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.Scanner;
public class Main {
	public static void main(String[] args){
		Scanner stdIn=new Scanner(System.in);
		int N=stdIn.nextInt();
		int ir=1;
		if(N<0)
			ir=-1;
		int a[]=new int[N*ir*2];
		int ans[]=new int[N*ir*2];
		String A="";String s="";
		int z=1,pl=0,mi=0,x=0,n=N*ir;
		boolean key=false;
		if(N!=0)
		while(true){
			if(z>0)
				pl+=z;
			if(z<0)
				mi+=z;
			a[x]=z;
			z*=-2;
			if(N<0&&mi<=N){
				N-=a[x];
				ans[x]=1;
				z=1;mi=0;pl=0;x=-1;
			}
			if(N>0&&pl>=N){
				N-=a[x];
				ans[x]=1;
				z=1;mi=0;pl=0;x=-1;
			}
			if(N==0)
				break;
			x++;
		}n*=2;n--;
		while(n>=0){
			if(ans[n]==1)
				key=true;
			if(key)
				A+=String.valueOf(ans[n]);
			n--;
		}
		if(A.equals(s))
			System.out.println(0);
		else
			System.out.println(A);
	}
}