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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List
import Data.Char

div' :: Int -> Int -> Int
div' a b
  | a`mod`b == 0 = a`div`b
  | otherwise    = a`div`b+1
  
mod' :: Int -> Int -> Int
mod' a b
  | a`mod`b==0 = 0
  | otherwise  = a`mod`b-b

f :: Int -> Maybe (Char, Int)
f i
  | i == 0    = Nothing
  | i == 1    = Just ('1',0)
  | otherwise = Just (chr (ord '0'+(i`mod'`(-2))), i`div'`(-2))

main :: IO ()
main = do
  n <- readLn :: IO Int
  let cs = unfoldr f n

  putStrLn $ if null cs
    then "0"
    else foldl' (\ans c -> c : ans)  "" cs