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;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp90 {
    class Program {
        static void Main(string[] args) {
            long N = long.Parse(Console.ReadLine());

            int k = 0;
            int keta = 0;

            if (N > 0) {
                k = (int)Math.Ceiling(Math.Log10(3 * N + 1) / Math.Log10(4)) - 1;
                keta = 2 * k + 1;
            } else if (N < 0) {
                k = (int)Math.Ceiling(Math.Log10(1 - 1.5f * N) / Math.Log10(4));
                keta = 2 * k;
            } else {
                Console.WriteLine(0);
                return;
            }

            string ans = "";

            for (int i = 0; i < keta; i++) {
                if (N % 2 == 0) {
                    ans = "0" + ans;
                } else {
                    ans = "1" + ans;
                    N -= 1;
                }
                N /= -2;
            }

            Console.WriteLine(ans);
        }

    }
}