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: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
    static void Main(string[] args)
    {
		string[] str = Console.ReadLine().Split(' ');
		int n = int.Parse(str[0]);
		string output = "";
		int baseNum = -2;
		List<int> nums = new List<int>();
		while(n != 0){			
			nums.Add(seizyoyo(n, baseNum));
			n = (n - seizyoyo(n, baseNum)) / baseNum;
			//Console.WriteLine(n);
		}

		for (int i = 0; i < nums.Count;i++){
			output += nums[nums.Count-1-i].ToString();
		}
		//出力        
		Console.WriteLine(output);

    }

	static int seizyoyo(int n,int m){
		int amari=0;
		if (n >= 0){
			amari = n % m;
		}
		else{
			amari = (-n) % m;
		}
			return amari;
	}
}