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::cmp;
use std::io;

fn main() {
	let mut n: i32 = read_line().parse().unwrap();
	let mut s = String::new();
	while n != 0 {
		let c =
			if n % 2 == 0 {
				'0'
			}
			else {
				n -= 1;
				'1'
			};
		s.push(c);
		n /= -2;
	}
	s = s.chars().rev().collect();
	if s.is_empty() {
		s.push('0');
	}
	println!("{}", s);
}

fn read_line() -> String {
	let mut ln = String::new();
	io::stdin().read_line(&mut ln).ok();
	ln.pop();
	return ln;
}