# Polyhedron

# Polyhedron

You are given a set of points in 3-D space. Your task is to calculate the number of **k** vertex sides of the convex polyhedron with minimal volume that contains the whole given set of points.

**Input**

First line of input contains the quantity of tests **T** (**1** ≤ **T** ≤ **100**). First line of each test case contains the number of points in given set **N** (**4** ≤ **N** ≤ **30**). Then **N** lines follow, each of which contains **3** integer numbers: **X**, **Y**, **Z** (**–1000** ≤ **X**, **Y**, **Z** ≤ **1000**) – coordinates of points. Some points can have the same coordinates! It’s guaranteed, that any convex polyhedron, that contains all given points, has a positive volume.

**Output**

For each of **T** test cases output a line of the form "**Case** #**A**:", where **A** is the number of test (beginning from **1**), and then – **M** more lines, where **M** is the quantity of different side types (a side type means quantity of its vertices). In each of the next **M** lines you have to output two numbers: **k** – the number of vertices in the side and **q _{k}** – the number of

**k**vertex sides in the polyhedron. After

**k**you must print a colon ":" and then – a space. You have to output the result in ascending order of

**k**. The quantity of vertices in a side is determined only by geometrical meanings. That is, if a given point lies on an edge of a side, it mustn’t be considered as a vertex, and if some such point lie in one vertex, they must be considered as a single vertex.

2 6 0 0 0 2 0 0 0 2 0 2 2 0 3 1 0 1 1 1 5 0 0 0 1 1 0 0 2 0 2 1 0 1 1 1

Case #1: 3: 5 5: 1 Case #2: 3: 4