Tree

You are given a rooted tree with $n$ vertices. The vertices are numbered from 1 to $n$, and vertex 1 is the root. A rooted tree is a connected undirected graph with one vertex chosen as the root. For every vertex, the neighbor closest to the root is its parent, and the other neighbors are its children. The root has no parent.

Two kinds of queries are processed in the given order.

The first kind removes a vertex. When vertex $u$ is removed, every child of $u$ becomes a child of the parent of $u$. The root is never removed.

The second kind asks for a distance. It is the length of the path between two vertices in the current tree, counted as the number of edges on that path.

Answer every distance query.

The first line contains the number of vertices $n$ in the initial tree ($1 \le n \le 100000$).

The second line contains the parents $p_i$ of vertices $2, 3, \ldots, n$ in this order ($1 \le p_i \le n$). When $n$ is 1, the second line is empty.

The third line contains the number of queries $q$ ($1 \le q \le 100000$).

Each of the next $q$ lines holds one query. A query starts with an integer that is either 1 or 2. If that integer is 1, two integers $a$ and $b$ follow ($1 \le a, b \le n$), and you must report the distance between $a$ and $b$ in the current tree. If it is 2, one integer $v$ follows ($1 \le v \le n$), and vertex $v$ must be removed.

The initial tree is always valid. Every vertex named in a query is still present, and the root is never given as a vertex to remove.

For each query that starts with 1, print the distance between the two vertices on its own line.