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.*;

public class Main{
    public static void main(String []args){
        Scanner sc = new Scanner(System.in);

        double n = sc.nextDouble();
        double checkx;
        double x = 0;
        double checky;
        double y = 0;


        for(checkx = 1;checkx <= n;checkx++){
            checky = (double)n/checkx;
            if(x ==0 && y == 0){
                x = checkx;
                y = checky;
            }else if(checky == (int)checky && checkx + checky <  x +y){
                x = checkx;
                y = checky;
            }
        }

        System.out.println(x+y-2);
    }
}