Construct Sequences

AtCoder

IDagc007_b

Time2000ms

Memory256MB

Difficulty—

#nck { width: 30px; height: auto; }You are given a permutation $p$ of the set {$1, 2, ..., N$}. Please construct two sequences of positive integers $a_1$, $a_2$, ..., $a_N$ and $b_1$, $b_2$, ..., $b_N$ satisfying the following conditions: * $1 \leq a_i, b_i \leq 10^9$ for all $i$ * $a_1 < a_2 < ... < a_N$ * $b_1 > b_2 > ... > b_N$ * $a_{p_1}+b_{p_1} < a_{p_2}+b_{p_2} < ... < a_{p_N}+b_{p_N}$ ## Constraints * $2 \leq N \leq 20,000$ * $p$ is a permutation of the set {$1, 2, ..., N$} ## Input The input is given from Standard Input in the following format: $N$ $p_1$ $p_2$ $...$ $p_N$ [samples]

Samples

Input #1

2
1 2

Output #1

1 4
5 4

$a_1 + b_1 = 6$ and $a_2 + b_2 = 8$. So this output satisfies all conditions.

Input #2

3
3 2 1

Output #2

1 2 3
5 3 1

Input #3

3
2 3 1

Output #3

5 10 100
100 10 1

API Response (JSON)

{
  "problem": {
    "name": "Construct Sequences",
    "description": {
      "content": "#nck { width: 30px; height: auto; }You are given a permutation $p$ of the set {$1, 2, ..., N$}. Please construct two sequences of positive integers $a_1$, $a_2$, ..., $a_N$ and $b_1$, $b_2$, ..., $b_N",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc007_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "#nck { width: 30px; height: auto; }You are given a permutation $p$ of the set {$1, 2, ..., N$}. Please construct two sequences of positive integers $a_1$, $a_2$, ..., $a_N$ and $b_1$, $b_2$, ..., $b_N...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments