left=-3, a_bottom=-3, a_right=-1, a_top=-1, b_left=1, b_bottom=0, b_right=2, b_top=5 → 9

The rectangles do not touch: 4 + 5 = 9.

Example 3

a_left=0, a_bottom=0, a_right=10, a_top=10, b_left=2, b_bottom=2, b_right=5, b_top=5 → 100

Constraints

-10⁴ ≤ every coordinate ≤ 10⁴
a_left ≤ a_right, a_bottom ≤ a_top
b_left ≤ b_right, b_bottom ≤ b_top

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Geometry Math

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Input

a_left=0, a_bottom=0, a_right=4, a_top=3, b_left=2, b_bottom=1, b_right=6, b_top=5

Expected

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