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.Scanner;
public class Main {
  public static void main( String[] args ) {
	  Scanner scan = new Scanner(System.in);
	  long N = scan.nextLong();
	  long moveCnt = ( N - 1 ) * ( N - 1 );
	  for( int i = 1;i <= Math.sqrt(N);i++ ) {
		  for( int j = 1;j <= Math.sqrt(N);j++ ) {
			  //System.out.println("処理中…");
			  if( i * j == N && ( i - 1 ) + ( j - 1 ) < moveCnt ) {
				  moveCnt = ( i - 1 ) + ( j - 1 );
			  }
		  }
	  }
	  System.out.println(moveCnt);
  }
}