Rectangle Overlap

Given two rectangles on a 2D plane, determine whether they overlap.

The first rectangle is defined by its top-left corner (a, b) and bottom-right corner (c, d), and the second rectangle is defined by its top-left corner (a₁, b₁) and bottom-right corner (c₁, d₁). They are said to overlap if and only if all the following conditions hold:

\[ \begin{aligned} a &< c_1, \\ a_1 &< c, \\ b &< d_1, \\ b_1 &< d. \end{aligned} \]

Note: If the rectangles touch only at the edges or corners, they are considered not to be overlapping.

inputFormat

The input consists of a single line containing eight space-separated integers: a b c d a1 b1 c1 d1.

Here:

• \(a, b\) and \(c, d\) are the coordinates of the top-left and bottom-right corners of the first rectangle respectively.
• \(a_1, b_1\) and \(c_1, d_1\) are the coordinates of the top-left and bottom-right corners of the second rectangle respectively.

outputFormat

Output a single line containing the string true if the two rectangles overlap, otherwise output false.

## sample

0 0 1 1 2 2 3 3

false

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