Jumping Through the Array

Description:

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.

Sample 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

Sample Output:

13
16
11

Sample 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

Sample Output:

61
45
22
461
301

Sample Input:

1
1
1
1
1 1 1

Sample 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 $$$a_1 + a_2 + a_3 + a_4 + a_5 = 6 + 9 + (-5) + 2 + (-1) = 11$$$.