You are given a $0$ indexed integer array parents of length n, representing a binary tree rooted at node $0$, where parents[i] is the parent of node i. Since node $0$ is the root, parents[0] is $-1$.

Each node has a score. To compute the score of a node:

1. Remove the node and all of its connected edges from the tree.

2. The remaining nodes will form one or more non empty subtrees.

3. The score of the node is the product of the sizes of all these remaining subtrees. If there are no remaining subtrees, the score is $0$.

Return the number of nodes that achieve the maximum possible score.

Constraints:

• n $==$ parents.length

• $2 \leq$ n $\leq 10^5$

• parents[0] $== -1$

• $0 \leq$ parents[i] $\leq$ n $- 1$ for all i $\neq 0$

• parents represents a valid binary 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.