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
UTKARSH: 2013-06-27 14:12:13

ppl remember \n it costed me two wa's.

Rana Saha: 2013-06-14 00:34:36

No need of float and double .. No tricks.. Simple differentiation..

Rana Saha: 2013-06-14 00:27:22

Forgot to print Case....and got 2 WA :) .. Move it to tutorials ..

shashank: 2013-05-08 16:54:32

my 26 question AC. and this was done in first attemt , you just have to know differentiation and then this will be easy one.

ওয়াসী (Wasi): 2013-04-06 09:27:26

I just solved it only using integers!!! and a little trick not even used any float variable.

Juɑƞ Chɑpɑrro: 2013-03-29 02:41:23

Easy!

Rohan Joshi: 2013-02-03 09:18:27

move to tutorial pls...more emphasis on formatting output...

rishabhshinghal: 2013-01-25 20:36:10

should be moved to tutorial

#vaidy_MIT#: 2012-12-10 07:53:28

ANd it is my 50 th problem :) learnt a lot from spoj :) Love you so much :)

sunny: 2012-11-21 05:51:31

getting tle for%Lf.plz explain


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)