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 Java7 (OpenJDK 1.7.0) (judge verdict: Runtime Error)

import java.util.*;
 
class Main{
  public static void main(String[] args){
    Scanner scan = new Scanner(System.in);
    long n = scan.nextLong();
    long c1[] = new long[1000];
    long c2[] = new long[1000];
    long a=Long.MAX_VALUE;
    int g = 0;
    
    for(long i=1;i<(long)Math.sqrt(n)+1;i++){
    	if(n%i==0){
        	c1[g]=i;
          	c2[g]=n/i;
          	g++;
        }
    }
    
    for(int j=0;j<g;j++){
      a = Math.min(a,c1[j]+c2[j]-2);
    }
    System.out.println(a);
  }
}