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;
using System.Numerics;
using static System.Console;
using static System.Math;

class Program
{
    static void Main()
    {
        var N = long.Parse(ReadLine());
        var d = SortedYakusuu(N);
        if (d.Length == 2)
        {
            WriteLine(N-1);
            return;
        }
        if (d.Length % 2 == 1)
        {
            WriteLine((d[d.Length / 2] - 1) * 2);
        }
        else
        {

            WriteLine(d[d.Length / 2] + d[d.Length / 2 - 1] - 2);
        }

    }


    public static long[] SortedYakusuu(long n)//O(sqrt(N) + d(N)) 
    {
        if (n < 1) return new long[0];//Assert
        var r = new List<long>();
        for (long i = 1; i * i <= n; i++)
        {
            if (n % i == 0)
            {
                r.Add(i);
                if (i * i != n) r.Add(n / i);
            }
        }
        var k = r.ToArray();
        Array.Sort(k);//自前ソートd(N)のほうが速いか･･･？
        return k;
    }
}