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.Scanner;

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

        long answer = input - 1;
        if (input % 2 == 0) {
            answer = getAnswer(input, answer, 1);
        } else {
            answer = getAnswer(input, answer, 2);
        }
        System.out.println(answer);
    }

    private static long getAnswer(long input, long answer, long minus) {
        int newStart = (int) Math.sqrt(input);
        for (long i = newStart; i > 1; i -= minus) {
            if (input % i == 0) {
                long divisible = input / i;
                long possibleAnswer = (i - 1) + (divisible - 1);
                return possibleAnswer;
            }
        }
        return answer;
    }
}