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 n = read::<i32>();
    println!("{}",  q3(n, 100));
}

fn q3(mut n:i32, max: i32) -> String {
    let mut done = false;
    let mut i: i32 = 1;
    let mut vec: Vec<&str> = Vec::with_capacity(max as usize);
    while !done {
        match (n % (i*2).abs() == 0){
            true => vec.push("0"),
            false => {
                vec.push("1");
                n -= i;
            }
        }
        i = i * -2;
        if(n == 0 || vec.len() > max as usize){
            done = true;
        }
    }
    vec.reverse();
    return vec.join("");
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}