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.

Sample Input 1

5
1 2 3 3
5
2 4
1 4 2
2 4
1 5 1
2 4

Sample Output 1

4
2
1

• At the time of the first query, only vertex $4$ is reachable from vertex $4$ via some edges on $G$.
• At the time of the third query, vertices $2$, $3$, $4$, and $5$ are reachable from vertex $4$ via some edges on $G$.
• At the time of the fifth query, vertices $1$, $2$, $3$, $4$, and $5$ are reachable from vertex $4$ via some edges on $G$.

Sample Input 2

7
1 1 2 2 3 3
10
2 5
1 5 2
2 5
1 2 1
1 7 1
1 6 3
2 5
2 6
2 1
1 7 1

Sample Output 2

5
2
1
1
1