You are given an array nums of distinct positive integers.

You want to sort nums such that each element is ordered primarily in ascending order of its digit sum. If two elements have the identical digit sum, they should be ordered in ascending order of their values.

Return the minimum number of swaps required to sort nums into this order.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

• nums consists of distinct positive integers.

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.