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;
public class Main{

	public static void main(String[] args) throws Exception{
		Scanner stdIn = new Scanner(System.in);
		Long n = stdIn.nextLong();
		Long min = Long.MAX_VALUE;

		for(int i = 1; i < Math.sqrt(n); i++) {
			if(n%i == 0) {
				long b = n/i; //商
				long c = compare(i,b);
				if(min > c) {
					min = c;
				}
			}

		}
		System.out.println(min);

	}
	static long compare(long a, long b) {  //移動回数の合計を出すメソッド
		long count = 0;
		count += a-1;
		count += b-1;
		return count;
	}


}