### Problem Statement

Let's consider a standard six-sided die. Each side contains a distinct number between 1 and 6. We can represent a single die as a sequence of 6 digits in the following order: the number on its top side, bottom side, left, right, front and back sides. You are given a String[] givenDice, each element of which represents a single die in the described format.

Your task is to determine the number of distinct dice in givenDice. Two dice are considered equal if they can be rotated in such a way that the numbers on the corresponding sides are all equal.

### Definition

 Class: DistinctDice Method: getDistinct Parameters: String[] Returns: int Method signature: int getDistinct(String[] givenDice) (be sure your method is public)

### Constraints

-givenDice will contain between 1 and 50 elements, inclusive.
-Each element of givenDice will contain exactly 6 characters.
-Each character of each element of givenDice will be a digit between '1' and '6', inclusive.
-Within each element of givenDice, all characters will be distinct.

### Examples

0)

 `{"123456","654321"}`
`Returns: 1`
1)

 `{"145326","154236","216543"}`
`Returns: 3`
2)

 `{"165324"}`
`Returns: 1`
3)

 ```{"546231", "245631", "531462", "524631", "614235", "415623", "423651", "316254", "432165", "316452", "135426", "643512"}```
`Returns: 10`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6512

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10064&pm=6512

Pawa

#### Testers:

PabloGilberto , brett1479 , Olexiy

#### Problem categories:

Simulation, Sorting