Maximize non-adjacent sum on an N-ary tree

You are given an **N-ary tree** (each node may have 0..k children). Each node contains an integer value (can be 0 or positive). You want to select a set of nodes such that **no selected node is directly connected to another selected node** (i.e., you cannot select both a node and any of its children). Return the **maximum possible sum** of selected node values. ### Requirements - Implement a tree node structure yourself, e.g.: - `value: int` - `children: List[Node]` - Write a function `maxNonAdjacentTreeSum(root) -> int`. ### Input / Output - **Input:** `root` pointer/reference to the root node (or `null` for empty tree). - **Output:** an integer representing the maximum achievable sum. ### Example If the tree is: - Root 3 with children 2 and 3 - Node 2 has child 3 - Node 3 (child of root) has child 1 One optimal selection is nodes with values `3 (root) + 3 (grandchild under 2) + 1 = 7`, so return `7`. ### Constraints - Number of nodes `n` up to ~10^5. - Aim for **O(n)** time. - Extra space should be proportional to recursion depth or explicit stack size.