Bloodlust

Kryptonyte NSU Code Masters 2016
Limits 500ms, 1.0 GB

Mr. X is a dangerous criminal. He likes to draw some geometric random stuff and get motivated for his evil work.

FBI knows that MR. X is planning something new and he may sacrifice innocent people for his bloodlust. So they raided Mr. X's apartment, but found nothing except the following geometric drawing.
From the forensic department, we got the following information,

  1. Initially there was only segment ABAB.

  2. From point AA and BB (taking each as center) two circles were drawn with radius ABAB. Let's assume that these two circles intersect at points SS and RR.

  3. Then ABAB segment was extended as long as it intersects the circle (centered at AA) at point CC.

  4. From the point CC, another circle was drawn taking CBCB as radius which intersects one of the circles at point QQ.

  5. QRQR segment intersects segment ABAB at point PP.

As a programmer and geometry lover you think, this holds the information about where the ritual will occur. So you are extracting information from the drawing.

In order to search the city database (maps and building planning), you need to know the length of CPCP. So each time you are given a value for ABAB and you need to calculate the value of CPCP.

Input

Input starts with a positive integer TT (T1000 T ≤ 1000), denoting the number of test cases. Each case contains a floating point value RR (1R10000001 ≤ R ≤ 1000000) denoting the length of the segment ABAB.

Output

For each case, print the length of CPCP. Errors less than 10410^{-4} will be ignored.

Sample

InputOutput
1
5
8.09016

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Statistics

74% Solution Ratio
alvee9Earliest, Jun '16
raselrokyFastest, 0.0s
himuhasibLightest, 131 kB
bokaifShortest, 44B
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