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: Wrong Answer)

object Main {
  def main(args:Array[String]) = {
    val sc = new java.util.Scanner(System.in)
    var n = sc.nextLong
    var norg = n
    var ns = new Array[Int](0)
    var a, b = 1L
    for(i <- 2 to Math.sqrt(n).toInt+1 if n%i == 0) {
      while(n%i ==0) {
        n = n / i
        ns :+= i
      }
    }
    if (n == norg) {
      println(n-1)
      System.exit(0)
    }
    a = n
    ns.reverse.foreach { v =>
      if (a < b) {
        a = a*v
      } else {
        b = b*v
      }
    }
    println(ns.deep)
    //println(a)
    //println(b)
    println((a-1)+(b-1))
  }
}