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 <string>
#include <algorithm>
#include <vector>
#include <numeric>
//#include <stdio.h>
//#include <stack>
//#include <queue>
#include <cstdio>
#include <cmath>
#include <iterator>
#include <map>
//#include <fstream>
//#include <list>
//#include <iomanip>
#include <cctype>

using namespace std;

#define MOD 1000000007
#define Int int64_t
#define PI 3.14159265358979
#define ssort(z) sort(z.begin(),z.end())
#define eerase(z) z.erase(unique(z.begin(),z.end()),z.end())
#define ccnt(z,w) count(z.begin(),z.end(),w)


void printVec(std::vector<int> & vec) {
	std::cout << "";
	for (auto it = vec.begin(); it != vec.end(); ++it) {
		std::cout << *it << " ";
	}
	std::cout << std::endl;
}
void printVec1(std::vector<string>& vec) {
	std::cout << "";
	for (auto it = vec.begin(); it != vec.end(); ++it) {
		std::cout << *it << " ";
	}
	std::cout << std::endl;
}
void printVec2(std::vector<Int>& vec) {
	std::cout << "";
	for (auto it = vec.begin(); it != vec.end(); ++it) {
		std::cout << *it << " ";
	}
	std::cout << std::endl;
}

Int gcd(Int a, Int b) {
	return b != 0 ? gcd(b, a % b) : a;
}
Int lcm(Int a, Int b) {
	return a * b / gcd(a, b);
}

bool comp(const string a, const string b) {
	return a.length() < b.length();
}

bool integer(double num) {
	return floor(num) == num;
}

string gen(int num) {
	string str = "";
	for (int i = 0; i < num; i++) str += ".";
	return str;
}
Int fact(int num) {
	if (num == 0) return 1;
	else return num * fact(num - 1);
}

int main() {
	///stuck for 90min
	Int n; cin >> n;
	Int num =n;
	if (n == 0) {
		cout << 0;
		return 0;
	}
	Int temp = 0;
	vector<int> ans;
	Int i = 0;
	while (num != 0) {
		temp = abs(num) % 2;
		ans.push_back(temp);
		if (i % 2 == 0)  num -= temp;
		else num += temp;
		num = num / 2;
		i++;
	}
	reverse(ans.begin(), ans.end());
	for (int i = 0; i < ans.size(); i++) {
		cout << ans[i];
	}


	
	//cout << (-9) % (-2);

	cout << endl;
	return 0;
}