Young Maids

AtCoder

IDarc080_c

Time2000ms

Memory256MB

Difficulty—

Let $N$ be a positive even number. We have a permutation of $(1, 2, ..., N)$, $p = (p_1, p_2, ..., p_N)$. Snuke is constructing another permutation of $(1, 2, ..., N)$, $q$, following the procedure below. First, let $q$ be an empty sequence. Then, perform the following operation until $p$ becomes empty: * Select two adjacent elements in $p$, and call them $x$ and $y$ in order. Remove $x$ and $y$ from $p$ (reducing the length of $p$ by $2$), and insert $x$ and $y$, preserving the original order, at the beginning of $q$. When $p$ becomes empty, $q$ will be a permutation of $(1, 2, ..., N)$. Find the lexicographically smallest permutation that can be obtained as $q$. ## Constraints * $N$ is an even number. * $2 ≤ N ≤ 2 × 10^5$ * $p$ is a permutation of $(1, 2, ..., N)$. ## Input Input is given from Standard Input in the following format: $N$ $p_1$ $p_2$ $...$ $p_N$ [samples]

Samples

Input #1

4
3 2 4 1

Output #1

3 1 2 4

The solution above is obtained as follows:

$p$

$q$

$(3, 2, 4, 1)$

$()$

↓

↓

$(3, 1)$

$(2, 4)$

↓

↓

$()$

$(3, 1, 2, 4)$

Input #2

2
1 2

Output #2

1 2

Input #3

8
4 6 3 2 8 5 7 1

Output #3

3 1 2 7 4 6 8 5

The solution above is obtained as follows:

$p$

$q$

$(4, 6, 3, 2, 8, 5, 7, 1)$

$()$

↓

↓

$(4, 6, 3, 2, 7, 1)$

$(8, 5)$

↓

↓

$(3, 2, 7, 1)$

$(4, 6, 8, 5)$

↓

↓

$(3, 1)$

$(2, 7, 4, 6, 8, 5)$

↓

↓

$()$

$(3, 1, 2, 7, 4, 6, 8, 5)$

API Response (JSON)

{
  "problem": {
    "name": "Young Maids",
    "description": {
      "content": "Let $N$ be a positive even number. We have a permutation of $(1, 2, ..., N)$, $p = (p_1, p_2, ..., p_N)$. Snuke is constructing another permutation of $(1, 2, ..., N)$, $q$, following the procedure be",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc080_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Let $N$ be a positive even number.\nWe have a permutation of $(1, 2, ..., N)$, $p = (p_1, p_2, ..., p_N)$. Snuke is constructing another permutation of $(1, 2, ..., N)$, $q$, following the procedure be...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments