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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php

fscanf(STDIN, "%d", $num);
$bit = decbin(abs($num));
$bstr = array_reverse(str_split($bit));

$buff = 0;
foreach($bstr as $n => $value){
    if($buff > 0){
        if($value == 1){
            $bstr[$n] = 0;
            $value = 0;
        }else{
            $bstr[$n] = 1;
            $value = 1;
            $buff--;
        }
    }
    if(((($num < 0) && ($n % 2 == 0))|| (($num >= 0) && $n % 2 == 1)) && $value == 1){
        $buff += 1;
    }
    $last = $n;
}


while($buff > 0){
    if(((($num < 0) && ($last % 2 == 1))|| (($num >= 0) && $last % 2 == 0))){
        $bstr[] = 1;
    }else{
        $bstr[] = 1;
        $buff--;
    }
    $last++;
}


echo implode("", array_reverse($bstr));