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: Wrong Answer)

N = int(input())
k=[]
if N%2==1:
  N = N-1
  k.append(1)
for i in range(1,50):
  if (N//(-2)**i)%2==1:
    N -=(-2)**i 
    k.append(1)
  else:
    k.append(0)
  if N==0:
    break
for i in range(len(k)-1,-1,-1):
  print(k[i],end="")

"""
for bit in range(1<<30):
  ans = 0
  an = 0
  for i in range(30):
    if bit&(1<<i):
      an += k[i]
      ans += 1<<i
  if an==N:
    ans =  format(ans, 'b')
    print(ans)
    exit()
"""