You are given a string word containing distinct lowercase English letters.

Telephone keypads have keys numbered from $2$ to $9$, offering $8$ keys in total. You can map the letters of the English alphabet to these keys such that each letter is assigned to at most one key.

When a letter is typed, the key it is assigned to must be pressed a number of times equal to the letter’s position on that key. Specifically, the first letter placed on a key requires $1$ push, the second letter requires $2$ pushes, the third letter requires $3$ pushes, and so forth.

Return the minimum total number of pushes required to type word after choosing an optimal key mapping.

Constraints:

• $1 \leq$ word.length $\leq 26$

• word consists of lowercase English letters.

• All letters in word are distinct.

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.