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.Text;
using System.Threading.Tasks;
using System.IO;

using static Input;
using static Util;
class Program
{
    static long N;
    static void INPUT()
    {
        N = NextLong();
    }
    static void OUT()
    {
        var p = PrimeFactor(N);
        var n = p.Count();
        var s = n / 2 + n % 2;
        var l = 1L;
        var r = 1L;
        var a = 0;
        for (var i = 0; i < n; i++)
        {
            r *= p.ElementAt(i);
        }
        for (var i = 0; i < n; i++)
        {
            var nn = p.ElementAt(i);
            var ll = l * nn;
            var rr = r / nn;
            if (ll > rr) break;
            l = ll;
            r = rr;
        }

        Console.WriteLine(l + r - 2);
    }
    static void Main(string[] args)
    {
#if DEBUG  
        TESTINPUT();
        //INPUT();

#else
        INPUT();
#endif
        OUT();
    }

    static void TESTINPUT()
    {
        N = 123456789012;
    }

}

public class Input
{
    public const long MOD = 1000000007;
    public const int INF = 1000000007;
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}

class Util
{
    /// <summary>
    /// 素因数分解
    /// </summary>
    /// <param name="n"></param>
    /// <returns></returns>
    public static IEnumerable<long> PrimeFactor(long n)
    {
        var i = 2L;
        var tmp = n;

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