A ↔ BB

AtCoder

IDarc136_a

Time2000ms

Memory256MB

Difficulty—

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: $N$ $S$ [samples]

Samples

Input #1

4
CBAA

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`.

Input #2

1
A

Output #2

A

We do no operation.

Input #3

6
BBBCBB

Output #3

ABCA

API Response (JSON)

{
  "problem": {
    "name": "A ↔ BB",
    "description": {
      "content": "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 i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc136_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $S$ of length $N$ consisting of `A`, `B`, `C`.\nYou can do the following two kinds of operations on $S$ any number of times in any order.\n\n*   Choose `A` in $S$, delete it, and i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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