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.IO;
using System.Linq;
using System.Diagnostics;
using System.Collections.Generic;
using System.Text.RegularExpressions;
using static System.Math;

class P
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        int[] l = new int[65536 * 2];
        for (int i = 0; i < l.Length; i++)
        {
            int[] a = Convert.ToString(i, 2).Reverse().Select(x => x == '1' ? 1 : 0).ToArray();
            int current = 1;
            int resasd = 0;
            for (int j = 0; j < a.Length; j++)
            {
                resasd += current * a[j];
                current <<= 1;
                current *= -1;
            }
            l[i] = resasd;
        }
        long res = 0;
        while (true)
        {
            int[] a = Convert.ToString(res, 2).Reverse().Select(x => x == '1' ? 1 : 0).ToArray();
            long current = 1;
            long resasd = 0;
            for (int j = 0; j < a.Length; j++)
            {
                resasd += current * a[j];
                current <<= 1;
                current *= -1;
            }
            if (resasd - 43690 <= n && n <= resasd + 87381)
            {
                long target = n - resasd;
                for (int i = 0; i < l.Length; i++)
                {
                    if(l[i] == target)
                    {
                        Console.WriteLine(string.Join("", Convert.ToString(res + i, 2).Select(x => x == '1' ? 1 : 0)));
                        return;
                    }
                }
                int[] mle = new int[int.MaxValue];
            }
            res += 65536 * 2;
        }
        //Console.WriteLine(string.Join(",", l));
    }
}