Least Size

You are given a tree with $N$ nodes where each node is numbered from $1$ to $N$. Suppose you root the tree at node $R$. Then, the score of a permutation $P$ of length $N$ is defined as the **size** of the set $S$ containing $\texttt{LCA}(P_i, P_{i+1})$ for all $1\leq i \lt N$. Find the **minimum** score of a permutation over all possible roots and all possible permutations of length $N$. You