# Coprime Game I

Let $$N \ge 2$$ be a positive integer. Dan and Sam play the following coprime game: starting with the set $$C_N$$ of coprime positive integers of $$N$$ that are less than $$N$$, the players take turns removing some elements from the set. At a player's turn, he chooses a number $$m$$ that remains, and removes $$m$$ and any integer that is not coprime of $$m$$ that remains. The player who moves last loses.

For example: $$N =7, C_N = \{ 1,2,3,4,5,6\}$$. Dan chooses $$m=6$$, so he removes $$2$$, $$4$$, $$3$$ and $$6$$. The remaining set is $$\{1,5\}$$. Sam chooses $$m=5$$. The remaining set is $$\{1\}$$. Dan is forced to take $$1$$, so he loses.

Let $$n \ge 2$$ be the largest positive integer $$\le 200$$ such that if Dan and Sam play the divisor game for $$n$$ and both of them play optimally, the second player wins. Find $$n$$. If no such $$n$$ exists, enter $$1$$.

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