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.Text;
using System.Numerics;
using System.IO;

namespace SolutionCS
{
    class Program
    {
        static List<ulong> Divisor(ulong input)
        {
            List<ulong> result = new List<ulong>();

            for (ulong i = 1; i * i <= input; i++)
            {
                if (0 == input % i)
                {
                    result.Add(i);
                    if (i * i != input)
                    {
                        result.Add(input / i);
                    }
                }
            }

            return result;
        }
        static void Main(string[] args)
        {
            ulong A = ulong.Parse(Console.ReadLine());

            List<ulong> d = Divisor(A);

            ulong ans = ulong.MaxValue;

            for (int i = 0; i < d.Count; i++)
            {
                ulong d0 = d[i];
                ans = (d0 + A / d0) - 2;
            }

            Console.WriteLine(ans);
        }
    }
}