Description

Dear Melo

Walking alone in darkness, lonely and never knew what I would go through. How many times I walked lonely in the campus, how many times I woke up with a start at midnight, and how many times I sang a sorrow song but no one cared about? The terrible feeling is just like a albatross around my neck until I met you. My door is opened and the sky is lightened.It is a moment for my renaissance, which makes me understand the meaning of sunshine and rainbow once again. When I catch sight of you, you are the only one in my view. When you are out of sight, you are the only one in my heart. When I am awake, you are the only one in my mind. When I am asleep, you are the only one in my dream. You are my only one.I want to catch sight of you every minute and every second.

I never forget the moment that I met with you on campus.You carefully asked me: “I have a very difficult problem. Can you teach me?”.I replied with a courteous smile, “of course”.

$I = \int_a^b {\frac{dx}{\sqrt{(x-c)(d-x)}}} \quad (c<a<b<d)$

Yours sincerely,

Y

This is A letter write to Melo.As we all know,Melo is the most glamourous man.But he is busy(conscious) now, so he wants you to help him calculate the result of this definite integral.

Format

Input

The first line of input contains a single integer $T$, indicating the number of test cases to follow.

Each case contains four real numbers $a,b,c,d.(c<a<b<d)$。

Output

For each case, print a floating number $I$ in one line, result rounds to 4 decimal places.

Samples

1
2 3 1 4

0.6797

Hint