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
ashish jaiswal: 2014-08-17 22:28:43

@ravi thanx bro..i did d same mistake twice

ravi: 2014-08-16 22:27:05

use calculus to derive formula...
case instead of Case caused me 3 WA...

rituraj: 2014-08-10 22:41:06

there is a simple sequence in the outputs... :) for 2 its 16.25
catch it if you can :p

mohsin mohammad: 2014-08-09 20:23:50

Can anyone help me?

karan: 2014-07-30 11:06:38

question says test radius are integer but it contains float as well..@admin correct the question

Samar Holkar: 2014-07-08 13:20:15

simple math....no need of calculus...

Abhishek Kumar: 2014-06-27 16:40:26

just basic maths..!!!..although got AC in 4th times bcoz of wronlgy taken word "case"...itz better u take care of this word..!!

Last edit: 2014-06-27 16:41:15
shreya sahu: 2014-06-03 05:40:19

was missing endl... caused me 3 WA :-p

arunrjit: 2014-05-28 02:43:29

WTF? test cases also contain float value of radius

pvkcse: 2014-05-20 14:07:40

four lines of code in python but printing case causes 6 WA...finally got AC...!!!


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)