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);
		long N = sc.nextLong();
		long ans = 0;
		
		if (Math.floor(Math.sqrt(N)) * Math.floor(Math.sqrt(N)) == N) {
			ans = (long)((Math.sqrt(N) - 1) + (Math.sqrt(N) - 1));
		} else if (N % 3 == 0) {
			ans = N / 3 + 1;
		} else if (N % 2 == 0) {
			ans = N / 2;
		} else if (N % 2 != 0) {
			ans = N - 1;
		}
		
		System.out.println(ans);
	}
}