Given two strings a and b. In one operation, you can change any character in a or b to any lowercase English letter.

Return the minimum number of operations required to satisfy at least one of the following three conditions:

$1$. Every letter in a is strictly smaller in alphabetical order than every letter in b.
$2$. Every letter in b is strictly smaller in alphabetical order than every letter in a.
$3$. Both a and b consist of only one distinct letter (the exact same letter across all characters in both strings).

Constraints:

• $1 \leq$ a.length, b.length $\leq 10^5$

• a and b consist only of 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.