Reserve or Reverse

AtCoder

IDarc134_b

Time2000ms

Memory256MB

Difficulty—

Given is a string $s$ of length $N$. Let $s_i$ denote the $i$\-th character of $s$. Snuke will transform $s$ by the following procedure. * Choose an **even length** (not necessarily contiguous) subsequence $x=(x_1, x_2, \ldots, x_{2k})$ of $(1,2, \ldots, N)$ ($k$ may be $0$). * Swap $s_{x_1}$ and $s_{x_{2k}}$. * Swap $s_{x_2}$ and $s_{x_{2k-1}}$. * Swap $s_{x_3}$ and $s_{x_{2k-2}}$. * $\vdots$ * Swap $s_{x_{k}}$ and $s_{x_{k+1}}$. Among the strings that $s$ can become after the procedure, find the lexicographically smallest one. 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 * $1 \leq N \leq 2 \times 10^5$ * $s$ is a string of length $N$ consisting of lowercase English letters. ## Input Input is given from Standard Input in the following format: $N$ $s$ [samples]

Samples

Input #1

4
dcab

Output #1

acdb

*   When $x=(1,3)$, the procedure just swaps $s_{1}$ and $s_{3}$.
*   The $s$ after the procedure is `acdb`, the lexicographically smallest possible result.

Input #2

2
ab

Output #2

ab

*   When $x=()$, the $s$ after the procedure is `ab`, the lexicographically smallest possible result.
*   Note that $x$ may have a length of $0$.

Input #3

16
cabaaabbbabcbaba

Output #3

aaaaaaabbbbcbbbc

Input #4

17
snwfpfwipeusiwkzo

Output #4

effwpnwipsusiwkzo

API Response (JSON)

{
  "problem": {
    "name": "Reserve or Reverse",
    "description": {
      "content": "Given is a string $s$ of length $N$. Let $s_i$ denote the $i$\\-th character of $s$. Snuke will transform $s$ by the following procedure. *   Choose an **even length** (not necessarily contiguous) sub",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc134_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a string $s$ of length $N$. Let $s_i$ denote the $i$\\-th character of $s$.\nSnuke will transform $s$ by the following procedure.\n\n*   Choose an **even length** (not necessarily contiguous) sub...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments