Increasing Decreasing String

You are given a string s, and your task is to rearrange its characters following a repeated “up and down” selection process.

The process works as follows:

• First, take characters in increasing alphabetical order, each time picking the smallest character greater than the previous appended one.

• When no more characters can be chosen in increasing order, switch direction.

• Now pick characters in decreasing alphabetical order, each time choosing the largest character smaller than the last appended one.

• Alternate between ascending and descending phases until all characters in s have been used.

Whenever multiple copies of a character exist, any instance can be used.

Return the final string produced after applying this pattern.