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)

use std::io::stdin;
fn get_string() -> String {
    let mut s = String::new();
    stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

macro_rules! input {
    ($single:ty) => ( get_string().parse::<$single>().unwrap() );
    ($plural:ty,) => ({
        let line = get_string();
        line.split_whitespace().map(|v| v.parse::<$plural>().unwrap()).collect::<Vec<$plural>>()
    });
    ($($plural:ty),+) => ({
        let line = get_string();
        let mut iter = line.split_whitespace();
        ($(iter.next().unwrap().parse::<$plural>().unwrap()),+)
    });
    ($single:ty; $times:expr) => ( (0..$times).map(|_| input!($single)).collect::<Vec<$single>>() );
    ($($plural:ty),+; $times:expr) => ( (0..$times).map(|_| input!($($plural),+)).collect::<Vec<($($plural),+)>>() );
}

#[allow(dead_code)]
fn get_value<T: std::str::FromStr>() -> T {
    get_string().parse().ok().unwrap()
}
#[allow(dead_code)]
fn get_values_for<T: std::str::FromStr>(times: u64) -> Vec<T> {
    (0..times).map(|_| get_value()).collect()
}
#[allow(dead_code)]
fn get_vector<T: std::str::FromStr>() -> Vec<T> {
    get_string()
        .split_whitespace()
        .map(|v| v.parse().ok().unwrap())
        .collect()
}
#[allow(dead_code)]
fn get_vectors_for<T: std::str::FromStr>(times: u64) -> Vec<Vec<T>> {
    (0..times).map(|_| get_vector()).collect()
}

fn main() {
    let mut n = input!(i64);
    let mut ans = Vec::new();
    if n == 0 {
        ans.push(0)
    }
    while n != 0 {
        let m = (n % 2).abs();
        ans.push(m);
        if n < 0 && m == 1 {
            n = n / -2 + 1;
        } else {
            n = n / -2;
        }
    }
    println!(
        "{}",
        ans.iter().rev().map(i64::to_string).collect::<String>()
    );
}