### 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 $x$).

### 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.

### 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.

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.