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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		long N = long.Parse(Console.ReadLine());
		long ans = 9999999999999999;
		var list = enum_div(N);
		for(var i=0;i<list.Count;i++){
			long n1 = list[i];
			long n2 = N/list[i];
			ans = Math.Min(ans,n1-1+n2-1);
		}
		Console.WriteLine(ans);
	}
	
	public static List<long> enum_div(long n){
		long tmp = n;
		var list = new List<long>();
		for(long i=1;i*i<=n;i++){
			if(n%i==0){
				list.Add(i);
				if(i*i!=n){
					list.Add(n/i);
				}
			}
		}
		return list;
	}
}