Compute minimum added stones to balance a tree

You are given a **rooted tree** with `n` nodes labeled `1..n` (root is node `1`). Each node `i` initially contains `stones[i]` stones. Define the **subtree sum** of a node as the total number of stones in that node’s subtree (including itself). A node is considered **balanced** if **all of its children’s subtree sums are equal**. (Leaves are automatically balanced.) You are allowed to perform the following operation any number of times: - Choose any node and **add 1 stone** to it. **Task:** Return the **minimum number of stones you must add** so that **every node in the tree is balanced**. #### Input - `n` — number of nodes - `edges` — `n-1` undirected edges describing the tree - `stones[1..n]` — initial stone counts (non-negative integers) #### Output - An integer: the minimum total number of added stones. #### Constraints (typical) - `1 ≤ n ≤ 2e5` - `0 ≤ stones[i] ≤ 1e9` (You should aim for an `O(n)` or `O(n log n)` solution.)