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;
fn main() {
    let stdin = io::stdin();
    let mut s = String::new();
    stdin.read_line(&mut s).ok();
    s.trim();
    s.pop();
    let mut n : i64 = i64::from_str(&s).expect("e");
    let mut ans : Vec<i64> = Vec::new();
    let mut pow : i64 = 1;
    while n != 0 || ans.is_empty() {
        ans.push(if n % (pow * 2) == 0 {0} else {1});
        n -= pow * ans[ans.len() - 1];
        pow *= -2;
    }
    ans.reverse();
    for i in &ans {
        print!("{}",i);
    }
    println!();
}