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;

namespace Contest
{

    class Scanner
    {
        private string[] line = new string[0];
        private int index = 0;
        public string Next()
        {
            if (line.Length <= index)
            {
                line = Console.ReadLine().Split(' ');
                index = 0;
            }
            var res = line[index];
            index++;
            return res;
        }
        public int NextInt()
        {
            return int.Parse(Next());
        }
        public long NextLong()
        {
            return long.Parse(Next());
        }
        public string[] Array()
        {
            line = Console.ReadLine().Split(' ');
            index = line.Length;
            return line;
        }
        public int[] IntArray()
        {
            var array = Array();
            var result = new int[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = int.Parse(array[i]);
            }

            return result;
        }
        public long[] LongArray()
        {
            var array = Array();
            var result = new long[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = long.Parse(array[i]);
            }

            return result;
        }
    }

    class Program
    {
        private long N;
        private long[] Pow;
        private void Scan()
        {
            Scanner sc = new Scanner();
            N = sc.NextInt();
        }

        public void Solve()
        {
            Scan();
            Pow = new long[32];
            Pow[0] = 1;
            for (int i = 1; i < 32; i++)
            {
                Pow[i] = Pow[i - 1] * -2;
            }
            Console.WriteLine(Calc(N));
        }

        private string Calc(long n)
        {
            if (n == 1 || n==0)
            {
                return n.ToString();
            }
            if (n > 0)
            {
                long nn = 0;
                int i;
                for (i = 0; true; i += 2)
                {
                    nn += Pow[i];
                    if (nn >= n) break;
                }

                string child = Calc(n - Pow[i]);
                return "1" + child.PadLeft(i, '0');
            }
            else if (n < 0)
            {
                long nn = 0;
                int i;
                for (i = 1; true; i += 2)
                {
                    nn += Pow[i];
                    if (nn <= n) break;

                }

                string child = Calc(n - Pow[i]);
                return "1" + child.PadLeft(i, '0');
            }

            return "";
        }

        static void Main() => new Program().Solve();
    }
}