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: Wrong Answer)

import java.util.*;
 
public class Main {
    public static void main(String args[]) {
        
       Scanner sc = new Scanner(System.in);
       long num = sc.nextLong();
       
       long x =num;
       long a=1;
       long b=1;
       //素因数分解を一度行う
       for (long i = 2;i <= num;) {
            if (x % i == 0) { // 最小の因数を求める 
                if(a<b){
                    
                    a=a*b;//項が3ついじょうある場合、小さい項同士はかけあわせる
                    b=i;//最大項は代入
                    
                }else{
                    b=a*b;
                    a=i;
                }
                
                x /= i; // 最小の因数で割った数を代入する
            } else
                i++;
        }
        long answer = (a-1)+(b-1);
        
        System.out.println(answer);
        
        
       
       
       
    
        
    }
    
}