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.IO;
using System.Linq;
using static ABC105_20200320C.Input;

namespace ABC105_20200320C
{
    static class Input
    {
        /// <summary>
        /// 1行の入力をTに応じてリストに変換する関数を返す
        /// </summary>
        static Func<string, List<T>> Cast<T>() => _ => _.Split(' ').Select(Convert<T>()).ToList();

        /// <summary>
        /// 1行の入力をTに応じて変換する関数を返す
        /// </summary>
        static Func<string, T> Convert<T>()
        {
            Type t = typeof(T);
            if (t == typeof(string)) return _ => (T) (object) _;
            if (t == typeof(int)) return _ => (T) (object) int.Parse(_);
            if (t == typeof(long)) return _ => (T) (object) long.Parse(_);
            if (t == typeof(double)) return _ => (T) (object) double.Parse(_);
            if (t == typeof(List<string>)) return _ => (T) (object) Cast<string>()(_);
            if (t == typeof(List<int>)) return _ => (T) (object) Cast<int>()(_);
            if (t == typeof(List<long>)) return _ => (T) (object) Cast<long>()(_);
            if (t == typeof(List<double>)) return _ => (T) (object) Cast<double>()(_);

            throw new NotSupportedException(t + "is not supported.");
        }

        static T Convert<T>(string s) => Convert<T>()(s);

        static string String() => Console.ReadLine();

        static List<string> String(long rowNumber) => new bool[rowNumber].Select(_ => String()).ToList();

        /// <summary>
        /// 1行の値の入力
        /// </summary>
        public static void Cin<T>(out T a) => a = Convert<List<T>>(String())[0];

        public static void Cin<T1, T2>(out T1 a1, out T2 a2)
        {
            var v = Convert<List<string>>(String());
            a1 = Convert<T1>(v[0]);
            a2 = Convert<T2>(v[1]);
        }

        public static void Cin<T1, T2, T3>(out T1 a1, out T2 a2, out T3 a3)
        {
            var v = Convert<List<string>>(String());
            a1 = Convert<T1>(v[0]);
            a2 = Convert<T2>(v[1]);
            a3 = Convert<T3>(v[2]);
        }

        public static void Cin<T1, T2, T3, T4>(out T1 a1, out T2 a2, out T3 a3, out T4 a4)
        {
            var v = Convert<List<string>>(String());
            a1 = Convert<T1>(v[0]);
            a2 = Convert<T2>(v[1]);
            a3 = Convert<T3>(v[2]);
            a4 = Convert<T4>(v[3]);
        }

        public static void Cin<T1, T2, T3, T4, T5>(out T1 a1, out T2 a2, out T3 a3, out T4 a4, out T5 a5)
        {
            var v = Convert<List<string>>(String());
            a1 = Convert<T1>(v[0]);
            a2 = Convert<T2>(v[1]);
            a3 = Convert<T3>(v[2]);
            a4 = Convert<T4>(v[3]);
            a5 = Convert<T5>(v[4]);
        }

        public static void Cin<T1, T2, T3, T4, T5, T6>(out T1 a1, out T2 a2, out T3 a3, out T4 a4, out T5 a5, out T6 a6)
        {
            var v = Convert<List<string>>(String());
            a1 = Convert<T1>(v[0]);
            a2 = Convert<T2>(v[1]);
            a3 = Convert<T3>(v[2]);
            a4 = Convert<T4>(v[3]);
            a5 = Convert<T5>(v[4]);
            a6 = Convert<T6>(v[5]);
        }

        /// <summary>
        /// 複数行の値の入力
        /// </summary>
        public static void Cin<T>(long n, out List<T> l) => l = String(n).Select(Convert<T>()).ToList();

        public static void Cin<T1, T2>(long n, out List<T1> l1, out List<T2> l2)
        {
            l1 = new List<T1>();
            l2 = new List<T2>();
            foreach (List<string> l in String(n).Select(Convert<List<string>>()))
            {
                l1.Add(Convert<T1>(l[0]));
                l2.Add(Convert<T2>(l[1]));
            }
        }

        public static void Cin<T1, T2, T3>(long n, out List<T1> l1, out List<T2> l2, out List<T3> l3)
        {
            l1 = new List<T1>();
            l2 = new List<T2>();
            l3 = new List<T3>();
            foreach (List<string> l in String(n).Select(Convert<List<string>>()))
            {
                l1.Add(Convert<T1>(l[0]));
                l2.Add(Convert<T2>(l[1]));
                l3.Add(Convert<T3>(l[2]));
            }
        }

        public static void Cin<T1, T2, T3, T4>(long n, out List<T1> l1, out List<T2> l2, out List<T3> l3,
            out List<T4> l4)
        {
            l1 = new List<T1>();
            l2 = new List<T2>();
            l3 = new List<T3>();
            l4 = new List<T4>();
            foreach (List<string> l in String(n).Select(Convert<List<string>>()))
            {
                l1.Add(Convert<T1>(l[0]));
                l2.Add(Convert<T2>(l[1]));
                l3.Add(Convert<T3>(l[2]));
                l4.Add(Convert<T4>(l[3]));
            }
        }

        /// <summary>
        /// 1行に書かれた複数の値の入力
        /// </summary>
        public static void Cin<T>(out List<T> lArr) => lArr = Convert<List<T>>(String());

        /// <summary>
        /// h行の行列の入力
        /// </summary>
        public static void Cin<T>(long h, out List<List<T>> map) => map = String(h).Select(Convert<List<T>>()).ToList();
    }

    class Program
    {
        public static void Main(string[] args)
        {
            StreamWriter streamWriter = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(streamWriter);
            new Solver().Solve();
            Console.Out.Flush();
        }

        public static void Debug()
        {
            new Solver().Solve();
        }
    }

    class Solver
    {
        private long N;

        public void Solve()
        {
            Cin(out N);

            List<char> ans = new List<char>();

            if (N == 0)
            {
                Console.WriteLine(0);
                return;
            }

            long b = 1;
            while (N != 0)
            {
                if (N % (b * 2) == 0)
                {
                    ans.Add('0');
                }
                else
                {
                    ans.Add('1');
                    N -= b;
                }

                b *= -2;
            }

            ans.Reverse();
            bool one = false;
            foreach (char c in ans)
            {
                if (!one && c == '0') continue;
                one = true;
                Console.Write(c);
            }

            Console.WriteLine();
        }
    }
}