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: Accepted)

import java.io.{BufferedOutputStream, BufferedReader, InputStreamReader, PrintWriter}

import scala.annotation.tailrec

object Main {
  def main(args: Array[String]): Unit = {
    val in = new BufferedReader(new InputStreamReader(System.in))
    val out = new PrintWriter(new BufferedOutputStream(System.out))
    val n = in.readLine().toInt

    def negbin(n: Int): List[Int] = {
      @tailrec
      def inner(n: Int, acc: List[Int]): List[Int] = {
        if (n == 0) {
          acc match {
            case Nil => 0 :: Nil
            case acc => acc
          }
        } else if (n % 2 == 0) {
          inner(n / -2, 0 :: acc)
        } else {
          inner((n - 1) / -2, 1 :: acc)
        }
      }

      inner(n, Nil)
    }

    out.println(
      negbin(n).mkString("")
    )

    out.flush()
  }
}