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: Time Limit Exceeded)


import java.util.Scanner;
public class Main {
	public static void main(String[] args) {
		//long startTime = System.currentTimeMillis();
		Scanner sc = new Scanner(System.in) ;
		long thing = sc.nextLong();
		//System.out.println(thing*thing+thing+thing);
		//System.out.println(Integer.MAX_VALUE);
		long i = thing;
		long j = thing;
		for (long ii = 1 ; ii <= thing ; ii ++ ) {
			if (thing % ii != 0) { continue;}
			if ((ii+(thing/ii)) < i+j) {
				i=ii;j=(thing/ii);
			}
			//System.out.println(thing/ii+" "+ii);
		}
		//System.out.println(System.currentTimeMillis()-startTime);
		System.out.println(i+ j-2);
		
	}
}