Problem:
Score : 300 points

Problem Statement

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

Output

Print the minimum number of moves needed to reach a square that contains the integer N.

Sample Input 1

10

Sample Output 1

5

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

Sample Input 2

50

Sample Output 2

13

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

Sample Input 3

10000000019

Sample Output 3

10000000018

Both input and output may be enormous.

Solution in Scala (2.11.7) (judge verdict: Accepted)

import java.io.{BufferedReader, InputStreamReader}

object Main {
  def main(args: Array[String]): Unit = {
    val n = new BufferedReader(new InputStreamReader(System.in)).readLine().toLong
    val sqrt_of_n = Math.sqrt(n).toLong

    System.out.println(
      (sqrt_of_n to 2 by -1).find(d => n % d == 0) match {
        case Some(d) => n / d + d - 2L
        case None => n + 1L - 2L
      }
    )
  }
}