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.Text;

namespace AtCoder
{
	public class Program
	{
		// ABC105-C
		static void Main(string[] args)
		{
			int N = int.Parse(Console.ReadLine());
			long posi = 0, nega = 0, diff = N;

			long[] pattern = new long[64];
			long m = 1;
			for (long i = 0; i < pattern.Length; i++) {
				pattern[i] = m;
				m = (m << 1) | i % 2;
			}

			while (true) {
				if (diff == 0) {
					// 終了
					Console.WriteLine(Convert.ToString(posi + nega, 2));
					return;
				} else if (diff > 0) {
					// 正
					int i = 0;
					while (pattern[i] < diff) {
						i += 2;
					}
					posi += 1L << i;
				} else {
					// 負
					int i = 1;
					while (-1 * pattern[i] > diff) {
						i += 2;
					}
					nega += 1L << i;
				}
				diff = N - (posi + (-1 * nega));
			}
		}
	}
}