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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

class Cmondai
{
    static void Main()
    {
        var N = Int32.Parse(Console.ReadLine());
        const int constant = -2;
        var num = 1;
        var ans = new Stack<char>();
        if (N == 0) ans.Push('0');
        while (N != 0)
        {
            //余りが0
            //1が立たないので数に変化なし
            if (N % (num * constant) == 0)
            {
                ans.Push('0');
            }
            //余りが1
            //1が立つのでその分Nから数を引く
            else
            {
                ans.Push('1');
                N -= num;
            }
            num *= (-2);
        }
        for(int i=0;i<ans.Count();++i)Console.Write(ans.Pop());
        Console.WriteLine();
    }
}