Solve two online assessment problems

An online assessment contained two coding problems:

1. Maximize skipped positions You are given an array of length n indexed from 0 to n - 1 . Start at index 0 and reach index n - 1 . At any index i , you may:
   • move to i + 1 , if it exists; or
   • jump to any index j > i such that j is a prime number and the decimal representation of j ends with 3 .
   If you jump from i to j , you gain j - i - 1 points, equal to the number of positions skipped. Moving one step to the right gives 0 points. Compute the maximum total score achievable when you reach the last index.
2. Count palindromic-anagram ancestors in a rooted tree An undirected tree with tree_nodes nodes is rooted at node 0 . The nodes are numbered from 0 to tree_nodes - 1 . Each node i stores a lowercase character arr[i] . You are also given an array queries of length m . For each query node q = queries[i] , consider every node v on the path from q to the root, including q itself. Count how many such nodes v have the property that the characters on the path from q up to v can be rearranged to form a palindrome. Return an integer array of length m , where the i -th value is the answer for queries[i] . Example:
   • tree_nodes = 4
   • arr = ['z', 'a', 'a', 'a']
   • edges: (0, 1) , (0, 2) , (1, 3)
   • queries = [3]
   Output: [3] Explanation: For query node 3 , the path segments ending at nodes 3 , 1 , and 0 all have character counts that can be rearranged into a palindrome.