Concatenate Subsequences

AtCoder

IDarc134_d

Time2000ms

Memory256MB

Difficulty—

Given is an integer sequence $a$ of length $2N$. Snuke is going to make a sequence using a **non-empty** (not necessarily contiguous) subsequence $x=(x_1,x_2,\ldots,x_k)$ of $(1,2, \ldots, N)$. The sequence will be made by extracting and concatenating the $x_1$\-th, $x_2$\-th, $\ldots$, $x_k$\-th, $(x_{1}+N)$\-th, $\ldots$, $(x_{k}+N)$\-th elements of $a$ in this order. Find the lexicographically smallest sequence that Snuke can make. Lexicographical order on sequencesHere is the algorithm to determine the lexicographical order between different sequences $S$ and $T$. Below, let $S_i$ denote the $i$\-th element 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 $S_j$ is smaller than $T_j$ in numerical order, we determine that $S \lt T$ and quit; if $S_j$ is greater 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 * All values in input are integers. * $1 \leq N \leq 10^5$ * $1 \leq a_i \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $a_{1}$ $\cdots$ $a_{2N}$ [samples]

Samples

Input #1

3
2 1 3 1 2 2

Output #1

1 2

*   We choose $x = (2)$.
*   Then, the resulting sequence will be $(1,2)$, the lexicographically smallest possible result.

Input #2

10
38 38 80 62 62 67 38 78 74 52 53 77 59 83 74 63 80 61 68 55

Output #2

38 38 38 52 53 77 80 55

Input #3

12
52 73 49 63 55 74 35 68 22 22 74 50 71 60 52 62 65 54 70 59 65 54 60 52

Output #3

22 22 50 65 54 52

API Response (JSON)

{
  "problem": {
    "name": "Concatenate Subsequences",
    "description": {
      "content": "Given is an integer sequence $a$ of length $2N$. Snuke is going to make a sequence using a **non-empty** (not necessarily contiguous) subsequence $x=(x_1,x_2,\\ldots,x_k)$ of $(1,2, \\ldots, N)$. The se",
      "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_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is an integer sequence $a$ of length $2N$.\nSnuke is going to make a sequence using a **non-empty** (not necessarily contiguous) subsequence $x=(x_1,x_2,\\ldots,x_k)$ of $(1,2, \\ldots, N)$. The se...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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