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 (2.7.1) (judge verdict: Accepted)

n = gets.to_i
ans = []
div = 2
while n != 0
  if n % div != 0
    n -= n % div
    ans << 1
  else
    ans << 0
  end
  div *= 2
  if n % div != 0
    n += n % div
    ans << 1
  else
    ans << 0
  end
  div *= 2
end
ans = ans.reverse
ans.shift if ans[0] == 0
ans << 0 if ans.length == 0
ans.each do |x|
  print x
end
puts ""