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())
ans=''
for i in range(40,-1,-1):
  if i==0:
    if n==1:
      ans+='1'
      n=n-1
    else:
      ans+='0'
  elif i==1:
    if -2<=n<=-1:
      ans+='1'
      n=n-(-2)
    else:
      ans+='0'
  elif i%2==1:
    l=-(2*(4**((i+1)//2)-1)//3)
    r=-2**i+(1*(4**((i+1)//2)-1)//3)
    if l<=n<=r:
      ans+='1'
      n=n-((-2)**i)
    else:
      ans+='0'
  else:
    l=2**i-(2*(4**(i//2)-1)//3)
    r=1*(4**(i//2+1)-1)//3
    if l<=n<=r:
      n=n-((-2)**i)
      ans+='1'
    else:
      ans+='0'
if '1' not in ans:
  print(0)
else:
  ans=ans[ans.index('1'):]
  print(ans)