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: Runtime Error)

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

namespace C
{
    public class MainClass
    {
        public static void Main(string[] args)
        {
            long N = Int64.Parse(Console.ReadLine());
            var factors = PrimeFactors(N);

            List<long> steps = new List<long>();
            for (int count = 1; count < factors.Count; count++)
            {
                foreach (var item in combinations(factors, count))
                {
                    long l = 1;
                    foreach (var n in item)
                    {
                        l *= n;
                    }
                    steps.Add(l + (N / l) - 2);
                }
            }
            
            Console.WriteLine(steps.Min());
        }

        public static List<long> PrimeFactors(long n)
        {
            long i = 2;
            long tmp = n;
            List<long> factors = new List<long>();

            while(i <= n)
            {
                if(tmp % i == 0)
                {
                    tmp /= i;
                    factors.Add(i);
                }
                else
                {
                    i++;
                }
            }
            if (tmp != 1) factors.Add(i);
            return factors;
        }

        static IEnumerable<List<TSrc>> combinations<TSrc>(List<TSrc> src, int n)
        {
            return Enumerable.Range(0, n - 1)
                .Aggregate(
                    Enumerable.Range(0, src.Count() - n + 1)
                        .Select(num => new List<int>() { num }),
                    (list, _) => list.SelectMany(c =>
                        Enumerable.Range(c.Max() + 1, src.Count() - c.Max() - 1)
                            .Select(num => new List<int>(c) { num })
                        )
                    )
                .Select(c => c
                    .Select(num => src[num])
                    .ToList()
                    );
        }

    }
 
}