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 Rust (1.15.1) (judge verdict: Accepted)

fn main() {
    let mut input = String::new();
    std::io::stdin().read_line(&mut input).unwrap();

    let mut n = input.trim().parse::<i32>().unwrap();

    let mut answer = String::new();
    loop {
        let div: i32;
        let amari: i32;

        if n > 0 {
            div = n / -2;
            amari = n % -2;
        } else {
            if n % -2 == 0 {
                div = n / -2;
                amari = n % -2;
            } else {
                div = n / -2 + 1;
                amari = 1;
            }
        }

        // eprintln!("div = {}, amari = {}", div, amari);

        answer.insert(0, match amari {
            0 => '0',
            1 => '1',
            _ => panic!(),
        });
        if div != 0 {
            n = div;
        } else {
            break;
        }
    }

    if answer.len() != 1 {
        answer = answer.trim_left_matches('0').to_string();
    }
    println!("{}", answer);
}