Choose root to minimize edge reversals

## Problem You are given a connected graph with `n` nodes labeled `0..n-1` and `n-1` directed edges. If you ignore directions, the edges form a **tree** (i.e., the underlying undirected graph is a tree). You may pick any node `r` as the **root**. You are allowed to **reverse** the direction of any edge; reversing one edge costs `1`. Your goal is to choose a root `r` and reverse as few edges as possible so that, in the final directed tree, **every edge points away from the root** (equivalently: for every node `v != r`, the unique path from `r` to `v` follows edge directions from parent to child). ### Input - Integer `n` - List of directed edges `edges`, where each edge is a pair `(u, v)` meaning a directed edge `u -> v` ### Output Return the **minimum number of edge reversals** needed over all choices of root `r`. ### Constraints (typical) - `1 <= n <= 2 * 10^5` - `len(edges) = n - 1` - The underlying undirected graph is connected (a tree) ### Example If `n = 3` and `edges = [(0,1), (2,0)]`: - Choosing root `0` requires reversing `(2,0)` to `(0,2)` → cost `1` - Choosing root `2` requires reversing `(0,1)` and `(2,0)`? (check orientation away from 2) → higher So the answer is `1`.