Compute sums and max path in N-ary tree

You are given the root of an **N-ary tree** (each node can have 0..k children). Implement the `Node` class yourself. Assume each node stores an integer `value` and a list of child nodes `children`. Complete the following tasks: 1. **Sum of all nodes**: Return the sum of `value` over **all** nodes in the tree. 2. **Maximum path value**: Define a *path* as a sequence of nodes from the **root to any leaf** (a node with no children). The *path value* is the sum of node values along that path. Return the **maximum** root-to-leaf path value. 3. **Return the max path**: Return the list of node values along one root-to-leaf path that achieves the maximum path value from (2). If multiple paths tie, you may return any one of them. ### Input / Output - Input: `root: Node | null` - Output: - (1) an integer total sum - (2) an integer maximum root-to-leaf path sum - (3) an array/list of integers representing the values along the chosen max path ### Notes / Constraints - The tree can be empty (`root = null`). - Node values can be negative, zero, or positive. - Aim for linear time in the number of nodes.