# Practice on Toph

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## Minimizing Sphere

Limits: 20s, 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 of the points.

#### Input

The first line of the input contains the number of testcases **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** to **100**.

#### Output

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

#### Samples

Input | Output |
---|---|

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

#### forthright48

Samiul is a student at North South University and a part-time Software Engineer at Mukto Software Ltd. Sport programming is one of his hobbies. He loves reading manga - One Piece being his favorite. →