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: Wrong Answer)

#[test]
fn test_solve() {
    assert_eq!(solve("-9\n"), "1011\n");
    assert_eq!(solve("123456789\n"), "11000101011001101110100010101\n");
    assert_eq!(solve("0\n"), "0\n");
}

fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let mut n: i64 = sc.read();
    if n == 0 {
        return "0\n".to_string();
    }

    let mut s = String::new();
    s.push('\n');

    for i in 0..31 {
        if n == 0 {
            break;
        }
        if n.abs() & (1 << i) != 0 {
            s.push('1');
            n -= (-2i64).pow(i);
        } else {
            s.push('0');
        }
    }

    s.chars().rev().collect()
}

fn main() {
    let mut buf = String::new();
    use std::io;
    use std::io::{Read, Write};
    io::stdin().read_to_string(&mut buf).unwrap();
    io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}

struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}