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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;

class Program
{
    static void Main(string[] args)
    {
        //string[] str = Console.ReadLine().Split(' ');//2つ以上のスペース区切り入力の取得
        string str = Console.ReadLine();
        long A = Int64.Parse(str);
        //int B = int.Parse(str[1]);
        //string[] strHeight = Console.ReadLine().Split(' ');//2つ以上のスペース区切り入力の取得
        //string[] results = new string[N];

        decimal max = Math.Floor((decimal)A / 2);
        long min = A;

        var list = PrimeFactors(A);
        long count = list.Count();
        foreach( var each_num in list )
        {
            long B = A / each_num;

            long num = each_num + B - 2;
            if (min > num) min = num;
        }

        Console.WriteLine((min).ToString());
    }
    
    public static List<long> PrimeFactors(long n)
    {
        List<long> array = new List<long>();
        array.Add(1);

        long i = 2;
        long tmp = n;

        while (i * i <= n) //※1
        {
            if (tmp % i == 0)
            {
                tmp /= i;
                array.Add(i);
            }
            else
            {
                i++;
            }
        }
        if (tmp != 1) array.Add( tmp );//最後の素数も返す

        return array;
    }
}