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 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

#define F first 
#define S second
#define PB push_back

using namespace std;

typedef long long LL;
typedef pair<int, int> PII;
typedef priority_queue<int> HEAP;
typedef priority_queue<int, vector<int>, greater<int> > RHEAP;

const int N = 100010, M = 1010;

int n, m = -2;
string res;

int main()
{
	cin >> n;
	if (!n) puts("0");
	else
	{
		for (int i = n; i; i /= m)
		{
			if (i % abs(m))
			{
				res += "1";
				if (m < 0) i -- ;
			}
			else res += "0";
		}
		reverse(res.begin(), res.end());
	}
	cout << res << endl;
    return 0;
}