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)

object Main extends App {
	import scala.math._
	var n = scala.io.StdIn.readLong

	var ans = List[Int]()
	var f = 0L
	var v = 0L

	for(i<-32L to 0L by -1L){
		if(i%2 == 0){
			v = powL(2L, i)
		}else{
			v = powL(-2L, i)
		}

		var sup = v
		var inf = v

		for(j<-i-1L to 0L by -1L){
			if(j%2L == 0L){
				sup += powL(2L, j)
			}else{
				inf += powL(-2L, j)
			}
		}

		if(inf <= n && n <= sup){
			ans = 1 :: ans
			n -= v
			f = 1 
		}else{
			if(f == 1){
				ans = 0 :: ans
			}
		}
	}

	if(ans.size == 0) println(0)
	else println(ans.reverse.mkString)

	def powL(x: Long, y: Long) = pow(x, y).toLong
}