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: Accepted)

import java.util.*;
import java.util.ArrayDeque;
import java.util.Queue;
import java.math.RoundingMode;
import java.math.BigDecimal;


public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		double lim = Math.sqrt(n);
		long i = 2;
		long sub = n-1;
		long a = n;
		long b = 1;
		while(i <= lim) {
			long memo = n-i;
			if(n%i==0&&sub>memo) {
				a = n/i;
				b = i;
				sub = memo;
			}
			i++;
		}
		System.out.println(a+b-2);
	}	
}