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.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) throws Exception {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		// StringTokenizer st = new StringTokenizer(br.readLine());
		long n1 = Long.parseLong(br.readLine());
		long tmp = 0;
		long insuu1 = 0;
		long insuu2 = 0;

		for (int i = 1; i < 10; i++) {
			for (int j = 1; j < 10; j++) {
				if (i * j == n1) {
					if (i + j < tmp || tmp == 0) {
						insuu1 = i;
						insuu2 = j;
					}
					tmp = i + j;
				}
			}
		}

		System.out.println(insuu1 + insuu2 - 2);
	}
}