MAXLN - THE MAX LINES

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

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)

hide comments
2013-11-30 15:51:34 Tarun Garg
output formatting cost 2 WA...Case(space)I:(space)no.
2013-11-16 22:46:00 Dinesh
haha..i/o practice..:)
2013-11-06 18:32:31 Abhishek Pasayat
why cant we take "s" as float??Its working for "s" as double but not for float.
2013-11-06 01:57:57 Shashank Gupta
Hint: Read wikipedia articles on "Thales' theorem" and "Quadratic functions". Also, know how to handle large integers in whatever language you are in. :) Good problem.
2013-10-30 20:36:39 Kyuubi Sage Mode
i ignored the formatting like case #x: ans somehow and that cost me 2 WAs :P
2013-09-15 21:11:58 Aswin Murugesh
One liner in python. Solved it with just a simple trick for decimal place
2013-08-13 15:49:48 KESHAV BANSAL
Got WA Due to Case(c)in capital
just concentrate on the way of presentation:
2013-07-12 15:04:05 Rudradeep Mukherjee
Got WA due to different data types. Got AC in 2nd attempt ! :)
2013-07-02 11:52:26 Hasil Sharma
yeah true , it can be solved without using any float or double
2013-06-28 13:35:00 pika_pika
really should be moved to tutorial. The wrong output format costed me 2 WA.. just a whitespace missing and the spoj engine goes of crazy... :P
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