162. Pyramids

time limit per test: 0.25 sec.
memory limit per test: 65536 KB
input: standard input
output: standard output



Recently in Farland, a country in Asia, a famous scientist Mr. Log Archeo has discovered ancient pyramids. But unlike those in Egypt and Central America, they have triangular (not rectangular) foundation. That is, they are tetrahedrons in 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 in tight connection with Farland 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
The file contains 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
A real number - the volume printed accurate to four digits after decimal point.

Sample test(s)

Input
Sample input #1 
1 1 1 1 1 1 
 
Sample input #2 
1000 1000 1000 3 4 5  

Output
Sample output #1 
0.1179 
 
Sample output #2 
1999.9937 

Note
  
  
Author:Nikolay Durov 
Resource:ACM ICPC 2002-2003 NEERC, Northern Subregion 
Date:November, 2002