201360: [AtCoder]ARC136 A - A ↔ BB

Memory Limit：1024 MB Time Limit：2 S
Judge Style：Text Compare Creator：
Submit：0 Solved：0

Description

Score : $300$ points

Problem Statement

You are given a string $S$ of length $N$ consisting of A, B, C.

You can do the following two kinds of operations on $S$ any number of times in any order.

  • Choose A in $S$, delete it, and insert BB at that position.
  • Choose two adjacent characters that are BB in $S$, delete them, and insert A at that position.

Find the lexicographically smallest possible string that $S$ can become after your operations.

What is the lexicographical order?

Simply speaking, the lexicographical order is the order in which words are listed in a dictionary. As a more formal definition, here is the algorithm to determine the lexicographical order between different strings $S$ and $T$.

Below, let $S_i$ denote the $i$-th character of $S$. Also, if $S$ is lexicographically smaller than $T$, we will denote that fact as $S \lt T$; if $S$ is lexicographically larger than $T$, we will denote that fact as $S \gt T$.

  1. Let $L$ be the smaller of the lengths of $S$ and $T$. For each $i=1,2,\dots,L$, we check whether $S_i$ and $T_i$ are the same.
  2. If there is an $i$ such that $S_i \neq T_i$, let $j$ be the smallest such $i$. Then, we compare $S_j$ and $T_j$. If $S_j$ comes earlier than $T_j$ in alphabetical order, we determine that $S \lt T$ and quit; if $S_j$ comes later than $T_j$, we determine that $S \gt T$ and quit.
  3. If there is no $i$ such that $S_i \neq T_i$, we compare the lengths of $S$ and $T$. If $S$ is shorter than $T$, we determine that $S \lt T$ and quit; if $S$ is longer than $T$, we determine that $S \gt T$ and quit.

Constraints

  • $1 \leq N \leq 200000$
  • $S$ is a string of length $N$ consisting of A, B, C.

Input

Input is given from Standard Input in the following format:

$N$
$S$

Output

Print the answer.

Sample Input 1

4
CBAA

Sample Output 1

CAAB

We should do the following.

  • Initially, we have $S=$CBAA.
  • Delete the $3$-rd character A and insert BB, making $S=$CBBBA.
  • Delete the $2$-nd and $3$-rd characters BB and insert A, making $S=$CABA.
  • Delete the $4$-th character A and insert BB, making $S=$CABBB.
  • Delete the $3$-rd and $4$-th characters BB and insert A, making $S=$CAAB.

We cannot make $S$ lexicographically smaller than CAAB. Thus, the answer is CAAB.

Sample Input 2

1
A

Sample Output 2

A

We do no operation.

Sample Input 3

6
BBBCBB

Sample Output 3

ABCA

Input

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