How Big Is It? 
Time Limit: 1000ms, Special Time Limit:2500ms, Memory Limit:32768KB 
Total submit users: 13, Accepted users: 10 
Problem 10044 :
No special judgement

Problem description 
Ian¡¯s going to California, and he has to pack his things, including his collection of circles. Given a
set of circles, your program must find the smallest rectangular box in which they fit.
All circles must touch the bottom of the box. The figure below shows an acceptable packing
for a set of circles (although this may not be the optimal packing for these particular circles). Note
that in an ideal packing, each circle should touch at least one other circle (but you probably figured
that out).

Input 
The first line of input contains a single positive decimal integer n, n < 50. This indicates the
number of lines which follow. The subsequent n lines each contain a series of numbers separated
by spaces. The first number on each of these lines is a positive integer m, m < 8, which indicates
how many other numbers appear on that line. The next m numbers on the line are the radii of the
circles which must be packed in a single box. These numbers need not be integers.

Output 
For each data line of input, excluding the first line of input containing n, your program must
output the size of the smallest rectangle which can pack the circles. Each case should be output on
a separate line by itself, with three places after the decimal point. Do not output leading zeroes
unless the number is less than 1, e.g. 0.543.

Sample Input 
3
3 2.0 1.0 2.0
4 2.0 2.0 2.0 2.0
3 2.0 1.0 4.0 
Sample Output 
9.657
16.000
12.657 
Problem Source 
2006 MSU Local Programming Contest

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