class PermutationGame
{
private:
    unordered_set<string> _winningNumbers;

    bool isIncreasing(string str)
    {
        if (str.size() == 1) return 1;        
        auto it = str.begin();
        int prev = *it++;
        for (; it != str.end(); it++)
        {
            if (*it <= prev) return false;
            prev = *it;
        }
        return true;
    }

    string encode(vector<int> arr)
    {
        string s;
        for (auto number : arr)
            s.push_back(number < 10 ? (number + '0') : 
                                      (number - 10 + 'A'));
        return s;
    }

    bool checkCurrentPlayerWins(string numbers)
    {
        // With this sequence, the current player has already won 
        // => player wins
        if (_winningNumbers.find(numbers) !=_winningNumbers.end())
            return true;

        // Sequence increases after opponent's turn =>
				// current player loses
        if (isIncreasing(numbers))
            return false;

        for (int i = 0, len = (int)numbers.size(); i < len; i++)
        {
            char erased = numbers[i];
            // Making a move
            numbers.erase(i, 1);     
            
            // Checking if the opponent wins
            bool opponentWins = checkCurrentPlayerWins(numbers);
            
            // Reverse the move
            numbers.insert(i, 1, erased);

            // If the opponent loses, then the current player wins
            if (!opponentWins)
            {
                // Keeping the Winning Sequence
                _winningNumbers.insert(numbers);                      
                return true;
            }           
        }
        // None of the moves resulted in the player's victory => 
        // player loses
        return false;
    }

public:
    bool checkCurrentPlayerWins(vector<int> arr)
    {                
        bool result = checkCurrentPlayerWins(encode(arr));
        _winningNumbers.clear();
        return result;
    }
};

string permutationGame(vector<int> arr) 
{
    PermutationGame pg;
    return pg.checkCurrentPlayerWins(arr) ? "Alice" : "Bob";
}