i i's

AtCoder

IDagc064_a

Time2000ms

Memory256MB

Difficulty—

You are given a positive integer $N$. Print an integer sequence of length $L \coloneqq N(N+1)/2$, $A = (A_1, A_2, \ldots, A_L)$, that satisfies all of the following conditions. * $A$ contains exactly $i$ occurrences of $i$ for every $i = 1, 2, \ldots, N$. * $1 \leq |A_i - A_{i+1}| \leq 2$ for every $i = 1, 2, \ldots, L$. Here, $A_{L+1}$ means $A_1$. It can be proved that, under the Constraints of this problem, there is always an integer sequence $A$ of length $L$ that satisfies all of the above conditions. ## Constraints * $3 \leq N \leq 1000$ * $N$ is an integer. ## Input The input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

1 3 4 2 4 3 4 2 4 3

The integer sequence $A = (1, 3, 4, 2, 4, 3, 4, 2, 4, 3)$ contains exactly one $1$, two $2$s, three $3$s, and four $4$s, satisfying the first condition. The second condition is also satisfied, as follows:

*   $|A_1 - A_2| = |1 - 3| = 2$
*   $|A_2 - A_3| = |3 - 4| = 1$
*   $|A_3 - A_4| = |4 - 2| = 2$
*   $|A_4 - A_5| = |2 - 4| = 2$
*   $|A_5 - A_6| = |4 - 3| = 1$
*   $|A_6 - A_7| = |3 - 4| = 1$
*   $|A_7 - A_8| = |4 - 2| = 2$
*   $|A_8 - A_9| = |2 - 4| = 2$
*   $|A_9 - A_{10}| = |4 - 3| = 1$
*   $|A_{10} - A_1| = |3 - 1| = 2$

API Response (JSON)

{
  "problem": {
    "name": "i i's",
    "description": {
      "content": "You are given a positive integer $N$. Print an integer sequence of length $L \\coloneqq N(N+1)/2$, $A = (A_1, A_2, \\ldots, A_L)$, that satisfies all of the following conditions. *   $A$ contains exact",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc064_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a positive integer $N$. Print an integer sequence of length $L \\coloneqq N(N+1)/2$, $A = (A_1, A_2, \\ldots, A_L)$, that satisfies all of the following conditions.\n\n*   $A$ contains exact...",
      "is_translate": false,
      "language": "English"
    }
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}

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