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intersect – Do two rectangles intersect?

Orthogonal rectangles are those with edges parallel to the axes of the cartesian plane. Two rectangles may intersect with each other when there are points that are over or inside both of them. In other words, they intersect when they share common surface or border area. This includes when they are inside each other. They do not intersect when they do not have common points.

Rectangle intersection in the cartesian plane

The above figure shows four orthogonal rectangles with edges parallel to the x and y axes. The one with the bottom-left corner at (1,1) and top-right corner at (4,3) intersects with the one with the bottom-left corner at (3,2) and top-right corner at (6,4). The one with the bottom-left corner at (7,1) and top-right corner at (9,3) does not intersect with the one with the bottom-left corner at (10,2) and top-right corner at (11,3).

Write a program that given the bottom-left and top-right corners of two rectangles computes whether they intersect.

Input and Output

Input will consist of several lines each with eight integers x₀, y₀, x₁, y₁, x₂, y₂, x₃ and y₃ where the first rectangle has the bottom-left coordinate of (x₀,y₀) and top-right coordinate of (x₁,y₁) and the second rectangle has the bottom-left coordinate of (x₂,y₂) and top-right coordinate of (x₃,y₃).

For each line of input there should be a line of output with either yes or no depending on whether the two rectangles intersect.

Example Input

1 1 4 3 3 2 6 4
10 2 11 3 7 1 9 3

Example Output

yes
no

Scoring

Hints

If you are not able to get a full score at first, try drawing a few pairs of rectangles on graph paper to come up with test cases for your solution. Try to come up with different ways rectangles can intersect.

For the purposes of this exercise, if rectangles touch on a single point they are considered intersecting rectangles.

try first: timetable discount

try next: bool-calc

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