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;



class Program
{
    const int MOD = 1000000007;
    const int INF = 1 << 30;

    static void Main(string[] args)
    {
        Solve();
    }

    //static long GCD(long x,long y)
    //{
    //    if (y == 0) return x;
    //    return GCD(y, x % y);
    //}

    //static long LCM(long x,long y)
    //{
    //    return x * y / GCD(x, y);
    //}

    //static int keta(int x)
    //{
    //    string s = x.ToString();
    //    return s[s.Length - 1]-'0';
    //}

    static void Solve()
    {
        Scan sc = new Scan();
        write wr = new write();

        int N = sc.intarr[0];
        if (N == 0)
        {
            wr.wri(0);
            return;
        }
        string s = "";
        while (N != 0)
        {
            if (N % 2 !=0)
            {
                N = (N - 1) / -2;
                s = "1" + s;
            }
            else
            {
                N /= -2;
                s = "0" + s;
            }
        }

        wr.wri(s);
    }


}
    




class Scan
{
        public string str => Console.ReadLine();

        public string[] strarr => str.Split(' ');

        public long[] longarr => strarr.Select(long.Parse).ToArray();
        public int[] intarr => strarr.Select(int.Parse).ToArray();
    public char[] chararr => str.ToArray();


}



class write
{
    public void wri<Type>(Type x)
    {
        Console.WriteLine(x);
    }
}