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: 2015-06-22 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: 2015-06-19 14:11:21

1999.9933 intead of 1999.9937 and it shows WA
what should i do next

[Mayank Pratap]: 2015-06-18 11:17:23

Piece of Cake :)
I got 1999.9947 instead of 1999.9937 then also AC:)

e_coder: 2015-06-15 16:58:21

there is no blank line... :D

Luk: 2015-03-18 13:20:16

I do not understand.
When I run program in "http://ideone.com/" I see:
Sukces comments (0)
stdin copy
2
1 1 1 1 1 1
1000 1000 1000 3 4 5
stdout copy
0.1179
1999.9937

Why SPOJ do not accept my solution?

P.S.
I use Python 2.7

Last edit: 2015-03-18 13:21:16
HITESH GARG: 2015-01-13 14:39:46

not an easy one

agaurav77: 2014-12-12 12:21:43

Don't forget the newline.

gamer496: 2014-12-03 15:41:36

http://en.wikipedia.org/wiki/Tetrahedron
if you know next to nothing go through this link and solve it

Kid Algorist: 2014-10-03 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: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