Assuming that two points are chosen randomly (with uniform distribution) within a rectangle, it is possible to determine the expected value of the distance between these two points.

It can be verified that, within a rectangle of sides `a` and `b`,
the expected value of the distance between two random points is

Now, point `A` is chosen randomly (with uniform distribution) within rectangle `P`,
while point `B` is chosen randomly within rectangle `Q` similarly.
Both sides of rectangle `P` and `Q` are parallel to the axes.
Your task is to find the expected value of the distance between `A` and `B`.

There are multiple test cases. The first line of input is an integer `T` ≤10^{4} indicates the number of test cases.
For each test case:

There are 8 integers `x _{1}`,

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