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)

#![allow(dead_code, unused_imports, non_snake_case)]

use std::io::*;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::str::FromStr;

const MOD: i32 = 1_000_000_007;

fn main() {
    let mut n: i32 = input();
    let mut v: Vec<char> = Vec::new();
    let mut i: u32 = 1;
    if n == 0 {
        println!("0");
        return;
    }
    loop {
        if n.abs() % 2i32.pow(i) == 0 {
            v.push('0');
        } else {
            v.push('1');
            n -= (-2 as i32).pow(i-1);
        }
        i += 1;
        if n == 0 { break; }
    }
    println!("{}", v.into_iter().rev().collect::<String>());
}

trait Read {
    fn read(s: &str) -> Self;
}

fn input<T: Read>() -> T {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    T::read(buf.trim_right())
}

macro_rules! read_impl {
    ($($t:ty)*) => ($(
        impl Read for $t {
            fn read(s: &str) -> $t{
                s.parse().unwrap()
            }
        }
    )*)
}
read_impl! { usize u8 u16 u32 u64 isize i8 i16 i32 i64 f32 f64 }

impl Read for String {
    fn read(s: &str) -> Self {
        s.to_string()
    }
}

impl Read for Vec<char> {
    fn read(s: &str) -> Self {
        s.chars().collect()
    }
}

impl<T: Read> Read for Vec<T> {
    fn read(s: &str) -> Self {
        s.split_whitespace().map(T::read).collect()
    }
}

impl<A: Read, B: Read> Read for (A, B) {
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]))
    }
}

impl<A: Read, B: Read, C: Read> Read for (A, B, C) {
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]), C::read(tokens[2]))
    }
}

impl<A: Read, B: Read, C: Read, D: Read> Read for (A, B, C, D) {
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]), C::read(tokens[2]), D::read(tokens[3]))
    }
}