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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
class Program{
	static void Main(){
		int s=int.Parse(Console.ReadLine());

		int[] h=new int[31];
		int[] h2=new int[31];
		for(int i=0;i<31;i++){
			h[i]=(1<<i)*((i&1)*-2+1);
			h2[i]=h[i]+(i>1?h2[i-2]:0);
		}

		int p=0,q=0,ans=0,stk=0;
		if(s<0){
			for(int i=1;i<31;i+=2){if(s>=h2[i]){q=i;break;}}
			ans|=1<<q;
			p+=h[q];
			stk=h2[q];

			while(q>0){
				q--;
				if((q&1)==0){if(s>=stk+(1<<q)){ans|=1<<q;p+=h[q];stk+=(1<<q);}}
				else{
					if(s<stk+(1<<q)){ans|=1<<q;p+=h[q];}
					else{stk+=(1<<q);}
				}
			}
		}
		else if(s>0){
			for(int i=0;i<31;i+=2){if(s<=h2[i]){q=i;break;}}
			ans|=1<<q;
			p+=h[q];
			stk=h2[q];

			while(q>0){
				q--;
				if((q&1)==0){
					if(s>stk-(1<<q)){ans|=1<<q;p+=h[q];}
					else{stk-=(1<<q);}
				}
				else{if(s<=stk-(1<<q)){ans|=1<<q;p+=h[q];stk-=(1<<q);}}
			}
		}
		Console.WriteLine("{0}",Convert.ToString(ans,2));
	}
}