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.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Math;

namespace C_ABC144
{
    class MainClass
    {

        static long[] s;

        public static void Main(string[] args)
        {
            s = Array.ConvertAll(ReadLine().Split().ToArray(), long.Parse);
            long srt = (long)Ceiling(Sqrt(s[0]));
            //WriteLine(srt);
            long u = s[0];
            for(long i = srt;i>=1;i--){
                //WriteLine("i : {0}  u : {1}",i,u);
                if(u%i==0){
                    WriteLine((u/i - 1)+i - 1);
                    return;
                }
            }
        }
    }
}