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;
using System.Linq;

public class Solution
{
    public static List<long> GetDivisors(long n)
    {
        var divisors = new List<long>();
        for (int i = 1; i <= Math.Sqrt(n) + 1; i++)
        {
            if (n % i == 0)
            {
                divisors.Add(i);
                if (i != n / i)
                {
                    divisors.Add(n / i);
                }
            }
        }
        return divisors;
    }

    public static void Main()
    {
        var n = long.Parse(Console.ReadLine());
        var divs = GetDivisors(n);

        var min = divs.Min(d => d - 1 + n / d - 1);
        Console.WriteLine(min);
    }
}