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.*;

class Point{
  private long i;
  private long j;
  
  Point(long i,long j){
    this.i=i;
    this.j=j;
  }

  public long getter(){
    return (this.i-1)+(this.j-1);
  }
}

class Main{
  public static void main(String[] args){
    Scanner scan=new Scanner(System.in);
    long N=scan.nextLong();
    int k=0;
    Point[] points=new Point[10*10*10*10*10*10];
    for(long i=1;i<=N;i++){
      if(N%i==0){
        long j=N/i;
        points[k++]=new Point(i,j);
      }
    }
    long min=points[0].getter();
    for(int i=0;i<k;i++){
      if(min>points[i].getter()){
        min=points[i].getter();
      }
    }
   System.out.println(min); 
  }
}