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 quot_m2(int x){
	if(x>0)return -1*(x/2);
	return (-1*x+1)/2;
}

int ab(int x){
	if(x<0)return -x;
	return x;
}

int main(){
	int N,i=0;
	int ans[256];
	scanf("%d",&N);
	
	if(N==0){
		printf("0\n");
		return 0;
	}
	
	while(N!=0){
		ans[i]=ab(N)%2;
		N=quot_m2(N);
		i++;
	}
	for(i=i-1;i>=0;i--)printf("%d",ans[i]);
	printf("\n");
	return 0;
}