CF850C Arpa and a game with Mojtaba

Mojtaba and Arpa are playing a game. They have a list of $ n $ numbers in the game. In a player's turn, he chooses a number $ p^{k} $ (where $ p $ is a prime number and $ k $ is a positive integer) such that $ p^{k} $ divides at least one number in the list. For each number in the list divisible by $ p^{k} $ , call it $ x $ , the player will delete $ x $ and add  to the list. The player who can not make a valid choice of $ p $ and $ k $ loses. Mojtaba starts the game and the players alternatively make moves. Determine which one of players will be the winner if both players play optimally.

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In the first sample test, Mojtaba can't move. In the second sample test, Mojtaba chooses $ p=17 $ and $ k=1 $ , then the list changes to $ [1,1,1,1] $ . In the third sample test, if Mojtaba chooses $ p=17 $ and $ k=1 $ , then Arpa chooses $ p=17 $ and $ k=1 $ and wins, if Mojtaba chooses $ p=17 $ and $ k=2 $ , then Arpa chooses $ p=17 $ and $ k=1 $ and wins.