You are given an integer array vals of length $n$ and an integer array par of length $n$, representing a rooted tree with $n$ nodes indexed from $0$ to $n - 1$. The tree is rooted at node $0$, with par[0] == -1, and for each node i where $1 \leq i < n$, par[i] represents the parent of node i. Each node i is assigned the value vals[i].

For each node i, consider the subtree rooted at node i. A subset of nodes from this subtree is called good if each decimal digit from $0$ to $9$ appears at most once across the decimal representations of all values in the subset.

The score of a good subset is the sum of the values of the nodes in that subset. The score of an empty subset is $0$.

Let maxScore[i] be the maximum score among all good subsets chosen from the subtree rooted at node i.

Return the sum of maxScore[i] across all nodes i from $0$ to $n - 1$.

Constraints:

• $1 \leq n ==$ vals.length $\leq 500$

• $1 \leq$ vals[i] $\leq 10^9$

• par.length $== n$

• par[0] $== -1$

• $0 \leq$ par[i] $< n$ for i in $[1, n - 1]$

• The input is generated such that the parent array par represents a valid tree.

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.