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.*;
import java.io.*;
import java.lang.*;
// ArrayList<Integer>[] arr=new ArrayList[n];
public class Main{    
public static void main(String[] args) throws FileNotFoundException, IOException{
        Scanner s = new Scanner(System.in);
         StringBuilder sb=new StringBuilder();
         BufferedWriter out=new BufferedWriter(new OutputStreamWriter(System.out));
         long n=s.nextLong();
        //Set<Integer>ss=new HashSet<>();
         long res=Long.MAX_VALUE;
         for(long i=1;i<=1000000;i++){
            if(n%i==0){
                res=(long)Math.min(res,i-1+n/i -1);
            }
         }
         /*if(res==(long)1e9+7){
            System.out.println(n-1);
         }
         else{
            System.out.println(res);
         }*/
        System.out.println(res);
    }
}