Compute outer boundary of an N-ary tree

You are given the root of a rooted **N-ary tree**. Each node contains: - An integer value. - An ordered list of children from left to right (0 or more children). Consider all nodes grouped by their depth (root at depth 0, its children at depth 1, etc.). For each depth `d`: - Let **L_d** be the *leftmost* node at depth `d` (the first node at that depth when scanning children from left to right). - Let **R_d** be the *rightmost* node at depth `d` (the last node at that depth when scanning children from left to right). We define the **outer boundary path** of the tree as the sequence of nodes you would "see" when walking around the outside of the tree, starting from the lowest leftmost node, going up to the root, then going down to the lowest rightmost node: 1. Starting from the **maximum depth D** down to `0`, take `L_D, L_{D-1}, ..., L_0` (bottom-left up to the root). 2. Then from depth `1` up to `D`, take `R_1, R_2, ..., R_D` (top-right down to bottom-right), **skipping** `R_d` when `R_d` is the same node as `L_d` to avoid duplicates on levels with only one node. Return the list of node values in this exact order. Assume: - Total number of nodes `n` satisfies `1 <= n <= 10^5`. - Tree height `h` can be up to `n` in the worst case. **Task**: Design an efficient algorithm to compute and return this outer boundary path. Specify the time and space complexity of your approach.