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: Accepted)

n = gets.chomp.to_i

def digit(i)
  (i % 2 == 0 ? +1 : -1) * (1 << i)
end

def stoi(s)
  n = 0
  
  s.split('').each_with_index do |c, i|
    j = s.size - i - 1
    n += c.to_i * digit(j)
  end
  
  return n
end

def solve(n)
  s = ''
  
  i = 0
  while i < 32 do
    k = n % (1 << (i + 1))
    
    if i % 2 == 0 then
      if k == digit(i) then
        n -= digit(i)
        s = '1' + s
      else
        s = '0' + s
      end
    else
      if k == -digit(i) then
        n -= digit(i)
        s = '1' + s
      else
        s = '0' + s
      end
    end
    
    i += 1
  end
  
  return s.gsub(/^0*/, '')
end

if n == 0 then
  puts '0'
else
  puts solve(n)
end