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
davidgalehouse: 2016-10-12 05:51:26

For C# I experienced no problems with I/O, reading ints was fine (doesn't mean you work with them as ints).

mkfeuhrer: 2016-06-06 13:07:36

silly CE .... easy one ,my 50th green light :-)

parth43: 2016-05-30 11:00:24

I tried the formula- square root of( 4u2v2w2 – u2(v2+w2–U2)2 – v2(w2+u2–V2)2 – w2(u2+v2–W2)2 +
+ (v2+w2–U2)(w2+u2–V2)(u2+v2–W2) )/12.
but still it is not giving the correct output.
what should I do?

Alex Anderson: 2016-04-02 20:37:57

If you need to read as Double instead of Int to solve the problem... you are doing something wrong. Something is wrong with your input reader. I got AC 5 years ago reading int, I resubmitted same problem now, still AC. There's nothing wrong with reading Int. Only something wrong with your code that reads the int.

dokz: 2016-01-18 08:51:35

Read as integers -> WA
Read as doubles -> AC

Wrong input info.

Fz: 2015-10-23 19:25:58

Useless problem. It says for 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)"
JUST try and see what will happen when you will take it INT --- >>>>>>>>>>>>> WA WA WA!

alexbandeira: 2015-10-10 20:33:19

warning : can and can not be blanks !
Let your program without inserting new lines and attempt to submit more than once . My code failed the first time and the second was accepted without any changes in it.

sy_117: 2015-08-16 22:09:44

Just a formula.......for help go through the link=http://zobayer.blogspot.in/2009/11/volume-of-irregular-tetrahedron.html

karthik1997: 2015-07-07 19:54:23

thanxss @gamer496
your comment really helped me :)
simply formula based problem
ac in 1 go :D
use double for all values except testcases :D

Ankush : 2015-06-27 13:14:25

My 100th :D


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