PROBLEM STATEMENT
Consider a meeting of n businessmen sitting around a circular table. To start the meeting, they 
must shake hands. Each businessman shakes the hand of exactly one other businessman. All 
handshakes happen simultaneously. We say that the shake is perfect if no arms cross each other. 
Given an int n, return the number of perfect shakes that exist for n businessmen. See examples for 
further clarification.

DEFINITION
Class:HandsShaking
Method:countPerfect
Parameters:int
Returns:long long
Method signature:long long countPerfect(int n)


NOTES
-Businessmen are distinguishable. Rotating a perfect shake can yield a different perfect shake 
(see example 1).


CONSTRAINTS
-n will be between 2 and 50, inclusive.
-n will be even.


EXAMPLES

0)
2

Returns: 1

Two businessmen have only one possibility - just to shake each other's hand.

1)
4

Returns: 2

Two out of three possible shakes are perfect.
? ? 

2)
8

Returns: 14



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 TopCoder, Inc. is strictly prohibited. (c)2010, TopCoder, Inc. All rights reserved.
 
  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.