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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.ArrayDeque;
import java.util.Deque;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		sc.close();

		if(N == 0){
			System.out.println(0);

		}
		else{
			Deque<Integer> stack = new ArrayDeque<Integer>();

			int tmp = 0;
			for(int i = 1 ; i <2000000000 ; i*=(-2)){
				//System.out.println("i : " + i);
				if(N%(i*(-2))==0){
					//System.out.print(0);
					stack.push(0);
				}
				else{
					if(tmp == 0){
					tmp = N-i;
					}
					else{
						tmp = tmp-i;
					}
					//System.out.println("tmp :" + tmp);
					if(tmp%(i*(-2)) == 0){
						//System.out.print(1);
						stack.push(1);
					}
					else{
						//System.out.print(0);
						stack.push(0);
						tmp = tmp+i;
					}
				}
			}
			int flag = 0;
			int ff = stack.size();
			for(int i = 0 ; i < ff ; i++){
				int a = stack.poll();
				if(flag == 0 && a == 0){
					continue;
				}else{
					System.out.print(a);
					flag++;
				}
			}
		}

	}
}