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 <bits/stdc++.h>
typedef long long int lint;

#define PI acos(-1)
#define INF64 1LL << 60
#define INF32 1 << 29
#define LIMIT(d_in, d_min, d_max) max(d_min, min(d_max, d_in))
#define all(a) (a).begin(), (a).end()
#define INV ((long long int)1000000007)

using namespace std;

void execute()
{
	int N;
	cin >> N;

	lint base = 1;
	int posneg = 1;
	stack<int> S;

	if (N == 0)
	{
		cout << 0 << endl;
		return;
	}

	for (; N != 0;)
	{
		lint absN = abs(N);
		if (absN % (base * 2))
		{
			N -= (base * posneg);
			S.push(1);
		}
		else
		{
			S.push(0);
		}

		base *= 2;
		posneg *= -1;
	}

	for (; !S.empty();)
	{
		cout << S.top();
		S.pop();
	}

	cout << endl;
	return;
}

int main()
{
	cin.tie(0);
	ios_base::sync_with_stdio(false);
	std::cout << std::fixed << std::setprecision(15);
	execute();

	int stop;
	cin >> stop;

	return 0;
}