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();
		sc.close();
		long save = n;
		ArrayList<Long> list = new ArrayList<Long>();

		for (int i = 2; i <= Math.sqrt(n);) {
			if (n % i == 0) { // 最小の因数を求める
				n /= i; // 最小の因数で割った数を代入する
				list.add((long) i);
			} else {
				i++;
			}
		}
		long[] prod = new long[2];
		prod[0] = 1;
		prod[1] = save;
		long ans = save - 1;
		for (int i = 0; i < list.size(); i++) {
			prod[0] *= list.get(i);
			prod[1] /= list.get(i);
			long tmp = prod[0] + prod[1] - 2;
			if (tmp < ans) {
				ans = tmp;
			} else {
				break;
			}
		}
		System.out.println(ans);
	}

	public static int[] arrayInt(Scanner sc, int n) {
		int[] array = new int[n];
		for (int i = 0; i < n; i++) {
			array[i] = sc.nextInt();
		}
		return array;
	}

	public static long[] arrayLong(Scanner sc, int n) {
		long[] array = new long[n];
		for (int i = 0; i < n; i++) {
			array[i] = sc.nextLong();
		}
		return array;
	}

	public static double[] arrayDouble(Scanner sc, int n) {
		double[] array = new double[n];
		for (int i = 0; i < n; i++) {
			array[i] = sc.nextDouble();
		}
		return array;
	}
}