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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
      	//入力値
      	long n = sc.nextLong();
      
      	//入力値の平方根
      	int a = (int)Math.sqrt(n);
      
      	//移動回数
      	long b =0;
      	
      	for(long i = 1;i<a+1;++i){
          //約数だった場合
          if(n%i==0){
            
            if(b==0){
              b = (i-1)+(n/i - 1);
            }else if(b>(i-1)+(n/i - 1)){
              b = (i-1)+(n/i - 1);
            }
          }
        }
      System.out.println(b);
    }
}