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 $S \gt T$.

• 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.

• 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.

• 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.

Input

Input is given from Standard Input in the following format:
N
S

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分