def permutationGame(arr):
    memo = {}

    def winner(nums):
        if tuple(nums) in memo:
            return memo[tuple(nums)]

        if sorted(nums) == nums:
            memo[tuple(nums)] = 'Bob'
            return 'Bob'

        for i in range(len(nums)):
            if winner(nums[:i] + nums[i+1:]) == 'Bob':
                memo[tuple(nums)] = 'Alice'
                return 'Alice'

        memo[tuple(nums)] = 'Bob'
        return 'Bob'

    return winner(arr)