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

namespace C044
{
    class C105
    {
        static void Main(string[] args)
        {
            long N =int.Parse( Console.ReadLine());
            long x = N;
            char[] c = null;
            while (x != 0)
            {

                int i = 0;
                long s = 0, t = 0;
                while (true)
                {
                    long k = (long)Math.Pow(-2, i);
                    if (k < 0) s += k;
                    else t += k;
                    i++;

                    if(s <= x && x <= t)
                    {
                        x -= k;
                        if (c == null)
                        {
                            c = Enumerable.Repeat('0', i).ToArray();
                        }
                        c[c.Length-i] = '1';
                        break;
                    }
                }
            }
            if (c == null) c = new char[] { '0' };
            string str = new string(c);
            Console.WriteLine(str);
        }

    }
}