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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
using namespace std;

int main() {
    long long n;
    cin >> n;

    bool ans[1000] = {};
    while (n != 0) {
        int bit;
      	long long sum;
        if (n > 0) {
            sum = 0b01;
            for (bit = 0; n > sum; bit += 2) sum = (sum << 2) | 0b01;
            n -= (1 << bit);
        } else {
            sum = 0b10;
            for (bit = 0; abs(n) > sum; bit += 2) sum = (sum << 2) | 0b10;
            bit++;
            n -= -1 * (1 << bit);
        }
        ans[bit] = true;
    }

    int i = 1000 - 1;
    while (ans[i] == false && i > 0) i--;
    for (; i >= 0; i--) cout << (ans[i] ? 1 : 0);
    cout << endl;
}