Rvom and Rsrev

AtCoder

IDarc113_e

Time2000ms

Memory256MB

Difficulty—

Given is a string $S$ consisting of `a` and `b`. Find the lexicographically **greatest** string that can be obtained by applying the following operation to $S$ zero or more times: * Choose two characters of $S$ that are the same letter. Reverse the string between them and delete the chosen two characters. In other words: let $s_i$ denote the $i$\-th character of $S$. Choose $i < j$ such that $s_i = s_j$ and replace $S$ with $s_1\dots s_{i-1}s_{j-1}\dots s_{i+1}s_{j+1}\dots s_{|S|}$. In this problem, you are given $T$ test cases. The $i$\-th test case is represented as $S_i$ and asks you to solve the problem above for $S = S_i$. ## Constraints * $1 \leq T \leq 2\times 10^5$ * $1 \leq |S_i|\quad (i=1,\dots, T)$ * $1 \leq |S_1| + \dots + |S_T| \leq 2\times 10^5$ * $S_i$ consists of `a` and `b`. ## Input Input is given from Standard Input in the following format: $T$ $S_1$ $\vdots$ $S_T$ [samples]

Samples

Input #1

20
abbaa
babbb
aabbabaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
bbabaaaaabbaababaaabbabbbbbaaaaa
babbbaaaabaababbbabaabaaaaababaa
bbaababababbbaaabaabababaabbabab
abaabbabaabaaaaabaaaabbaabaaaaab
aabababbabbabbabbaaaabbabbbabaab
aabababbabbbbaaaabbaaaaabbaaaabb
abbbbaabaaabababaaaababababbaabb
aaaaaaaaaaaaaaaaaaaaaaabbbbbbbbb
aaaaaaaaaabbbbbbbbbbbbbbbbbbbbbb
abababaaababaaabbbbbaaaaaaabbbbb
aabbaaaaababaabbbbbbbbbaabaaabbb
babababbababbbababbbbbababbbabbb
bbbbababbababbbabababbabbabbbbbb
aaaaaaaaaaaaaaaaababababbbabbbbb
aabababbabbabababababababbbbabbb

Output #1

bba
bba
bbba
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
bbbbbbbbbbbbbbaaaaaaaa
bbbbbbbbbbbbbaaaaaaa
bbbbbbbbbbbbbbbb
bbbbbbbbbb
bbbbbbbbbbbbbbbbab
bbbbbbbbbbbbbb
bbbbbbbbbbbbbabb
abbbbbbbbb
bbbbbbbbbbbbbbbbbbbbbb
bbbbbbbbbbbbbaaaaaaaaa
bbbbbbbbbbbbbbbaaaaa
bbbbbbbbbbbbbbbbbbbbbb
bbbbbbbbbbbbbbbbbbbbba
bbbbbbbbbaaaaaaaaaaaaaaa
bbbbbbbbbbbbbbbbba

*   In the $1$\-st test case, we can do the operation for the $1$\-st and $4$\-th characters to make $S$ `bba`.
*   In the $2$\-nd test case, we can do the operation for the $1$\-st and $5$\-th characters to make $S$ `bba`.
*   In the $3$\-rd test case, we can do the operation for the $1$\-st and $2$\-nd characters to make $S$ `bbabaa`, then do it for the $3$\-rd and $5$\-th characters to make $S$ `bbba`.

API Response (JSON)

{
  "problem": {
    "name": "Rvom and Rsrev",
    "description": {
      "content": "Given is a string $S$ consisting of `a` and `b`. Find the lexicographically **greatest** string that can be obtained by applying the following operation to $S$ zero or more times: *   Choose two char",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc113_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a string $S$ consisting of `a` and `b`. Find the lexicographically **greatest** string that can be obtained by applying the following operation to $S$ zero or more times:\n\n*   Choose two char...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments