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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n=gets.to_i
flag=false
if n==0
  puts 0
end
countk=0
ss="1"
loop do
  count=0
  ans=ss.reverse.split("").map(&:to_i)
  ans.each_with_index{|a,i|count+=a*((-2)**i)}
  countk+=1
  if count == n
    puts ss
    break
  end

  if !ss.include?('0')
    size=ss.size
    ss="1"
    (size).times do
      ss=ss+'0'
    end
  else
    if ss[-1]=="0"
      ss[-1]="1"
    else
      ss[1..-1].size.times do |j|
        if ss[-1*(j+1)]=="0"
          ss[-1*(j+1)]="1"
          break
        else
          ss[-1*(j+1)]="0"
        end
      end
    end
  end
end