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 <algorithm>
#include <iostream>
#include <limits>
#include <numeric>
#include <string>
#include <cmath>

#define rep(i, x, n) for (int i = x; i < n; i++)
using namespace std;
const long long INF = 1LL << 60;

int main()
{
    long long N;
    cin >> N;
    int res[1000];
    int i = 0;
    if (N == 0)
    {
        res[0] = 0;
        i++;
    }
    while (N != 0)
    {
        int amari = N % 2;
        if (amari < 0)
        {
            amari += 2;
        }
        res[i] = amari;
        i++;
        N = (N - amari) / (-2);
    }
    rep(r, 0, i)
    {
        cout << res[i - 1 - r];
    }
    cout << endl;
}