PROBLEM STATEMENT
One day, I started writing out the following patterns (The procedure for constructing the pattern 
is deliberately not given, you must infer the procedure through the examples):

Input string: "HELLO" (quotes for clarity only)

Pattern:      O
             OLO
            OLLLO
           OLLELLO
          OLLEHELLO
           OLLELLO
            OLLLO
             OLO
              O


Input string: "TC" (quotes for clarity only)

Pattern:      C
             CTC
              C   


Input string: "ABCD" (quotes for clarity only)

Pattern:      D
             DCD
            DCBCD
           DCBABCD
            DCBCD
             DCD
              D


After constructing the patterns, I noticed something interesting. Starting with the first letter 
of the input string (which appears only once in the very center of the pattern), I can trace a 
path outwards toward the edges, spelling out the original input string. Of course, I only move Up, 
Down, Left and Right from any letter. I'm now perplexed because I want to know how many ways the 
original input string can be spelled out in the pattern. I must always end at an edge, and I can't 
go over one letter more than once while spelling a word.


Create a class WordPattern containing the method countWords which takes a string word as input. 
The method should return a long long which is the number of ways the original input can be spelled 
out in the pattern according to my rules.

DEFINITION
Class:WordPattern
Method:countWords
Parameters:string
Returns:long long
Method signature:long long countWords(string word)


NOTES
-Remember, I only move Up, Down, Left and Right from any letter to the next letter and never use a 
letter twice.


CONSTRAINTS
-word will contain between 1 and 50 characters inclusive.
-word will contain only uppercase letters ('A'-'Z').


EXAMPLES

0)
"HELLO"

Returns: 60

1)
"TC"

Returns: 4

2)
"ABCDEFGHIJKLMNOPQRST"

Returns: 2097148

3)
"ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJ"

Returns: 137438953468

 This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2010, TopCoder, Inc. All rights reserved.