Digit Sum of 2x

AtCoder

IDarc144_a

Time2000ms

Memory256MB

Difficulty—

For a positive integer $x$, let $f(x)$ be the sum of its digit. For example, $f(144) = 1+4+4 = 9$ and $f(1)=1$. You are given a positive integer $N$. Find the following positive integers $M$ and $x$: * The maximum positive integer $M$ for which there exists a positive integer $x$ such that $f(x)=N$ and $f(2x)=M$. * The minimum positive integer $x$ such that $f(x)=N$ and $f(2x)=M$ for the $M$ above. ## Constraints * $1\leq N\leq 10^5$ ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

6
3

We can prove that whenever $f(x)=3$, $f(2x) = 6$. Thus, $M=6$. The minimum positive integer $x$ such that $f(x)=3$ and $f(2x)=6$ is $x=3$. These $M$ and $x$ should be printed.

Input #2

Output #2

12
24

Input #3

Output #3

200
4444444444444444444444444

API Response (JSON)

{
  "problem": {
    "name": "Digit Sum of 2x",
    "description": {
      "content": "For a positive integer $x$, let $f(x)$ be the sum of its digit. For example, $f(144) = 1+4+4 = 9$ and $f(1)=1$. You are given a positive integer $N$. Find the following positive integers $M$ and $x$: ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc144_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For a positive integer $x$, let $f(x)$ be the sum of its digit. For example, $f(144) = 1+4+4 = 9$ and $f(1)=1$.\nYou are given a positive integer $N$. Find the following positive integers $M$ and $x$:\n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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