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: Accepted)

	import java.util.*;
	import java.util.Map.Entry;
	 
	 
	 class Main {
		 static int mod =  (int) (Math.pow(10,9)+7);
//		 static int mod =  (int) 998244353;
		 public static void main(String[] args) {
	    	
	        Scanner sc = new Scanner(System.in);
	        long N = sc.nextInt();
	        if(N==0) {
	        	System.out.println(0);
	        	return;
	        }
        	int cnt=0;
        	char[] c = new char[10000];
	        while(N!=0) {
	        	if(N%2==1||N%2==-1) {
        			c[cnt]='1';
	        		if(cnt%2==0) {
	        			N=N-1;
	        		} else {
	        			N=N+1;
	        		}
	        	} else {
	        		c[cnt]='0';
	        	}
        		N=N/2;
        		cnt++;
	        }
	        
	        StringBuffer ans = new StringBuffer();
	        for(int i=cnt-1;i>=0;i--) {
	        	ans.append(c[i]);
	        }
	        
	        System.out.println(ans);
	    }
	}