Problem Description

“Goodbye to the friends I’ve had, goodbye to my upstairs neighbor, goodbye to the kids downstairs, and anybody who lend me a favor.”

“Or, goodbye to the positive proper divisor?”

That game is popular these days. Two player take turns to choose a specific number and claim it. The player who takes the first turn chooses one positive proper divisor of given n. In the next rounds, player should choose one positive proper divisor (真因数) of the number claimed in the previous round. The player who can’t make a choice will win.