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;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            long N = long.Parse(Console.ReadLine());
            string ans = "";
            // 一番右の桁に注目する
            // Nが偶数なら一番右は0, 奇数なら1
            // なぜなら1を表現できるのは一番左のビットだけだから
            // 一番左がわかればNを1bit right shiftして同じことを考える
            while (N != 0)
            {
                if (N % 2 != 0)
                {
                    N--;
                    ans = "1" + ans;
                }
                else
                {
                    ans = "0" + ans;
                }
                N /= -2;
            }
            if (ans == "") ans = "0";
            Console.WriteLine(ans);
        }
    }
}