MAXLN - THE MAX LINES

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In this problem you will be given a half-circle. The half-circle’s radius is r. You can take any point A on the half-circle and draw 2 lines from the point to the two sides of the diameter(AB and AC). Let the sum of square of one line’s length and the other line’s length is s

Like in the figure s = AB2 + AC. And BC = 2r.

Now given r you have to find the maximum value of s. That is you have to find point A such that AB2 + AC is maximum.

Input

First line of the test case will be the number of test case T (1 ≤ T ≤ 1000). Then T lines follows. On each line you will find a integer number r (1 ≤ r ≤ 1000000); each representing the radius of the half-circle.

Output

For each input line, print a line containing "Case I: ", where I is the test case number and the maximum value of s. Print 2 digit after decimal (Errors should be less then .01).

Example

Sample Input:
1
1

Sample Output:
Case 1: 4.25

hide comments
bigBOSS: 2012-09-28 08:48:40

too simple......if u know a bit of maths......ac in first attempt

Shubham: 2012-08-03 04:37:09

@tjandra agree
@darky1 disagree

Fish3R: 2012-06-30 19:49:11

Use long long and use lf to avoid WA...

marwan akkad: 2012-06-22 20:05:14

Brilliant problem, it reminds me of my baccalaureate
Thanks Muhammad Ridowan

stranger: 2012-06-15 14:01:14

At least I've learned smth new about java's casting

:): 2012-06-13 07:11:51

oh no i am getting TLE..used %Lf for answer and long long int for radius then also

gabber: 2012-04-17 08:47:09

very easy just see the output formatting cost me three wa

Darky: 2012-04-14 16:19:39

Somehow python gives wrong answer to this one.

(Tjandra Satria Gunawan)(曾毅昆): 2012-03-24 18:20:53

i can solve this problem without using floating point or double... just integer with few math tricks :)

ginnipkj: 2012-03-11 16:17:59

i totally agree with JVR
and it is a bonus Question


Added by:Muhammad Ridowan
Date:2011-03-28
Time limit:1s-1.679s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Own Problem(used for CSE,University of Dhaka, Newbies Contest)