Shell Game-Enumeration, find the law

Http://codeforces.com/contest/777/problem/A

Three shells 0 1 2, a ball placed under one of them, an odd number of exchanges 0 and 1, an even number of exchanges 1 and 2 (that is, the first Exchange 0 1 and 1 2 have been down), known n times ball corresponding shells, the ball corresponding to the beginning of the shell subscript.

Methods: Every 6 times for a period, enumeration, sub-case discussion.

Word: Index subscript Shuffle Shuffle initial initial, first letter

Shell Game-Enumeration, find the law