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 static System.Console;
using static System.Int32;

class Program
{
    static void Main(string[] args)
    {
        var line = Hoge(Parse(ReadLine()));
        WriteLine(line);
    }

    static string Hoge(int num)
    {
        if (num == 0) return "0";
        var list = new List<int>();
        Piyo(num, list);
        var ary = Enumerable.Repeat('0', list[0] + 1).ToArray();
        foreach (var i in list)
        {
            ary[ary.Length - i - 1] = '1';
        }
        return new string(ary);
    }

    static void Piyo(long num, List<int> list)
    {
        if (num == 0) return;

        long abs = Math.Abs(num);
        bool isPlus = 0 < num;
        long beki = isPlus ? 1 : 2;
        int sisu = isPlus ? 0 : 1;
        long ijou = 0;
        while (true)
        {
            ijou += beki;
            if (abs <= ijou) break;
            beki = beki << 2;
            sisu += 2;
        }
        list.Add(sisu);
        if (isPlus) Piyo(num - beki, list);
        else Piyo(num + beki, list);
    }

    //static string ReadLine()
    //{
    //    return _inputs[_inIndex++];
    //}

    //static string[] _inputs = @"3".Split(new string[] { Environment.NewLine }, StringSplitOptions.None);

    //static int _inIndex = 0;
}