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: Time Limit Exceeded)

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

namespace AtCoder
{
    class Program
    { 
        static void Main(string[] args)
        {
            //[summary]C - Base -2 Number
            int n = int.Parse(Console.ReadLine());

            //合計するための部品(-2のN乗)を用意しておく
            var parts = CollectParts().ToList();

            //計算のバリエーションを取得(何パターン計算すればよいか)
            long count = (long)Math.Pow(2, parts.Count);

            for(long i = 0; i < count; i++)
            {
                var binary = Convert.ToString(i, 2);
                long sum = 0;

                for(int j = 0; j < binary.Length; j++)
                {
                    if (binary[j] == '1')
                    {
                        sum += parts[j];
                    }
                }

                if (sum == n)
                {
                    string s = String.Join("", binary.Reverse());
                    Console.WriteLine(s);
                    break;
                }
            }
        }

        static IEnumerable<long> CollectParts()
        {
            for (int i = 0; i < 40; i++)
            {
                yield return (long)Math.Pow(-2, i);
            }
        }


        static List<int> ReadLine()
        {
            var line = Console.ReadLine().TrimEnd();
            var array = line.Split(' ');
            var numbers = new List<int>();

            foreach (var s in array)
            {
                int num = int.Parse(s);
                numbers.Add(num);
            }

            return numbers;
        }
    }
}