P9369 [ICPC 2022 Xi'an R] Tree

You are given a tree $T$ with $n$ nodes. The tree is rooted at $1$. Define $\mathrm{subtree}(u)$ as the set of nodes in the subtree of $u$. Call a subset of nodes $S$ good if and only if $S$ satisfies at least one of the following contidions: - For all $u, v\in S$ where $u\neq v$, either $u\in \mathrm{subtree}(v)$ or $v\in \mathrm{subtree}(u)$. - For all $u, v\in S$ where $u\neq v$, both $u\notin \mathrm{subtree}(v)$ and $v\notin \mathrm{subtree}(u)$. You need to partition all nodes of $T$ into several good subsets. Calculate the minimum number of subsets.

The first line contains a single integer $Q$ ($1\leq Q\leq 10 ^ 5$), denoting the number of test cases. For each test case, the first line contains an integer $n$ ($1\leq n\leq 10 ^ 6$). The next line contains $n - 1$ integers $p_2, p_3, \ldots, p_n$ ($1\leq p_i < i$), indicating that there is an edge between $p_i$ and $i$ for each $i=2,3,\ldots,n$. It is guaranteed that the sum of $n$ over all test cases is no more than $10 ^ 6$.

For each test case, output a single integer representing the answer.

**Source**: The 2022 ICPC Asia Xi'an Regional Contest Problem L. **Author**: Alex_Wei.