The Circular Chocolate Game

Two friends, Alice and Bob, are playing a game with N stacks of chocolates arranged in a circle. The stacks are numbered 0 to N-1 clockwise.

The rules of the game are as follows:

1) Alice always goes first.

2) The game starts with a pointer at stack 0.

3) On a player's turn, they must take exactly one chocolate from the stack indicated by the pointer.

4) After their turn, the pointer moves one position clockwise to the next stack.

5) If a player's turn begins and the pointer is at a stack that is already empty, that player has no valid move and loses the game immediately.

Given the initial number of chocolates in each stack, and assuming both Alice and Bob play optimally, your task is to determine the winner.

Input Format:

The first line of input contains an integer N, the number of stacks.

The second line contains N space-separated integers, where the i-th integer represents the number of chocolates in stack i.

Output Format:

Print a single string, either Alice or Bob, who will win the game.

Note:

The game is deterministic; there are no choices for the players to make. The outcome is pre-determined by the initial setup.

The key to solving this efficiently is to realize that the game will proceed for a certain number of full "laps" around the circle until the first stack is about to be depleted. The minimum number of chocolates in any stack determines how many full laps can be completed without anyone losing.

The winner is determined by who gets stuck on the final, partial lap after all full laps are completed.