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: Accepted)

import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		long N = sc.nextLong();
    long X = 1;
    ArrayList<Long> array = new ArrayList<>();

    for(long i = 1; i <= (long)Math.sqrt(N);i++){
      if(N%i == 0){
        array.add(i + (N/i));
      }
    }

    long culc = array.get(0);
    for(int i = 1; i < array.size(); i++){
      if(array.get(i) < culc)
        culc = array.get(i);
    }

    System.out.println(culc-2);
	}

  public static boolean isPrime(long num) {
    if (num < 2) return false;
    else if (num == 2) return true;
    else if (num % 2 == 0) return false; // 偶数はあらかじめ除く

    double sqrtNum = Math.sqrt(num);
    for (int i = 3; i <= sqrtNum; i += 2){
        if (num % i == 0){
            // 素数ではない
            return false;
        }
    }

    // 素数である
    return true;
  }
}