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

//C - Walk on Multiplication Table https://atcoder.jp/contests/abc144/tasks/abc144_c

public class ABC144_C // ←Class名変更！！    Program
{
    public static void Main()
    {
        var n = Rl();
        //var c = n / 2;

        double root = Math.Sqrt(n);
        var c = (int)Ceiling(root);   //切り上げ

        var min = n+2;
        for (long i = 1; i <= c; i++)
        {
            var a = n % i;
            if (a == 0)
            {
                var v = n / i;
                if (i + v < min)
                {
                    min = i + v;
                }
            }
        }

        WriteLine($"{min - 2}");
        return;

    } // Main

    public static string Rs() { return ReadLine(); }
    public static char Rc() { var c = ReadLine(); return c[0]; }    //最初の1文字だけ返す
    public static int Ri() { return int.Parse(ReadLine()); }
    public static long Rl() { return long.Parse(ReadLine()); }
    public static char[] Rca() { return ReadLine().ToCharArray(); }
    public static int[] Ria() { return Array.ConvertAll(ReadLine().Split(' '), int.Parse); }
    public static long[] Rla() { return Array.ConvertAll(ReadLine().Split(' '), long.Parse); }
} // Class