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: Time Limit Exceeded)

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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = long.Parse(Console.ReadLine());

            var pf = PrimeFactors(N).ToArray();
            long min = 0;
            for (int i = 1; i <= pf.Length || i<= 8; i++)
            {
                //var combination = Combination.Enumerate<long>(pf, i, false)
                //    .GroupBy(r => r.Sum()).Select(r => r.First()).ToList();

                var combination = pf.Comb(i).ToArray();

                foreach (var item in combination)
                {
                    long a = 1;
                    foreach (var aa in item)
                    {
                        a *= aa;
                    }
                    var b = N / a;

                    var c = a + b - 2;
                    if (c < min || min == 0)
                    {
                        min = c;
                    }
                }
            }

            Console.WriteLine(min);
        }

        public static IEnumerable<long> PrimeFactors(long n)
        {
            long i = 2;
            long tmp = n;

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

    }

    public static class Combination
    {
        public static IEnumerable<IEnumerable<T>> Comb<T>(this IEnumerable<T> items, int r)
        {
            if (r == 0)
            {
                yield return Enumerable.Empty<T>();
            }
            else
            {
                var i = 1;
                foreach (var x in items)
                {
                    var xs = items.Skip(i);
                    foreach (var c in Comb(xs, r - 1))
                        yield return c.Before(x);

                    i++;
                }
            }

        }
        public static IEnumerable<T> Before<T>(this IEnumerable<T> items, T first)
        {
            yield return first;

            foreach (var i in items)
                yield return i;
        }
        public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items, int k, bool withRepetition)
        {
            if (k == 1)
            {
                foreach (var item in items)
                    yield return new T[] { item };
                yield break;
            }
            foreach (var item in items)
            {
                var leftside = new T[] { item };

                var unused = withRepetition ? items : items.SkipWhile(e => !e.Equals(item)).Skip(1).ToList();

                foreach (var rightside in Enumerate(unused, k - 1, withRepetition))
                {
                    yield return leftside.Concat(rightside).ToArray();
                }
            }
        }
    }
}