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
2014-04-17 21:12:34 SHIVAM DIXIT
got wa for int and float, accepted for long long,double in c++

Last edit: 2014-04-17 21:14:32
2014-04-11 12:38:09 anon
easy :)
EDIT:
solved using int and without int

Last edit: 2014-04-11 12:41:31
2014-02-04 17:14:13 RAJAT SINGH
easy one got AC in first attempt........
simple maths is applied
2014-01-16 08:28:22 headfirstcoder
test cases even contain float values of radius also....
2013-12-13 16:51:53 Achmet ibn Rashid
Funniest solution ever; trivial to implement once you do the math.
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
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