[POJ2484]A Funny Game

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 4533		Accepted: 2780

Description

Alice and Bob decide to play a funny game. At the beginning of the game they pick n(1 <= n <= 10⁶) coins in a circle, as Figure 1 shows. A move consists in removing one or two adjacent coins, leaving all other coins untouched. At least one coin must be removed. Players alternate moves with Alice starting. The player that removes the last coin wins. (The last player to move wins. If you can't move, you lose.) 
 
Figure 1
Note: For n > 3, we use c1, c2, ..., cn to denote the coins clockwise and if Alice remove c2, then c1 and c3 are NOT adjacent! (Because there is an empty place between c1 and c3.) 

Suppose that both Alice and Bob do their best in the game. 
You are to write a program to determine who will finally win the game.

Input

There are several test cases. Each test case has only one line, which contains a positive integer n (1 <= n <= 10⁶). There are no blank lines between cases. A line with a single 0 terminates the input. 

Output

For each test case, if Alice win the game,output "Alice", otherwise output "Bob". 

Sample Input

1
2
3
0

Sample Output

Alice
Alice
Bob

Source

POJ Contest,Author:Mathematica@ZSU

THINKING

　　博弈论问题，如果n<=2那么先手的会获得胜利，当n>=3时，先手的走了一步以后，后手的可以把这个一个大图分成两个完全相同的小图，每步都是如此，则在n步以后，先手的总会无棋可取，后手的获得胜利。

var t,n,i:longint;
begin
    while true do
        begin
            readln(n);
            if n=0 then halt;
            if n<=2 then writeln('Alice')
            else writeln('Bob');
        end;
end.