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())
amari = 0
i = 0
result = []
while i <= 40:
  if i ==0:
   hoge =  n % 2
   if hoge ==1:
      result.append(1)
      amari = 1
      i += 1
   else:
    result.append(0)
    i += 1
  else:
    hoge = n % (2**(i+1))
    if (amari + (-2)**(i)) % (2**(i+1)) == hoge:
      result.append(1)
      amari = amari + (-2)**(i)
      i += 1
    else:
      result.append(0)
      i += 1
      
result = result[::-1]
if n == 0:
  print(0)
else:
  s = ""
  check = False
  for r in result:
    if r == 0 and check == True:
      s += str(r)
    if r == 1:
      s += str(r)
      check = True
  print(int(s))