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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
import java.util.ArrayList;

class Main{
	public static void main(String[] args){
      	ArrayList<Long> list = new ArrayList<>();
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
      	for (long i = 1; i*i <= n; i++) { 
          if (n%i == 0) {
              list.add(i);       
              if (i != n / i) {
                  list.add(n/i);
              }
          }
        }
		
        long min = n;
        for(int i = 0; i < list.size()-1; i+=2){
          long x = list.get(i);
          long y = list.get(i+1);
          if(min > (x+y-2)) min = x+y-2;
        }
        System.out.println(min);
          
	}
}