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)


fn func(input_str: &str) {
    let mut iter = input_str.split_whitespace();
    let mut k: i32 = iter.next().unwrap().parse().unwrap();
    if k == 0 {
        println!("0");
        return;
    }
    let mut ans = Vec::new();
    let mut c: u32 = 1;
    while k != 0 {
        if k % (-2_i32).pow(c) != 0 {
            ans.push(1);
            k -= (-2_i32).pow(c - 1);
        } else {
            ans.push(0);
        }
        c += 1;
    }
    ans.reverse();
    for a in ans {
        print!("{}", a);
    }
    println!("");
}

use std::io::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    func(&buf[..]);
}