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)(曾毅昆): 2013-08-22 04:11:28

Solved all problem in main SPOJ problemset with more than 2000 solver ;-)

Federico Lebrón: 2013-04-10 03:48:18

Be careful, the input contains needless empty lines - this was causing a runtime error in my program.

albertg: 2013-01-18 08:25:34

Interesing problem...

anuj kumar: 2012-08-28 16:08:39

I got 1999.9947 in the second case and still AC, can't believe.
Dear admin, kindly look in the case if this is a typo... B-)

[reply by cyclops: It's not a typo, 1999.9947 is wrong. Maybe the test data is a bit on the weak side.]

Last edit: 2014-11-04 17:11:54
Rishi Mukherje: 2012-05-25 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: 2011-12-08 15:59:53

OK.It's so strange that "double" can be accepted but "long double" will be wrong answer.

[edit by cyclops: long double is fine. You probably made a mistake reading the values or printing the result.]

Last edit: 2014-11-04 17:12:49
Mike: 2011-05-08 09:23:37

Please explain about the output format.. Any line breaks is there????

[reply by cyclops: The standard judge on SPOJ counts any runs of consecutive whitespace as equivalent, and also you can have arbitrary whitespace at the beginning or end of output.]

Last edit: 2016-02-26 04:31:56
numerix: 2010-12-03 13:38:30

1999.9937 is correct. The first 30 digits are 1999.993749990234344482302665188906.

Virgo: 2010-12-03 01:50:35

1999.9937 is not correct.
my answer is 1999.9937744141.So the result is printed :1999.9938
what should i do?
"printed accurate to four digits after decimal point."

shuaib akram: 2010-11-26 23:21:19

should we print an empty line at beginning??
can any one explain me output format to be printed?


Added by:Adam Dzedzej
Date:2004-05-14
Time limit:1s
Source limit:10000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6 VB.NET
Resource:ACM ICPC 2002-2003 NEERC, Northern Subregion