I am not requesting for a solution. I just need the question explained. I am a 
beginner python developer and i do not know where to start from to solve this 
problem. So anybody, somebody: please explain this question. Am i to create a 
testcase or create the code to display a value?

Challenge: FitFam

Problem

The aerobics class begins. The trainer says, "Please position yourselves on the 
training mat so that each one of you has enough space to move your arms around 
freely, and not hit anybody else." People start milling around on the mat, 
trying to position themselves properly. Minutes pass, and finally the trainer 
is so annoyed that he asks you to write a program that will position all the 
people correctly, hoping it will be quicker than letting them figure it out for 
themselves!

You are given the dimensions (width and length) of the mat on which the class 
takes place. For every student, there is a circular area she has to have for 
herself, with radius equal to the reach of her arms. These circles can not 
intersect, though they can touch; and the center of each circle (where the 
student stands) has to be on the mat. Note that the arms can reach outside the 
mat. You know that there's plenty of space on the mat — the area of the mat is 
at least five times larger than the total area of the circles required by all 
the people in the class. It will always be possible for all the people to 
position themselves as required.

Input

The first line of the input gives the number of test cases, T. T test cases 
follow. Each test case consists of two lines. The first line contains three 
integers: N, W and L, denoting the number of students, the width of the mat, 
and the length of the mat, respectively. The second line contains N integers 
ri, denoting the reach of the arms of the ith student.

Output

For each test case, output one line containing "Case #n: y", where n is the 
case number (starting from 1) and y is a string containing 2N numbers, each of 
which can be an integer or a real number: x1, y1, x2, y2, etc., where the pair 
(xi, yi) is the position where the ith student should stand (with 0 ≤ xi ≤ W 
and 0 ≤ yi ≤ L).

As there will likely be multiple ways to position the students on the mat, you 
may output any correct positioning; but remember that you may not submit an 
output file more than 200kB in size.

Limits

1 ≤ T ≤ 50.
1 ≤ W, L ≤ 109.
1 ≤ ri ≤ 105.
The area of the mat is at least 5 times larger than the total area of the 
circles:
5*π*(r12 + ... + rN2) ≤ W*L.
Small dataset

1 ≤ N ≤ 10.
Large dataset

1 ≤ N ≤ 103.
The total number of circles in all test cases will be ≤ 6000.
Sample


Input

Output

2
2 6 6
1 1
3 320 2
4 3 2
Case #1: 0.0 0.0 6.0 6.0
Case #2: 0.0 0.0 7.0 0.0 12.0 0.0

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