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;
class Program
{
	static void Main(string[] args)
	{
		string input = Console.ReadLine();
		double n = double.Parse(input);
		double sho1 = n;
		double sho2 = 0;
		double i1 = 1;
		double i2 = 0;
		for(double i =1; i < Math.Sqrt(n)+1; i++)
		{
			double amari = n%i; 
			if(amari==0)
			{
				sho2 = n / i;
				i2 = n / sho2;
				if(i1+sho1>i2+sho2)
				{
					i1 = i2;
					sho1 = sho2;
				}
				else
				{
					continue;
				}
			}
			else
			{
				continue;
			}
		}
		Console.WriteLine(i1+sho1-2);
	}
}