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
shivamyadav00: 2018-10-19 20:45:19

thanks @sy_117 for the formula :)

yuhta: 2018-10-11 23:50:39

Use long double

teja876__: 2018-10-04 10:04:54

AC in one go.

shepix: 2018-08-13 14:12:37

The main difficulty is to avoid numerical error during computation.

piyush490: 2018-06-11 15:21:31

use formulae.

shubhamshree10: 2018-05-26 16:24:08

Calculate volume using area of faces

find area of individual faces by heron's formula:D

Last edit: 2018-05-26 16:28:38
mayankdhyani: 2018-04-10 14:33:44

What is the formula for finding the volume and surface area of tertahedron ?

dsri_99: 2017-12-18 15:41:21

works for even 1999.9947.My 25th!!!!!!!!!!!!!!

harsh_03: 2017-12-12 22:19:15

WA for 1999.9947 and newline ???

Sushant Moon: 2017-10-03 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.


Added by:Adam Dzedzej
Date:2004-05-14
Time limit:0.143s
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