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)  (be sure your method is public) 




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

Examples 
0)  
  Returns: 2  Two lucky strings  "ab" and "ba". 


1)  
  Returns: 0  It's impossible to construct a lucky string. 


2)  
  Returns: 1  "abababa" is the only lucky string that can be generated. 


3)  
 