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());

            string minus2Str = ConvertBaseNumber(n, -2);
            Console.WriteLine(minus2Str);
        }

        static string ConvertBaseNumber(int sourceNum, int n)
        {
            //[summary]10進法の数字をn進法に変換
            //変換方法については、以下リンクの最下部を参照
            //http://manabi.matiralab.com/binary/

            var mods = new List<int>();
            int num = sourceNum;

            //元の数字が"n"で割れなくなるまで繰り返し
            while (num != 1)
            {
                if(num <0 && num % n != 0)
                {
                    mods.Add(1);
                    num = (num - 1) / n;
                }
                else
                {
                    mods.Add(num % n);
                    num /= n;
                }                
            }

            mods.Add(num);

            //記憶した数字の順番を入れ替える
            mods.Reverse();

            //Listの値を結合
            return string.Join("", mods);
        }
    }
}