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 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.math.BigDecimal;
import java.math.MathContext;

public class Main {
  public static void main(String[] args) {
    Scanner sc=new Scanner(System.in);
    long n=sc.nextLong();
    BigDecimal n1=BigDecimal.valueOf(n);
    BigDecimal nn=sqrt(n1,1);
    nn=nn.setScale(0,BigDecimal.ROUND_UP);
    int a=nn.intValue();
    long x=1;
    long y=1;
    for(int i=a;i>0;i--){
      if(n%i==0){
        x=i;
        y=n/i;
        break;
      }
    }
    System.out.println(x+y-2);
  }

  public static BigDecimal sqrt(BigDecimal a, int scale){
    BigDecimal x = new BigDecimal(Math.sqrt(a.doubleValue()), MathContext.DECIMAL64);
    if(scale < 17) return x;
    BigDecimal b2 = new BigDecimal(2);
    for(int tempScale = 16; tempScale < scale; tempScale *= 2){
      x = x.subtract(x.multiply(x).subtract(a).divide(x.multiply(b2), scale, BigDecimal.ROUND_HALF_EVEN));
    }
    return x;
  }
}