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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Collections;
namespace Ccs
{
    class Program
    {
        static void Main(string[] args)
        {

//            Console.WriteLine(-10 % 3);

            var n = Int32.Parse(Console.ReadLine());

            var log = new ArrayList();
            var i = 0;
            while(n != 0)
            {
                var r = n % (Int32)Math.Pow(2, i + 1);
                log.Add( r != 0 ? 1 : 0 );
                n +=Math.Abs( r) * (i % 2 == 0 ? -1 : 1);

                Console.WriteLine(i + " " + r + " " + n);
                ++i;
            }

            for (int j = 0; j < log.Count; ++j)
                Console.Write(
                        log[log.Count-j-1]
                    );

            Console.WriteLine();
            
        }
    }
}