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)

def make_digit x
    digit, min, max = 0, 0, 1
    while (x.positive? && x > max) || (x.negative? && x < min)
        digit += 1
        max += 2 ** digit if digit.even?
        min += (-2) ** digit if digit.odd?
    end
    return digit
end
 
n = gets.to_i
if n == 0
    puts 0
else
    arr = []
    x = n
    while x != 0
        arr << make_digit(x)
        x = x - (-2) ** arr.last
    end
    answer = Array.new(arr.max + 1, "0")
    arr.each{|i| answer[arr.max - i] = "1"}
    puts answer.join
end