Given a string s, reorder its characters using the following algorithm:

$1$. Choose the smallest character from s and append it to the result.
$2$. Choose the smallest character from s that is strictly greater than the last appended character, and append it to the result.
$3$. Repeat step $2$ until no further characters can be picked.
$4$. Choose the largest character from s and append it to the result.
$5$. Choose the largest character from s that is strictly smaller than the last appended character, and append it to the result.
$6$. Repeat step $5$ until no further characters can be picked.
$7$. Repeat steps $1$ to $6$ until all characters from s have been used.

Return the resulting string.

Constraints:

• $1 \leq$ s.length $\leq 500$

• s consists of only lowercase English letters.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.