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 Scala (2.11.7) (judge verdict: Wrong Answer)

object Main extends App {
  val in = new java.util.Scanner(System.in)
  val N = in.nextLong

  case class X(sum: Long, cur: Long, i: Int)
  def seq: Stream[Long] = 1L #:: seq.map(_ * -2)
  def scan(s: Stream[(Long, Int)]): Stream[X] = s.scanLeft(X(0L, 0L, 0)){
    case (x, (n, i)) => X(x.sum + n, n, i)
  }
  def minuses: Stream[X] = scan(seq.zipWithIndex.filter(_._1 < 0))
  def pluses: Stream[X] = scan(seq.zipWithIndex.filter(_._1 > 0))


  def exec(result: Long, n: Long): Long = {
    n match {
      case n if n < 0 =>
        val x = minuses.find(_.sum <= n).get
        exec(result | 1 << x.i, n - x.cur)
      case n if n > 0 =>
        val x = pluses.find(_.sum >= n).get
        exec(result | 1 << x.i, n - x.cur)
      case _ => result
    }
  }

  println(exec(0L, N).toBinaryString)
}