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.to_i
current = N
ans = ""
i = 1
until current == 0
  # puts "current: #{current}, i: #{i}, 2**i: #{2**i}"
  # puts "割り切れるか?: #{current % (2 ** i) == 0}"
  if current % (2 ** i) == 0
    ans += "0"
  else
    current -= (-2) ** (i-1)
    ans += "1"
  end
  i += 1
  # break if i == 100
end
puts ans.empty? ? 0 : ans.reverse