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
mayankdhyani:
20180410 14:33:44
What is the formula for finding the volume and surface area of tertahedron ? 

dsri_99:
20171218 15:41:21
works for even 1999.9947.My 25th!!!!!!!!!!!!!!


harsh_03:
20171212 22:19:15
WA for 1999.9947 and newline ???


Sushant Moon:
20171003 04:58:11
Following the comments, solving it now it looks like the test cases have been strengthen and approximate formulas for calculating the volume won't work. 

vinodjatav:
20170819 12:10:48
i do not understand this question


nadstratosfer:
20170805 06:39:17
Many bloody tears were shed trying to get past the WA. Turns out the input file indeed contains valid pyramid dimensions only (volume will not be a complex number), but DO pay attention to variable order. Test case that helped greatly:


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:

Added by:  Adam Dzedzej 
Date:  20040514 
Time limit:  0.143s 
Source limit:  10000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  ACM ICPC 20022003 NEERC, Northern Subregion 