### Problem Statement

The celebrated general Archibald Waving took charge of the second army in the occidental front. After losing the first army, Waving has become obsessed with effective organization of the army. As a part of this endeavor he has assigned numbers to each of his soldiers. He has also devised a rule which allows two soldiers to work together if and only if the numbers assigned to the soldiers are neighbouring numbers. Two numbers x and y are neighbouring numbers if there exists a permutation of digits of x and a permutation of digits of y such that they are equal if we ignore the leading zeros in the permutations. For example, the numbers 40020 and 204 are neighboring. To see this, permute the digits of 40020 to achieve 00042 and the digits of 204 to achieve 042. If you ignore the leading zeros, both numbers become equal to 42, so they are neighboring.

You are given a int[] numbers representing soldiers' numbers. Waving needs to pick two soldiers to send a telegram. He would like to know how many different pairs of soldiers are there who can work together to accomplish the task. Help Waving by returning the number of pairs of neighbouring numbers in the int[] numbers.

### Definition

 Class: NumberNeighbours Method: numPairs Parameters: int[] Returns: int Method signature: int numPairs(int[] numbers) (be sure your method is public)

### Constraints

-numbers will contain between 2 and 50 elements, inclusive.
-Each element of numbers will be between 1 and 1,000,000, inclusive.
-All elements of numbers will be distinct.

### Examples

0)

 `{10, 1, 100, 20, 2, 3}`
`Returns: 4`
 The pairs of neighbouring numbers are (10, 1), (1, 100), (20, 2) and (10, 100).
1)

 `{204, 42, 40020, 200}`
`Returns: 3`
2)

 `{1, 10, 100, 1000, 10000, 100000, 1000000}`
`Returns: 21`
 Any two numbers are neighbouring.
3)

 `{3, 33, 333, 3333}`
`Returns: 0`
 There are no two numbers that are neighbouring.
4)

 `{1024, 4021, 204, 303, 33, 603, 36, 55, 505}`
`Returns: 4`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10821

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14182&pm=10821

boba5551

#### Testers:

timmac , ivan_metelsky , gojira_tc , vexorian , keshav_57

#### Problem categories:

Simple Math, Simple Search, Iteration