Minimizing Sphere

jackal_1586 SUB 2022 Season Contest 5...
Limits 10s, 512 MB

You will be given some points in a 3D co-ordinate system. You have to find the minimum volume of the sphere which can enclose all the points.

Input

The first line of the input contains the number of test cases T (0 < T ≤ 20). Each test case begins with an integer N (1 < N ≤ 55). Next N line each contains three integers representing the x, y, z co-ordinates of the points. Absolute value of all co-ordinates lie between 0 and 100.

Output

For each case print the minimum volume of the sphere. Errors less than 10-4 will be ignored.

Sample

InputOutput
2
3
1 2 3
5 -2 3
9 5 -12
2
1 0 0
5 21 -11
2757.47031865
7275.96129172

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Contributors

Statistics

67% Solution Ratio
NirjhorEarliest, Jun '16
steinumFastest, 0.0s
sgtlaughLightest, 131 kB
Matrix.codeShortest, 1168B
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