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
wa = Array.new(34).map{[0,0]}
ans = "0"*34
wa[0][0] = 1
for i in 1..33
  if i%2 == 0
    wa[i][0] = 2**i
  else
    wa[i][1] = -2**i
  end
  wa[i][0] += wa[i-1][0]
  wa[i][1] += wa[i-1][1]
end
s = []
while n != 0
  if n > 0
    for i in 0..33
      if wa[i][0] >= n
        s << i
        n -= 2**i
        break
      end
    end
  else
    for i in 0..33
      if wa[i][1] <= n
        s << i
        n += 2**i
        break
      end
    end
  end
end
s.each do |i|
  ans[i] = "1"
end
p ans.reverse.to_i