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.HashMap;
import java.util.Scanner;

/**
 * Main
 */
public class Main {

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

        Long N = sc.nextLong();
        sc.close();

        HashMap<Long, Long> mul = new HashMap<Long, Long>();         
        for(int i = 1; i < N+1; i++){
            if((N % i) == 0){
                long j = N / i;
                mul.put((long) i, j);
            }
        }

        Long min = N;
        for (HashMap.Entry<Long, Long> entry : mul.entrySet()) {
            if(min > entry.getKey() +entry.getValue()){
                min = entry.getKey() +entry.getValue();
            }           
        }
        System.out.println(min-2);

    }
}