Number Game Revisited

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Alice and Bob play the following game.They choose a number N to play with.The runs are as follows :
1.Bob plays first and the two players alternate.
2.In his/her turn ,a player can subtract from N any prime number(including 1) less than N.The number thus obtained is the new N.
3.The person who cannot make a move in his/her turn loses the game.
Assuming both play optimally,who wins the game ?
Input format:
The first line contains the number of test cases T.Each of the next lines contains an integer N.
Output format:
Output T lines one for each test case,containing "ALICE" if Alice wins the game ,or "BOB" if Bob wins the game.
Example
Sample Input: 2 1 2
Sample Output: ALICE BOB
Constraints: 1 <= T <= 1000000 1 <= N <= 1000000000
Note : For the first test case, Bob cannot make any move and hence Alice wins the game. For the second test case, Bob subtracts 1 from N. Now, Alice cannot make a move and loses the game.
Author:  nssprogrammer 
Tester:  rajivka 
Editorial  http://discuss.codechef.com/problems/NUMGAME2 
Tags  april11 easy nssprogrammer 
Date Added:  23112010 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.3.2, CPP 4.9.2, CPP14, CS2, D, ERL, FORT, FS, GO, HASK, ICK, ICON, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, NODEJS, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.4, RUBY, SCALA, SCM guile, SCM qobi, ST, TCL, TEXT, WSPC 
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how is the if(n%4==1)
i got IT how it works!!!
Where can I get more Test
Please explain me this....
Any one can please explain me
hey can anyone tell me dat
hey...cn u plz tell tht how
@anick_gemini Both players
@adm why 1 cant be choosen as
I am not getting the logic of
If you try to solve the
How to get to the reasoning
Please dont post answers...
Nice one :)
what do you mean optimally?
can somebody explain me the
^No you got to choose a
how do u define optimal moves
I like this problem
for test case 100 and 101
not getting the %4 logic ,
@uniquephase if you will try
Given any n%4 != 1 and it's
For these problems in
If number selected at the
@singh_abhinav playing
BOB can't win for any N whose
for n=4 how bob will win
@learning_iitj ..a player can
not getting %4 logic
I hate this problem.