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
(Tjandra Satria Gunawan)(æ›¾æ¯…æ˜†):
20130822 04:11:28
Solved all problem in main SPOJ problemset with more than 2000 solver ;) 

Federico LebrÃ³n:
20130410 03:48:18
Be careful, the input contains needless empty lines  this was causing a runtime error in my program. 

albertg:
20130118 08:25:34
Interesing problem...


anuj kumar:
20120828 16:08:39
I got 1999.9947 in the second case and still AC, can't believe.


Rishi Mukherje:
20120525 21:22:35
My python code kept giving NZEC. The problem with input file makes me crazy. I had to code it in real inefficient way of taking inputs in python. Please think about users who use python language before uploading the input file. This wastes time also. 

Fei Wang:
20111208 15:59:53
OK.It's so strange that "double" can be accepted but "long double" will be wrong answer.


Mike:
20110508 09:23:37
Please explain about the output format.. Any line breaks is there????


numerix:
20101203 13:38:30
1999.9937 is correct. The first 30 digits are 1999.993749990234344482302665188906. 

Virgo:
20101203 01:50:35
1999.9937 is not correct.


shuaib akram:
20101126 23:21:19
should we print an empty line at beginning??

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 