Tautonym Puzzle

AtCoder

IDagc012_c

Time2000ms

Memory256MB

Difficulty—

We will call a string $x$ _good_ if it satisfies the following condition: * Condition: $x$ can be represented as a concatenation of two copies of another string $y$ of length at least $1$. For example, `aa` and `bubobubo` are good; an empty string, `a`, `abcabcabc` and `abba` are not good. Eagle and Owl created a puzzle on good strings. Find one string $s$ that satisfies the following conditions. It can be proved that such a string always exists under the constraints in this problem. * $1 ≤ |s| ≤ 200$ * Each character of $s$ is one of the $100$ characters represented by the integers $1$ through $100$. * Among the $2^{|s|}$ subsequences of $s$, exactly $N$ are good strings. ## Constraints * $1 ≤ N ≤ 10^{12}$ ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

4
1 1 1 1

There are two good strings that appear as subsequences of $s$: $(1,1)$ and $(1,1,1,1)$. There are six occurrences of $(1,1)$ and one occurrence of $(1,1,1,1)$, for a total of seven.

Input #2

Output #2

23
32 11 11 73 45 8 11 83 83 8 45 32 32 10 100 73 32 83 45 73 32 11 10

API Response (JSON)

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    "name": "Tautonym Puzzle",
    "description": {
      "content": "We will call a string $x$ _good_ if it satisfies the following condition: *   Condition: $x$ can be represented as a concatenation of two copies of another string $y$ of length at least $1$. For exa",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc012_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We will call a string $x$ _good_ if it satisfies the following condition:\n\n*   Condition: $x$ can be represented as a concatenation of two copies of another string $y$ of length at least $1$.\n\nFor exa...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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