F. Jumping Through the Array
time limit per test
8 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given an array of integers $a$ of size $n$ and a permutation $p$ of size $n$. There are $q$ queries of three types coming to you:

1. For given numbers $l$ and $r$, calculate the sum in array $a$ on the segment from $l$ to $r$: $\sum\limits_{i=l}^{r} a_i$.
2. You are given two numbers $v$ and $x$. Let's build a directed graph from the permutation $p$: it has $n$ vertices and $n$ edges $i \to p_i$. Let $C$ be the set of vertices that are reachable from $v$ in this graph. You should add $x$ to all $a_u$ such that $u$ is in $C$.
3. You are given indices $i$ and $j$. You should swap $p_i$ and $p_j$.
The graph corresponding to the permutation $[2, 3, 1, 5, 4]$.

Please, process all queries and print answers to queries of type $1$.

Input

The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the size of the array and permutation.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($-10^8 \le a_i \le 10^8$).

The third line contains $n$ distinct integers $p_1, p_2, \ldots, p_n$ ($1 \le p_i \le n$).

The fourth line contains a single integer $q$ — the number of queries ($1 \le q \le 2 \cdot 10^5$).

Next $q$ lines contain description of queries. The $i$-th of them starts with an integer $t_i$ ($1 \le t_i \le 3$) — the query type.

• If $t_i = 1$, then the $i$-th line also contains two integers $l$, $r$ ($1 \le l \le r \le n$).
• If $t_i = 2$, then the $i$-th line also contains two integers $v$, $x$ ($1 \le v \le n$, $-10^8 \le x \le 10^8$).
• If $t_i = 3$, then the $i$-th line also contains also two integers $i$, $j$ ($1 \le i, j \le n$).
Output

For every first type query, print a single integer — the answer to this query.

Examples
Input
5
6 9 -5 3 0
2 3 1 5 4
6
1 1 5
2 1 1
1 1 5
3 1 5
2 1 -1
1 1 5
Output
13
16
11
Input
8
-15 52 -4 3 5 9 0 5
2 4 6 8 1 3 5 7
10
2 2 2
2 5 -1
1 1 8
1 1 5
1 5 8
3 1 6
2 1 50
1 1 8
2 6 -20
1 1 8
Output
61
45
22
461
301
Input
1
1
1
1
1 1 1
Output
1
Note

In the first example:

The graph corresponding to the initial permutation.

There are $6$ queries.

1. The sum on the segment from $1$ to $5$ is $a_1 + a_2 + a_3 + a_4 + a_5 = 6 + 9 + (-5) + 3 + 0 = 13$.
2. If we start from $1$, we can reach $\{1, 2, 3\}$. After this query $a$ is: $[7, 10, -4, 3, 0]$.
3. The sum on the segment from $1$ to $5$ is $a_1 + a_2 + a_3 + a_4 + a_5 = 6 + 9 + (-5) + 3 + 0 = 16$.
4. After this query $p = [4, 3, 1, 5, 2]$.
The graph corresponding to the new permutation.
5. If we start from $2$, we can reach $\{1, 2, 3, 4, 5\}$. After this query $a$ is: $[6, 9, -5, 2, -1]$.
6. The sum on the segment from $1$ to $5$ is $a_1 + a_2 + a_3 + a_4 + a_5 = 6 + 9 + (-5) + 2 + (-1) = 11$.