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: Runtime Error)

import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        double roop = Math.sqrt(N);
      	double i = 1;
      	int x = 1;
        int y;
      	int count = 0;
        int endX = 0;
        int endY = 0;
        while(i < roop){
          if(N % x == 0){
            y = N / x;
            if(x + y - 2 < count || count == 0){
              endX = x;
              endY = y;
              count = x + y - 2;
            }
          }
          x += 1;
          i += 1;
        }
		 System.out.println(count);            
    }
}