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ZOJ Problem Set - 2075
Ellipsoid Volume

Time Limit: 10 Seconds      Memory Limit: 32768 KB      Special Judge

Angel is good at mathematics, but not is c.x. Angel always likes to solve some strange mathematic problems. Now, C.x. gives Angel a very hard problem, which he can't yet solve :(. Angel really doesn't know how c.x. can solve this problem, so he asked his best friend, you, to write a program to solve the problem.

There are N ellipsoids in a three-dimensional space. You should calculate the total volume of the N ellipsoids.

Input

For each testcase, first line contains an integer N (1 <= N <= 30). Then N lines follow. Every line contains 6 numbers. They are ai, bi, ci, di, ei and fi. The ellipsoid equation is:

(x-ai)^2/di^2 + (y-bi)^2/ei^2 + (z-ci)^2/fi^2 <= 1

All the ellipsoid are in range |x|<=0.5, |y|<=0.5, |z|<=0.5

Proceed to the end of file.

Output

For each testcase, you should output one number, indicating the volume of the ellipsoid. The result should be a floating-point number, having 3 digits after radix point. If your output is in range |YouAns - Sample Answer|<= 0.002, we will accept your program.

Sample Input

2
0 0 0 .5 .5 .5
.25 .25 .25 .25 .25 .25

Sample Output

0.549

Author: HOU, Qiming
Source: JIANG, Yanyan's Contest #1
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