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: Runtime Error)

using System;
class Atcoder_Templete
{
    static void Main(string[] args)
    {
        string input_string = Console.ReadLine();
        long input_int = long.Parse(input_string);
        decimal rootOfInputDouble = (decimal)Math.Sqrt(input_int);
        long result = 0;
        long niceX = 0;
        long niceY = 0;
        long rootOfInputInt = (long)rootOfInputDouble;
        if (rootOfInputDouble - rootOfInputInt == 0)
        {
            result = 2 * (rootOfInputInt - 1);
        }
        else
        {
            for (long i = rootOfInputInt - 1; i < rootOfInputInt; i--)
            {
                if (input_int % i == 0)
                {
                    niceX = i;
                    niceY = input_int / i;
                    break;
                }
            }
            result = niceX + niceY - 2;
        }
        //出力
        Console.WriteLine(result);
    }


}