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)

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()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn order(n: i64, lims: &Vec<i64>) -> usize {
    let mut ret: usize = 0;
    if n >= 0 {
        for i in 0..17 {
            if n <= lims[i * 2] {
                ret = i * 2;
                break;
            }
        }
    } else {
        for i in 0..16 {
            if n >= lims[i * 2 + 1] {
                ret = i * 2 + 1;
                break;
            }
        }
    }
    ret
}

fn main() {
    let mut n: i64 = read();

    let mut bits: Vec<i64> = vec![];
    let mut lims: Vec<i64> = vec![];
    let mut r: i64 = 1;
    let mut tmp: i64 = 0;
    for i in 0..33 {
        if i % 2 == 0 {
            bits.push(r);
            tmp += 2 * r - 1;
        } else {
            bits.push(-r);
            tmp += -2 * r + 1;
        }
        lims.push(tmp);
        r *= 2;
    }

    if n == 0 {
        println!("0");
    } else {
        let mut ans: Vec<char> = vec![];
        let mut lastketa: usize = order(n, &lims) + 1;
        while n != 0 {
            let keta = order(n, &lims);
            n -= bits[keta];
            for _ in 0..(lastketa - keta - 1) {
                ans.push('0');
            }
            lastketa = keta;
            ans.push('1');
        }
        let s: String = ans.into_iter().collect();
        println!("{}", s);
    }
}