Problem:
Score : 300 points

Problem Statement

Given an integer N, find the base -2 representation of N.

Here, S is the base -2 representation of N when the following are all satisfied:

S is a string consisting of 0 and 1.

Unless S = 0, the initial character of S is 1.

Let S = S_k S_{k-1} ... S_0, then S_0 \times (-2)^0 + S_1 \times (-2)^1 + ... + S_k \times (-2)^k = N.

It can be proved that, for any integer M, the base -2 representation of M is uniquely determined.

Constraints

Every value in input is integer.

-10^9 \leq N \leq 10^9

Input

Input is given from Standard Input in the following format:

N

Output

Print the base -2 representation of N.

Sample Input 1

-9

Sample Output 1

1011

As (-2)^0 + (-2)^1 + (-2)^3 = 1 + (-2) + (-8) = -9, 1011 is the base -2 representation of -9.

Sample Input 2

123456789

Sample Output 2

11000101011001101110100010101

Sample Input 3

0

Sample Output 3

0

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

public static partial class Program
{
    //テンプレここから
    public static int ToInt(this string str)
    {
        return int.Parse(str);
    }

    public static long ToLong(this string str)
    {
        return long.Parse(str);
    }
    public static IEnumerable<int> ToInt(this string[] strs)
    {
        return strs.Select(x => x.ToInt());
    }

    public static IEnumerable<long> ToLong(this string[] strs)
    {
        return strs.Select(x => x.ToLong());
    }
    public static IEnumerable<int> SplToInt(this string str, char opr = ' ')
    {
        return str.Split(opr).ToInt();
    }

    public static IEnumerable<long> SplToLong(this string str, char opr = ' ')
    {
        return str.Split(opr).ToLong();
    }
    public static string CRL()
    {
        return Console.ReadLine();
    }
    public static void CWL(object obj)
    {
        Console.WriteLine(obj);
    }
    public static int Diff(int a, int b)
    {
        return Math.Abs(Math.Max(a, b) - Math.Min(a, b));
    }
    public static long Diff(long a, long b)
    {
        return Math.Abs(Math.Max(a, b) - Math.Min(a, b));
    }
    public static int Sign(this int i)
    {
        return Math.Sign(i);
    }
    //テンプレここまで
}

public static partial class Program
{
    static void Main()
    {
        var n = CRL().ToInt();
        var ans = "";
        while (n != 0)
        {
            if (n % 2 != 0)
            {
                n--;
                ans = "1" + ans;
            }
            else
            {
                ans = "0" + ans;
            }

            n /= -2;
        }

        if (ans == "")
        {
            ans = "0";
        }
        CWL(ans);
    }
}