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
anup2raj: 2017-01-19 16:36:14

giving wa from r=1024
can some1 explain why is it happening?

narutohokage_1: 2017-01-17 06:36:16

long int can also be 32 bit on your compiler so it could also not work , please use long long int. Input cases are only integer, what happens is it overflows more than what int can contain , no need to use floating point or double.

narutohokage_1: 2017-01-17 06:20:03

TO ALL WHO FOUND output confusing , first of all radius given are in integer only no float , and yes the problem is as easy as you are thinking . Second if you take radius as integer and it is not accepting , it is because (for C) , int max size can be of 4,294,967,295 and if r = 1000000 , r * r = 1000000000000 which is above the range of int , so use long long in C. Format Specifier is %lld , that is all it is to this problem. Constant time is for any test case.

rohan2802: 2017-01-15 22:07:59

Be careful of the output format.The 'C' in case is capital.Cost me 7 wa........

kira28: 2016-12-14 22:30:41

AC by hook or crook...

shantanu_sarin: 2016-12-14 14:31:07

mathematical concept required......

asgupta_spoj: 2016-12-04 09:28:14

care of format of output required.

E Naveen Kumar: 2016-11-09 11:57:02

REMEMBER ans should be in format "Case I: ans"
It costed me 1 WA

wompowe: 2016-10-31 08:55:27

when you add that "fixed number" to the value of computed number,it gives WA but when you just print it it gives AC. Don't know why

roopansh: 2016-09-27 19:52:39

one WA for not printing "Case :".. took radius as double


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)