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 LuaJIT (2.0.4) (judge verdict: Accepted)

n = io.read("*n")
dig = 1
flg = 1
if(0 < n) then flg = 0 else n = -n end
t = {}
while(0 < n) do
  rem = n % 2
  if(dig % 2 == flg and rem == 1) then
    n = n + 1
  end
  table.insert(t, 1, rem)
  n = math.floor(n / 2)
  flg = (flg + 1) % 2
end
len = #t
for i = 1, len do
  io.write(string.format("%d", t[i]))
end
if(len == 0) then io.write(0) end
io.write("\n")