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 Python (3.4.3) (judge verdict: Accepted)

N = int(input())
if N >= 0:
  if N == 0:
    print(0)
  elif N == 1:
    print(1)
  else:
    s = 2
    j = 2
    i = 1
    while s + j**2 <= N:
      i += 1
      s += j**2
      j*= 2
  
    k = 2 * i + 1
    a  = bin(int('10'*i, 2)^(N-s))[2:]
    if len(a) < k-1:
      a = '0'*(k-1-len(a)) + a
    print('1' + a)
else:
  s = -1
  j = -2
  i = 1
  while N <= s + j:
    s += j
    j *= 4
    i += 1
  k = 2 * i
  print(bin(int('10'*i, 2)^(N-(s+j)-1))[2:])