Count Paths That Can Form a Palindrome in a Tree

You are given a 0-indexed tree with n nodes represented by a parent array parent, where parent[0] = -1 and parent[i] is the parent of node i for i > 0. You are also given a string s of length n, where s[i] is the lowercase character assigned to the edge between i and parent[i]. Since the root has no incoming edge, s[0] can be ignored. For any two nodes u and v, consider the characters assigned to the edges on the unique path between them. That path can form a palindrome if those characters can be rearranged into a palindrome. Return the number of unordered pairs of distinct nodes (u, v) such that the edge characters on the path between u and v can form a palindrome.

The valid pairs are (0,1), (0,2), (1,3), (1,4), (1,5), (2,3), (2,5), and (3,5). Each corresponding path has at most one character with odd frequency.

Every path consists only of the character a, so every pair of distinct nodes is valid.

The valid pairs are (0,1) and (1,2). The path (0,2) uses characters b and c, which cannot be rearranged into a palindrome.