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.util.Scanner;

/**
 * @author yoshizaki
 *
 */
public class Main {

    public static void main(String[] args) {
        Scanner scanner= new Scanner(System.in);
        long target = scanner.nextLong();
    //    long start = System.currentTimeMillis(); 
        long ans = calc(target);
    //    long end = System.currentTimeMillis(); 
    //    long time = end - start;
        System.out.println(ans );
    //    System.out.println(time +"ms");
    }
    
    /**
     * @param target
     * @return
     */
    public static  long calc(long target){
        long divNum = 0;
        long ansNum = 0;
        long sumNum = 0;
        for (long i = 1; i < (target / 2) + 1 ; i++)
        {
            if (target % i == 0)
            {
                divNum = i ;
                ansNum = target / i;
            }
            if ( divNum + ansNum < sumNum || sumNum == 0  )
                sumNum = divNum + ansNum ;
        }
        return sumNum -2;
    }
}