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

public class Main {
  public static void main(String[] args) throws IOException {
    execute();
  }

  private static void execute() throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    String line = br.readLine();
    long a = Long.parseLong(line);

    System.out.println((calc(a)));
  }

  private static long calc(long a) {
    long stepCount = a;
    for (long i = 1; i <= a; i++){
      double remain = (double)a / i;
      if(remain - (long) remain == 0.0){
        stepCount = Math.min(stepCount, i + (long) remain);
      }
      if(i*i > a){
        break;
      }
    }
    if(stepCount == a){
      return --stepCount;
    }
    return stepCount - 2;
  }
}