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();
		ArrayList<Long> ary = new ArrayList<Long>();
		for(int i = 2; i <= Math.sqrt(N); i++) {
			while(N % i == 0) {
				ary.add((long)i);
				N /= i;
			}
		}
		ary.add(N);
		Collections.sort(ary);
		long num1 = 1;
		long num2 = 1;
		for(int i = 0; i < ary.size(); i++) {
			if(num1 > num2) {
				num2 *= ary.get(i);
			} else {
				num1 *= ary.get(i);
			}
		}
		System.out.println((num1 - 1) + (num2 - 1));
	}
}