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: Time Limit Exceeded)

import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {
	
	static boolean isPerfectSquare(long x)  
    { 
          
        // Find floating point value of 
        // square root of x. 
        double sr = Math.sqrt(x); 
      
        // If square root is an integer 
        return ((sr - Math.floor(sr)) == 0); 
    } 
	
	
	 static boolean checkPrime(long n) 
	    { 
	        // Converting long to BigInteger 
	        BigInteger b = new BigInteger(String.valueOf(n)); 
	  
	        return b.isProbablePrime(1); 
	    } 
	
	static void canMultiply(long a) {
		
	
	long k=(long)Math.pow(10, 6);
	
	long prev=1,current;
	for(long i=1;i<=(long)a/2;i++) {
			if(a%i==0) {
				current=i;
				
				if(prev*current==a) {
					System.out.println(prev+current-2);
						return;
				}
				prev=current;
				
			}
		
	}
		
	}
	
	
	
	static void check(long a) {
		List<Long> list =new ArrayList<Long>();
		
		for(long i=1;i<=a;i++) {
			for(long j=1;j<=a;j++) {
				
				if(i*j==a) {
					list.add(i+j-2);
					
				}
				
			}
			
		}
		System.out.println(Collections.min(list));

	}
		public static void main(String[] args) {
			
			Scanner sc =new Scanner(System.in);
			
			
			long a,b;
			a=sc.nextLong();
			
			
			
			if(a<100) {
				check(a);
				
			}
			else {
			
			if(checkPrime(a)) {
				System.out.println(a-1);
			}
			else if(isPerfectSquare(a)) {
				System.out.println(2*(int)Math.sqrt(a)-2);

			}
			else {
			canMultiply(a);
			}
			
			
		
		}
		}
}