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.IO;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    class AtCoderr
    {
        static void Main(string[] args)
        {
            long n = long.Parse(ReadLine());
            var hoge = PrimeFactor(n).ToArray();
            long[] s = new long[2];
            if (hoge.Count() == 1)
            {
                WriteLine(n - 1);
            }
            else 
            {
                s[0] = hoge[0];
                s[1] = hoge[1];
                for (int i = 2; i < hoge.Length; i++)
                {
                    if (s[0] < s[1])
                    {
                        s[0] *= hoge[i];
                    }
                    else
                    {
                        s[1] += hoge[i];
                    }
                }
                WriteLine(s[0] + s[1] - 2);
            }
        }


        /// <summary>
        /// 素因数分解を行う関数
        /// 計算量は多分O(√n)
        /// </summary>
        /// <param name="n"></param>
        /// <returns></returns>
        static IEnumerable<long> PrimeFactor(long n)
        {
            int i = 2;
            long tmp = n;

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