[ARC136A] A ↔ BB

ID: 19748

远端评测题

2000ms

1024MiB

尝试: 0

已通过: 0

难度: (无)

上传者:

admin

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 $S \gt T$ .

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.

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.

4
CBAA

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.

1
A

We do no operation.

6
BBBCBB

ABCA

#ARC136A. [ARC136A] A ↔ BB

Problem Statement

Constraints

Input

Output

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