Definition:Fibonacci Nim

Definition
Fibonacci nim is a two-person game whose rules are as follows:


 * $(1): \quad$ The game starts with one pile of $n$ counters.


 * $(2): \quad$ The first player removes a number of counters $c_1$ such that $1 \le c_1 < n$.


 * $(3): \quad$ Each player takes it in turns to remove $c_n$ counters such that $1 \le c_n \le 2 c_{n - 1}$ where $c_{n - 1}$ is the number of counters taken in the other player's prevous move.


 * $(3): \quad$ The person who removes the last counter (or counters) is the winner.