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;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            long n = long.Parse(Console.ReadLine());
            var primes = FactorizePrimes(n);
            long x = primes.Take((int)Math.Ceiling((decimal)primes.Count() / 2)).Aggregate((res, e) => res * e);
            long y = primes.Count() == 1 ? 1 : primes.Skip((int)Math.Ceiling((decimal)primes.Count() / 2)).Aggregate((res, e) => res * e);

            Console.WriteLine((x - 1) + (y - 1));


        
        }

        static IEnumerable<long> FactorizePrimes(long n)
        {
            long i = 2;
            long temp = n;
            while (i < Math.Sqrt(n))
            {
                if (temp % i == 0)
                {
                    temp /= i;
                    yield return i;
                }
                else i++;
            }
            if (temp != 1) yield return temp;
        }
    }
}