CAGES - Lights, Snakes and Cages


In the zoo there are N cages in which we keep N snakes: each snake in its cage. For experimental reasons, in a month we will move each snake to a different cage: this reordering is given in the input.

Each cage is illuminated by special light, which may be of type A, type B or type C. Your task is to assign the lights A, B, C to the cages so that:

1) each snake will change its lighting, i.e. it will be moved to the cage illuminated differently from the cage it currently inhabits;

2) lightings are equally distributed, i.e. the number of cages A, the number of cages B and the number of cages C differ by at most one.

Input

The first line contains an integer N (2 N ≤ 300 000), the number of snakes and cages. Cages are numbered from 1 to N.

Each of the next N lines contains an integer. When K-th of these lines contains the number L, it means that the snake from the cage K will be moved to the cage L (K L). Two snakes will not move to the same cage.

Output

Print the string composed of the characters A, B and C, such that the K-th character denotes the lighting of the cage K.
If there are multiple solutions, print any.

Example

Input:
4
4
3
2
1

Output: ACBC

hide comments
aeon: 2016-09-17 23:00:58

@psetter Kindly have a look at my solution ( id : 17732677 ), I have considered even the cyclic cases, but still I am getting WA after 15 test cases.

avisheksanvas: 2016-07-06 11:15:11

@psetter please check my submission : 17234107!
Why is it not getting AC?

codeforsure: 2016-05-22 08:42:18

@author can you please check my submission: 16964085, getting wrong answer after 15 test cases.

rajatgupta: 2016-04-22 23:12:54

Cant find test cases... getting WA...HELP!!!!

lt: 2016-03-22 17:42:43

5 WAs :( , I'm to figure out what's wrong. Can somebody help me?

Sergio Vieri: 2015-06-14 06:17:02

Solved with 341 lines in Assembly.. yay

kancha: 2014-12-19 11:09:00

well, tried debugging with random case generator, no success :(

edit: Nice problem .. done :D:D

Last edit: 2014-12-20 13:40:55
Adrian Satja Kurdija: 2014-08-03 10:11:23

@Bhavik: have you written a random case generator and a checker? I'm sure you'll find your bug that way.

Bhavik: 2014-06-16 18:06:13

@psetter:can you look my id:11776229 and kindly tell if i my approach is right??

Last edit: 2014-06-17 17:23:28
Adrian Satja Kurdija: 2014-03-28 08:18:14

Many WAs in submissions :) I suggest using random case generator and a checker to find your bugs.


Added by:Adrian Satja Kurdija
Date:2014-03-24
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Croatia nationals 2014 (6th grade, 3rd problem "Zmije")