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

bit = ""

if n.odd?
  bit << "1"
  n -= 1
else
  bit << "0"
end

def pow?(num)
  (num & (num - 1)).zero?
end

tmp = -2
while n != 0
  if n == tmp
    bit << "1"
    break
  end
  if pow?(n.abs)
    if n.abs == tmp.abs
      bit << "1"
      n -= tmp
    else
      bit << "0"
    end
  else
    bit << "1"
    n -= tmp
  end
  tmp = tmp * -2
end

puts bit.reverse