Problem
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
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