Sphere in a tetrahedron

Problem code: TETRA

All submissions for this problem are available.

Given the lengths of the edges of a tetrahedron calculate the radius of a sphere inscribed in that tetrahedron (i.e. a sphere tangent to all the faces).

Input

An integer t, 1<=t<=30, denoting the number of test cases, followed by t lines, each containing 6 integers describing the lengths of the edges of a tetrahedron separated by single spaces. The edges are not longer than 1000 and for the tetrahedron WXYZ, the order of the edges is: WX, WY, WZ, XY, XZ, YZ.

Output

t lines, each consisting of a real number given with four digits decimal precision equal to the radius of a sphere inscribed in the given tetrahedron.

Example

Input:
2
1 1 1 1 1 1
1000 999 998 5 5 6

Output:
0.2041
1.4189

Date:	2008-12-01
Time limit:	1s
Source limit:	50000B
Languages:	All except: PERL6

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Program should read from standard input and write to standard output.

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