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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int main(void)
{
	int N;
	scanf("%d",&N);
	int c = -2,k = 2,e = N,w,r;
	if( N == 0){
		printf("0");
		return 0;
	}
	else printf("1");
	int h[100000];
	int count = 0,i;
	while(e!=0){
		r = e % c;
		w = e;
		e = e / c;
		if(r==-1) e++;
		r = w-c*e;
		h[count] = r;
		count++;
		
		if(e == 1) break;
	}
	
	for(i = count-1; i >= 0; i--)
	{
		printf("%d",h[i]);
	}
	//*/
	return 0;
}