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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Math;

class MainClass
{
    static void Main()
    {
        long N = long.Parse(ReadLine());
        if (N == 0)
        {
            WriteLine(0);
        }
        else
        {
            long index = 0;
            List<int> d = new List<int>();
            if (N > 0)
            {
                index = -2;
                long nummax = 0;
                while (nummax < N)
                {
                    index += 2;
                    nummax += (long)Pow(2, index);
                }
            }
            else
            {
                index = -1;
                long nummin = 0;
                while (nummin > N)
                {
                    index += 2;
                    nummin -= (long)Pow(2, index);
                }
            }
            long num = 0;
            while (index >= 0)
            {
                if (index % 2 == 0)
                {
                    if (num < N)
                    {
                        num += (long)Pow(2, index);
                        d.Add(1);
                    }
                    else d.Add(0);
                }
                else
                {
                    if (num > N)
                    {
                        num -= (long)Pow(2, index);
                        d.Add(1);
                    }
                    else d.Add(0);
                }
                index--;
            }
            //d.Reverse();
            WriteLine(string.Join("",d));
        }
    }
}