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 static System.Console;

class Program
{
    public static void Main()
    {
	long n = long.Parse(ReadLine());
	long m = 0;
	string ans = "";

	long x = 1; // (-2)^k
	long y = 2; // 2^(k+1)
	while (n != m)
	{

	    long mm = n%y;
	    if (mm < 0) mm += y;
	    
	    if (mm >= y/2)
	    {
		ans = "1" + ans;
		n -= x;
	    }
	    else
		ans = "0" + ans;

	    x *= -2;
	    y *= 2;
	}
	WriteLine(ans);
    }
}