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 1.8.0) (judge verdict: Time Limit Exceeded)

import java.math.*;
import java.util.Scanner;
import java.util.*;
public class Main {
	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		ArrayList<Long> arr=new ArrayList<Long>();
		long a = scn.nextLong();
		if(prime(a)) {
			System.out.println(a-1);
			return;
		}
		long ans = 0;
		long d1=0;
		long d2=0;
		long min=Integer.MAX_VALUE;
		for(long i=1;i<=a/2;i++) {
			if(a%i==0) {
				if(i + a/i < min) {
					min = i + a/i;
				}
			}
		}System.out.println(min-2);
	}
	public static boolean prime(long n) {
		 if (n <= 1) 
	            return false; 
	        if (n <= 3) 
	            return true; 
	        if (n % 2 == 0 || n % 3 == 0) 
	            return false; 
	  
	        for (long i = 5; i * i <= n; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	                return false; 
	  
	        return true; 
	}
}