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
2011-10-10 16:08:41 cc
for c++ users: use int for the test case, long long int for the radius, and double for the result :)
2011-09-24 06:10:02 Nnavneetsinha
some mathematics needed only.
tutorial problem.


Last edit: 2011-09-24 06:10:31
2011-07-28 10:30:22 manish kapoor
my code runs fine for d given test case ,pls give sm more test cases....pls (sm odd ones)
2011-06-12 19:08:36 oldmonk
do some math to get value of AC.. :)

Last edit: 2011-06-12 19:09:02
2011-06-02 08:39:11 Rohan Laishram
Tutorial
2011-05-22 11:00:33 Piotr KÄ…kol
@arshak minasyan - Yup.
2011-05-22 09:15:53 arshak minasyan
is the answer for r=2 16.25?
2011-05-12 15:59:03 Piotr KÄ…kol
@sikandar - That for example if the answer is 1.23 You can print both 1.229 and 1.231 as it's both rounded to 2 decimal point 1.23.
2011-05-12 10:57:29 sikandar
what means Errors should be less then .01 ?
2011-04-17 00:03:36 :(){ :|: & };:
Tutorial material.
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