You are given an unweighted undirected tree with n nodes labeled from $0$ to n $- 1$, represented by a $2$D integer array edges of length n $- 1$, where edges[i] $= [u_i, v_i]$ indicates an edge between nodes $u_i$ and $v_i$.

You are also given three pairwise distinct nodes x, y, and z.

For any node u in the tree, let $d_1$, $d_2$, and $d_3$ be the distances from u to nodes x, y, and z sorted in nondecreasing order such that $d_1 \leq d_2 \leq d_3$. A node u is called special if these distances satisfy the Pythagorean condition:

Return the number of special nodes in the tree.

Constraints:

• $4 \leq n \leq 10^5$

• $\text{edges.length} = n - 1$

• $\text{edges}[i] = [u_i, v_i]$

• $0 \leq u_i, v_i, x, y, z \leq n - 1$

• x, y, and z are pairwise distinct.

• The input is generated such that edges 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.