PROBLEM STATEMENT
John and Brus are studying string theory at the university.  According to Brus, a string is called 
lucky if no two consecutive characters are equal.  John is analyzing a string s, and he wants to 
know how many distinct lucky strings can be generated by reordering the letters in s.  If s is a 
lucky string in its original ordering, it should also be considered in the count.

DEFINITION
Class:TheLuckyString
Method:count
Parameters:string
Returns:int
Method signature:int count(string s)


CONSTRAINTS
-s will contain between 1 and 10 characters, inclusive.
-Each character of s will be a lowercase letter ('a' - 'z').


EXAMPLES

0)
"ab"

Returns: 2

Two lucky strings - "ab" and "ba".

1)
"aaab"

Returns: 0

It's impossible to construct a lucky string.

2)
"aabbbaa"

Returns: 1

"abababa" is the only lucky string that can be generated.

3)
"abcdefghij"

Returns: 3628800

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