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 Java (OpenJDK 11.0.6) (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();
        System.out.println(N);
        long p = N;
        List<Integer> primes = new ArrayList<Integer>();
//        long a = 0;
        long b = 0;
        long num = 0;
        long minNum = (long) Math.pow(10, 12);
        for (long a = 1; a <= Math.sqrt(N); a++){
            if (N % a != 0){
                continue;
            } else {
                b = N / a;
            }
            num = a + b - 2;
            if (num < minNum){
                minNum = num;
            }
        }
        System.out.println(minNum);



//        for (long i = Math.sqrt(N); i >= 1; i--){
//            while (p % i == 0){
//                p = p / i;
//                primes.add(i);
//            }
//        }
//        int a = 1; int b = 1;
//        for (int i = 0; i < primes.size(); i++){
//            if (a <= b) {
//                a *= primes.get(i);
//            } else {
//                b*=
//            }
//        }


    }
}