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)

include Math

POSITIVE = 0
NEGATIVE = 1

# P P
# P N
# N N
# N P
def add_pow2(v, sign, n)
  place = log2(n).round.to_i
  if place % 2 == sign
    if v[place] == 0
      v[place] = 1
    else
      v[place] = 0
      add_pow2(v, sign, n*2)
    end
  else
    if v[place] == 1
      v[place] = 0
    else
      v[place] = 1
      add_pow2(v, sign, n*2)
    end
  end
  v
end

def add_num(v, n)
  if n == 0
    v
  elsif n < 0
    inpow2(-n).each do |k|
      add_pow2(v, NEGATIVE,k)
    end
    v
  else
    inpow2(n).each do |k|
      add_pow2(v, POSITIVE,k)
    end
    v
  end
end

def inpow2(n)
  fail if n < 0
  exp = 0
  res = []
  while n > 0
    res << (1 << exp) if n & 1 == 1
    n >>= 1
    exp += 1
  end
  res
end

def zero
  [0] * 64
end

def tostr(v)
  s = v.join.reverse.sub(/\A0+/,'')
  if s.empty?
    '0'
  else
    s
  end
end

fail unless tostr(zero) == '0'
fail unless tostr(add_num(zero, 1)) == '1'
fail unless tostr(add_num(zero, -9)) == '1011'
fail unless tostr(add_num(zero,123456789)) ==
            "11000101011001101110100010101"

n = gets.to_i
puts tostr add_num(zero, n)