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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

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

            long tmp = 0;
            long ans = n;
            
            for (long i = 1; i <= n; i++)
            {
                if (i.ToString().Length > n.ToString().Length/2+1)
                {   
                    break;
                }
                if (n % i == 0)
                {
                    long j = n / i;
                    tmp = (i - 1) + (j - 1);
                    if (ans > tmp)
                    {
                        ans = tmp;
                    }
                    else if (ans < tmp)
                    {
                        break;
                    }
                }
            }

            Console.Write(ans);
            Console.ReadKey(true);
        }
    }
}