Walk on Multiplication Table

AtCoder

IDabc144_c

Time2000ms

Memory256MB

Difficulty—

Takahashi is standing on a multiplication table with infinitely many rows and columns. The square $(i,j)$ contains the integer $i \times j$. Initially, Takahashi is standing at $(1,1)$. In one move, he can move from $(i,j)$ to either $(i+1,j)$ or $(i,j+1)$. Given an integer $N$, find the minimum number of moves needed to reach a square that contains $N$. ## Constraints * $2 \leq N \leq 10^{12}$ * $N$ is an integer. ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

5

$(2,5)$ can be reached in five moves. We cannot reach a square that contains $10$ in less than five moves.

Input #2

Output #2

13

$(5, 10)$ can be reached in $13$ moves.

Input #3

10000000019

Output #3

10000000018

Both input and output may be enormous.

API Response (JSON)

{
  "problem": {
    "name": "Walk on Multiplication Table",
    "description": {
      "content": "Takahashi is standing on a multiplication table with infinitely many rows and columns. The square $(i,j)$ contains the integer $i \\times j$. Initially, Takahashi is standing at $(1,1)$. In one move, h",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc144_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is standing on a multiplication table with infinitely many rows and columns.\nThe square $(i,j)$ contains the integer $i \\times j$. Initially, Takahashi is standing at $(1,1)$.\nIn one move, h...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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