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
n = N

if n == 0
    puts '0'
    exit
end

len = 32
sign = 1
s = '10'*(len/2) + '1'
ret = ''
len.downto(0) do |i|
    if sign == 1
        upper = s.to_i(2)
        lower = upper - 2**i + 1
    else
        lower = s.to_i(2) * sign
        upper = lower + 2**i - 1
    end

    s = s[0..-2]

    # p [lower,n,upper]

    if lower <= n && n <= upper
        ret += '1'
        n -= 2**i * sign
    else
        ret += '0'
    end
    sign *= -1
end
puts ret[ret.index('1')..-1]