PIR  Pyramids
Recently in Farland, a country in Asia, the famous scientist Mr. Log Archeo discovered ancient pyramids. But unlike those in Egypt and Central America, they have a triangular (not rectangular) foundation. That is, they are tetrahedrons in the mathematical sense. In order to find out some important facts about the early society of the country (it is widely believed that the pyramid sizes are closely connected with Farland's ancient calendar), Mr. Archeo needs to know the volume of the pyramids. Unluckily, he has reliable data about their edge lengths only. Please, help him!
Input
t [number of tests to follow] In each of the next t lines six positive integer numbers not exceeding 1000 separated by spaces (each number is one of the edge lengths of the pyramid ABCD). The order of the edges is the following: AB, AC, AD, BC, BD, CD.
Output
For each test output a real number  the volume, printed accurate to four digits after decimal point.
Example
Input: 2 1 1 1 1 1 1 1000 1000 1000 3 4 5 Output: 0.1179 1999.9937
hide comments
Saurabh Pratap:
20150622 12:49:54
You can find help from http://www.cs.berkeley.edu/~wkahan/VtetLang.pdf as it was much of formula based question i assume.


iharsh234:
20150619 14:11:21
1999.9933 intead of 1999.9937 and it shows WA


[Mayank Pratap]:
20150618 11:17:23
Piece of Cake :)


e_coder:
20150615 16:58:21
there is no blank line... :D 

Luk:
20150318 13:20:16
I do not understand.


HITESH GARG:
20150113 14:39:46
not an easy one 

agaurav77:
20141212 12:21:43
Don't forget the newline. 

gamer496:
20141203 15:41:36
http://en.wikipedia.org/wiki/Tetrahedron


Kid Algorist:
20141003 21:10:19
Keep data types of edges and all variables storing such values as double. Edges in test cases aren't just integers, WA otherwise. 
Added by:  Adam Dzedzej 
Date:  20040514 
Time limit:  1s 
Source limit:  10000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  ACM ICPC 20022003 NEERC, Northern Subregion 