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: Wrong Answer)

use std::str::FromStr;

fn get_one<T : FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    return s.trim().parse().ok().unwrap();
}

fn get_vec<T : FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    return s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect();
}

fn get_vec_by_lines<T : FromStr>(n : usize) -> Vec<T> {
    let mut v : Vec<T> = Vec::new();
    for _i in 0..n {
        let x : T = get_one();
        v.push(x);
    }
    return v;
}


fn main() {
    let n : i64 = get_one();
    let d = -2863311530;
    let mut plus = false;
    let mut nd = n - d;
    let mut ans = String::new();
    for i in (0..33).rev() {
        let curp = 2_i64.pow(i);
        if nd < curp {
            ans.push(if plus { '1' } else { '0' });
        }
        else {
            ans.push(if plus { '0' } else { '1' });
            nd -= curp;
        }
        plus = !plus;
    }
    let mut ans2 = String::new();
    let mut valid = false;
    for c in ans.chars() {
        if !valid && c == '0' {
            continue;
        }
        valid = true;
        ans2.push(c);
    }
    println!("{}", ans2);
}