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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include<vector>
using namespace std;

int main() {
	long long n;cin>>n;
	long long a=1;
	if(n==0){
		cout<<0<<endl;
		return 0;
	}
	vector<long long> v;
	while(abs(a)<=abs(n)){
		a*=-2;
//		cout<<a<<endl;
//		cout<<n<<endl;
		if(n%a!=0){
			n-=a/(-2);
			v.push_back(1);
		}else{
			v.push_back(0);
		}
	}
	for(int i=0;i<v.size();i++){
		cout<<v[v.size()-1-i];
	}
	cout<<endl;
	return 0;
}