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::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

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

    if n == 0 || n == 1 {
        println!("{}", n);
        return;
    }

    if n > 0 {
        let mut cnt = 3;
        let mut tmp = 4;
        let mut sum = 5;

        while sum <= n - 1 {
            cnt += 2;
            tmp *= 4;
            sum += tmp;
        }
        let mut magic = n - (sum / 4) - 1;
        let mut ans = "1".to_string();
        let mut a: Vec<&str> = vec![];
        while a.len() * 2 < cnt - 1 {
            let amari = magic % 4;
            magic /= 4;
            a.push(match amari {
                0 => "10",
                1 => "11",
                2 => "00",
                3 => "01",
                _ => "",
            });
        }
        a.reverse();
        for i in (0..a.len()) {
            ans += a[i];
        }
        println!("{}", ans);
    } else {
        if n == -1 {
            println!("11");
            return;
        }
        if n == -2 {
            println!("10");
            return;
        }

        let rn = -n;
        let mut keta = 2;
        let mut sum = 2;
        let mut tmp = 2;
        let mut prev = 0;

        while sum < rn {
            keta += 2;
            tmp *= 4;
            prev = sum;
            sum += tmp;
        }
        // println!("keta:{}", keta);
        // println!("magic:{}", rn - prev);
        let mut magic = rn - prev - 1;
        let mut a: Vec<&str> = vec![];
        let mut ans = "1".to_string();

        while a.len() < keta - 1 {
            let amari = magic % 2;
            magic /= 2;
            if a.len() % 2 == 0 {
                a.push(match amari {
                    1 => "0",
                    0 => "1",
                    _ => "",
                })
            } else {
                a.push(match amari {
                    1 => "1",
                    0 => "0",
                    _ => "",
                })
            }
        }
        a.reverse();
        for i in (0..a.len()) {
            ans += a[i];
        }
        println!("{}", ans);
   }
}