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::stdin;

fn read_int() -> i32 {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    buf.trim_right().parse().unwrap()
}

fn main () {
    let mut n = read_int() as i64;

    let mut base2 = 1 as i64;
    let mut basem2 = 1 as i64;

    let mut digits: Vec<i32> = vec![];

    for _bit in 0..35 {
        if n & base2 != 0 {
            n -= basem2;
            digits.push(1);
        } else {
            digits.push(0);
        }

        base2 *= 2;
        basem2 *= -2;
    }

    digits.reverse();

    let mut seen = false;
    for &digit in digits.iter() {
        if digit == 1 {
            seen = true;
        }
        if seen {
            print!("{}", digit);
        }
    }
    if seen {
        println!();
    } else {
        println!("0");
    }
}

/*
base2, base -2
00001 = 00001  1
00010 = 00110  2
00100 = 00100  4
01000 = 11000  8
10000 = 10000 16
*/