Problem Statement

We have a directed graph $G_S$ with $N$ vertices numbered $1$ to $N$. It has $N-1$ edges. The $i$-th edge $(1\leq i \leq N-1)$ goes from vertex $p_i\ (1\leq p_i \leq i)$ to vertex $i+1$.

We have another directed graph $G$ with $N$ vertices numbered $1$ to $N$. Initially, $G$ equals $G_S$. Process $Q$ queries on $G$ in the order they are given. There are two kinds of queries as follows.

• 1 u v : Add an edge to $G$ that goes from vertex $u$ to vertex $v$. It is guaranteed that the following conditions are satisfied.
• $u \neq v$.
  • On $G_S$, vertex $u$ is reachable from vertex $v$ via some edges.
• 2 x : Print the smallest vertex number of a vertex reachable from vertex $x$ via some edges on $G$ (including vertex $x$).

Constraints

• $2\leq N \leq 2\times 10^5$
• $1\leq Q \leq 2\times 10^5$
• $1\leq p_i\leq i$
• For each query in the first format:
• $1\leq u,v \leq N$.
  • $u \neq v$.
  • On $G_S$, vertex $u$ is reachable from vertex $v$ via some edges.
• For each query in the second format, $1\leq x \leq N$.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N
p_1 p_2 \dots p_{N-1}
Q
\mathrm{query}_1
\mathrm{query}_2
\vdots
\mathrm{query}_Q

Here, $\mathrm{query}_i$ denotes the $i$-th query and is in one of the following formats:

1 u v

2 x

Output

Print $q$ lines, where $q$ is the number of queries in the second format. The $i$-th line $(1\leq j \leq q)$ should contain the answer to the $j$-th query in the second format.