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: Runtime Error)

fn main() {
    let mut i = String::new();
    std::io::stdin().read_line(&mut i).ok();
    let mut n = i.parse::<i32>().unwrap();

    println!("{}", if n == 0 { String::from("0") } else {
        let mut bin = String::new();
        let mut s = vec![];
        loop {
        	s.push(if n % 2 != 0 { 1 } else { 0 });
            if n % 2 != 0 { n -= 1; }
            n /= -2;
            if n == 0 { break; }
        }

        s.reverse();
        s.into_iter().map(|d| std::char::from_digit(d, 10).unwrap()).collect()
    });
}