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
d_y1997:
20170609 10:17:18
sample testcase passed in terminal , but on submitting shows wrong on the very first case


rishi_devan:
20170502 01:50:49
All sides can be stored as int


weathervane:
20170311 21:46:01
Interestingly, the question setter posted the problem a few days after posting the more difficult problem TETRA. Note about previous comment which says "Use doubles for input. Test cases contain decimal inputs." The question clearly says "six positive integer numbers". So there are no decimal inputs. There can't be, my answer was accepted. Last edit: 20170311 22:04:56 

epsilonalpha:
20170307 16:44:13
This is a purely formula based problem. If you want to learn something from it, read this article and learn the determinant from here:


nilabja16180:
20170304 13:42:20
AC in one Go!


cake_is_a_lie:
20170208 19:04:19
AC on the first try without having to do anything weird.


scorpion_ajay:
20170113 16:01:26
brain_fucked !!


Erick:
20161212 09:02:20
Solved using formula posted by @sy_117


yash_18121998:
20161113 04:52:29
Do remember the correct order of input...and the ans to the second test case given is not the one stated.


harsh_verma:
20161030 10:40:41
don't know about the myth but worked fine with int for me....just keep the order of edges in mind.... :) 
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 