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 AtTest.ABC_105
{
    class C
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            long n = long.Parse(Console.ReadLine());
            if (n == 0)
            {
                Console.WriteLine(0);
            }

            //指数が小さいほうからスタートするのがポイント
            var haveIndexList = new List<bool>();
            long checkIndex = 1;
            while (n != 0)
            {
                if (Math.Abs(n) % Math.Pow(2,checkIndex) != 0)
                {
                    haveIndexList.Add(true);
                    long val = (long)Math.Pow(2, checkIndex - 1);
                    if ((checkIndex - 1) % 2 == 1) val *= -1;
                    n -= val;
                }
                else
                {
                    haveIndexList.Add(false);
                }
                checkIndex++;
            }

            string result = "";
            for (int i = haveIndexList.Count - 1; i >= 0; i--)
            {
                result += haveIndexList[i] ? '1' : '0';
            }
            Console.WriteLine(result);
        }
    }
}