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 maxnum(n)
  (Math.log(3*n+1)/Math.log(4.0)).ceil
  # (Math.log(3*n/2.0+1)/Math.log(10.0)).to_i
end

# print(maxnum(n))

def minnum(n)
  (Math.log(3*n/2.0+1)/Math.log(4.0)).ceil
end
#
def count(input_num,sum)
  # p [input_num,sum]
  if input_num>0
    ketasu = 2*maxnum(input_num)-2
    sum += 10 ** ketasu
    count(input_num-2**ketasu,sum)
  elsif input_num < 0
    ketasu = 2*minnum(input_num.abs)-1
    sum += 10 ** ketasu
    count(input_num+2**ketasu,sum)
  else
    return sum
  end
end


puts count(n,0)