Triangle area
			---------------



There are many ways to compute the area of a triangle. An old paper (Baker, Marcus, "A 
collection of formulae for the area of a plane triangle," Annals of Mathematics, part 1, 
vol. 1(6), January 1885, 134-138; part 2 in vol. 2(1), September 1885, pp 11-18) gives 
over a hundred ways for finding the area of a triangle. 

In middle school, children learn that the area is 0.5*base*height. You can use this formula
along with problems in earlier contests to compute the area. Another easy one is the formula

A = sqrt [ s * (s - a) * (s - b) * (s - c) ], where s = (1 / 2)(a + b + c). 

Both of these are susceptible to numerical precision issues. You have to be very careful about 
this -- even if you are off by 1 in the least significant digit of your answer, the online judge 
will deem your program incorrect!

A simpler formula (that you should remember henceforth!) is as follows. Given 3 vertices of a 
triangle (xa,ya), (xb, yb) and (xc, yc), the area is the absolute value of the expression 
0.5*(xa*(yb-yc)+xb*(yc-ya) + xc*(ya-yb)).

In this problem you are asked to determine the highest area among a given list of 20 triangles.

Input

The first line is the number of instances n. Each following line contains 120 integers 
separated by spaces -- these are 20 sets of triangle coordinates -- xa,ya,xb,yb,xc,yc.  
All integers will have absolute values less than 6500.  

Output 

The output is the answer to the question "what is the area of the triangle with the biggest area?" 
to one decimal point -- see the sample output below for the precise format.  As always, make sure 
that your output matches the samples precisely, including in terms of upper/lowercases, punctuation 
and white spaces.
 
Sample input

2
14 33 15 11 48 4 49 22 36 11 44 5 63 52 34 24 7 27 57 19 47 32 62 35 7 52 11 33 14 4 35 30 25 6 55 20 1 46 59 16 34 20 54 12 59 10 5 6 49 58 64 25 62 61 22 47 8 57 59 35 47 30 49 56 11 1 6 3 19 43 8 44 12 2 26 26 9 43 57 16 38 38 50 60 19 40 49 55 15 9 43 0 24 8 64 48 45 9 60 15 51 39 39 11 58 31 9 42 20 3 10 36 15 47 59 31 36 54 18 7
55 4 47 27 40 54 15 46 53 1 32 54 54 6 2 55 60 62 19 8 7 52 12 23 15 3 27 20 55 52 6 55 24 58 24 21 25 59 26 61 42 5 52 51 34 61 2 5 26 11 41 24 25 1 38 18 13 46 59 48 55 9 27 11 28 3 52 54 6 55 41 48 16 27 40 21 52 31 59 6 46 47 12 8 6 59 15 32 39 8 4 21 43 45 34 62 55 26 38 18 17 61 5 9 59 30 23 33 58 11 62 33 22 57 62 46 40 63 57 26


Sample Output

Case 1: The maximum area is 747.5.
Case 2: The maximum area is 1603.0.