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
Aswin Murugesh: 2013-09-15 21:11:58

One liner in python. Solved it with just a simple trick for decimal place

KESHAV BANSAL: 2013-08-13 15:49:48

Got WA Due to Case(c)in capital
just concentrate on the way of presentation:

Rudradeep Mukherjee: 2013-07-12 15:04:05

Got WA due to different data types. Got AC in 2nd attempt ! :)

Hasil Sharma: 2013-07-02 11:52:26

yeah true , it can be solved without using any float or double

pika_pika: 2013-06-28 13:35:00

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

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.


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)