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: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;
using System.Numerics;

namespace abc144
{
    class Program
    {
        static void Main(string[] args)
        {
            //Console.SetIn(new StreamReader("input.txt"));
            solve_abc144C();
        }

        public static void solve_abc144C()
        {
            long n = Convert.ToInt64(Console.ReadLine());

            long t = n;
            long min = long.MaxValue;
            for (long i = 2; i * i <= n; i++)
            {
                if (n % i == 0)
                {
                    long d = n / i;
                    min = Math.Min(min, d - 1 + i - 1);
                }
            }

            Console.WriteLine(min == long.MaxValue ? n - 1 : min);
        }

        public static long gcd(long a, long b)
        {
            if (b == 0)
            {
                return a;
            }
            else
            {
                return gcd(b, a % b);
            }
        }

        public static void solve_abc144B()
        {
            int n = Convert.ToInt32(Console.ReadLine());
            for (int i = 1; i <= 9; i++)
            {
                for (int j = 1; j <= 9; j++)
                {
                    if (i * j == n)
                    {
                        Console.WriteLine("Yes");
                        return;
                    }
                }
            }
            Console.WriteLine("No");
        }

        public static void solve_abc144A()
        {
            int[] ab = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);

            int a = ab[0];
            int b = ab[1];

            Console.WriteLine(a < 10 && b < 10 ? a * b : -1);
        }

        /*
            BinarySearchIterativeLeft
         */
        public static int binarySearchIterativeLeft(long[] haystack, long needle)
        {
            int left = -1;
            int right = haystack.Length;
            while (left < right - 1)
            {
                int middle = left + (right - left) / 2;
 
                if (haystack[middle] < needle)
                {
                    left = middle;
                }
                else
                {
                    right = middle;
                }
            }
 
            return right;
        }
        
        public static int binSearch(int[] haystack, int needle)
        {
            int l = -1;
            int r = haystack.Length;
            while(l < r - 1)
            {
                int mid = (r + l) / 2;
                if (haystack[mid] <= needle)
                {
                    l = mid;
                }
                else 
                {
                    r = mid;
                }
            }
 
            return r;
        }                        
    }
}