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: Wrong Answer)

#include<stdio.h>
int inputi(){
	char c='0';
	int ans=0;
	signed char flg=1;
	do{
		c=getchar();
	}while(c<=32);
	if(c=='-'){
		flg=-1;
		c=getchar();
	}
	do{
		ans*=10;
		ans+=(c-'0');
		c=getchar();
	}while(c>32);
	return ans*flg;
}
int main(void){
	int n,j=0;
	char o[100]={0};
	n=inputi();
	while(n){
		if(n%2) o[j]=1;
		if(n>0)n=(n-n%2)/-2;else n=(n+n%2)/-2;
		j++;
	}
	while(j){
		j--;
		printf("%d",o[j]);
	}
	puts("");
	return 0;
}