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.Linq;
using System.Collections.Generic;
using System.Numerics;
namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var N = Inputer.Long1Char();
            var sosu = PrimeFactors.PrimeFactor(N).ToArray();
            if(sosu.Length == 1)
            {
                Console.Write(N - 1);
            }
            else
            {
                while (sosu.Length != 2)
                {
                    var kakezan = new List<long>();
                    if (sosu.Length % 2 != 0) { kakezan.Add(sosu[sosu.Length / 2 + 1]); }
                    for (int i = 0; i < sosu.Length / 2; i++)
                    {
                        kakezan.Add(sosu[i] * sosu[sosu.Length - i - 1]);
                    }
                    sosu = kakezan.ToArray();
                }
                Console.WriteLine(sosu.Sum() - 2);
                

            }


            
        }



    }

    /// <summary>
    /// 入力受付
    /// </summary>
    static class Inputer
    {
        /// <summary>
        /// A B C の複数整数からなる1行を受け取る
        /// </summary>
        /// <returns></returns>
        public static int[] IntArray1Line()
        {
            return Console.ReadLine().Split().Select(int.Parse).ToArray();
        }

        /// <summary>
        /// 整数N　のような１つの整数からなる入力を受け取る
        /// </summary>
        /// <returns></returns>
        public static int Int1Char()
        {
            return int.Parse(Console.ReadLine());
        }

        /// <summary>
        /// 大きい整数N　のような１つの整数からなる入力を受け取る
        /// </summary>
        /// <returns></returns>
        public static long Long1Char()
        {
            return long.Parse(Console.ReadLine());

        }

    }

    /// <summary>
    /// 順列を出すやつ
    /// </summary>
    /// <typeparam name="T"></typeparam>
    static class Permutation<T>
    {
        private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
        {
            int N = a.Length;
            if (N == 0)
            {
                perms.Add(stack.Reverse().ToArray());
            }
            else
            {
                var b = new T[N - 1];
                Array.Copy(a, 1, b, 0, N - 1);
                for (int i = 0; i < a.Length; ++i)
                {
                    stack.Push(a[i]);
                    Search(perms, stack, b);
                    if (i < b.Length) { b[i] = a[i]; }
                    stack.Pop();
                }
            }
        }
        public static IEnumerable<T[]> All(IEnumerable<T> src)
        {
            var perms = new List<T[]>();
            Search(perms, new Stack<T>(), src.ToArray());
            return perms;
        }
    }
    
    /// <summary>
    /// 素因数分解
    /// </summary>
    static class PrimeFactors
    {
        public static IEnumerable<long> PrimeFactor(long n)
        {
            long i = 2;
            long tmp = n;

            while (i * i <= n) 
            {
                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
        }

    }

}