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;


public class C{
	
	public static void Main(){
	
		int n = Int32.Parse( Console.ReadLine() );
		List<int> result = new List<int>();
		
		int rest = n;
		int i = 0;
		while(true){
			if( (rest & (1 << i)) == 0 ){
				result.Add(0);
				
			}else{
				result.Add(1);
				if( (i & 1) == 0 ){
					rest -= (1 << i);
				}else{
					rest += (1 << i);
				}
				
			}
			if( rest == 0 ) break;
			i++;
		}
		
		for( int j = 0; j < result.Count; j++ ){
			Console.Write( result[result.Count - 1 - j ] );
		}
		Console.WriteLine();
		
	}

}