SPOJ.com - Problem MAXLN

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

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	kobe24: 2015-05-30 14:18:49 stupid question
	BRAIN: 2015-04-29 03:50:31 4 * r * r + 0.25 ( using floating point )
	_R0b_: 2015-04-20 22:46:05 is it my answer's correct format ? 3 1 Case 1: 4.25 1000 Case 2: 4e+06 100000 Case 3: 4e+10
	NIKHIL KUMAR SINGH: 2015-04-18 19:05:20 Don't know that ....When i submitted in python got 4 WA's and AC in one go in C++
	burninggoku: 2015-04-01 20:23:34 iss prashan ne toh hume 12 kaksha ki yaad dilla di...waah......
	Dushyant Singh: 2015-03-26 20:26:21 Take radius as long long. Costed me many WA. -_-
	Andrey Kaygorodov: 2015-02-05 14:29:11 The input is correct. There is only integers values.
	LeppyR64: 2015-02-05 13:03:19 The input is definitely all in the set of integers.
	Francky: 2015-02-05 01:28:03 According to my tests there's some '.' in input, but reading input as integer leads to AC with my code. Edit : using Python ! Edit : My test was wrong, ~~as some input lines have only one char~~, and "assert '.' not in line" gave NZEC in such cases. "assert '.' not in list(line)" didn't give me NZEC, so there's no '.' in input. My conclusion, like Mitch, is that input is well formatted. Last edit : the real reason for my NZEC is not that some lines have only one char ; it was due to my curious way of reading input on that old code. Last edit: 2015-02-05 13:16:41

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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)