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data structures

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E. Intersection of Permutations

time limit per test

6 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputYou are given two permutations $$$a$$$ and $$$b$$$, both consisting of $$$n$$$ elements. Permutation of $$$n$$$ elements is such a integer sequence that each value from $$$1$$$ to $$$n$$$ appears exactly once in it.

You are asked to perform two types of queries with them:

- $$$1~l_a~r_a~l_b~r_b$$$ — calculate the number of values which appear in both segment $$$[l_a; r_a]$$$ of positions in permutation $$$a$$$ and segment $$$[l_b; r_b]$$$ of positions in permutation $$$b$$$;
- $$$2~x~y$$$ — swap values on positions $$$x$$$ and $$$y$$$ in permutation $$$b$$$.

Print the answer for each query of the first type.

It is guaranteed that there will be at least one query of the first type in the input.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 2 \cdot 10^5$$$, $$$1 \le m \le 2 \cdot 10^5$$$) — the number of elements in both permutations and the number of queries.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le n$$$) — permutation $$$a$$$. It is guaranteed that each value from $$$1$$$ to $$$n$$$ appears in $$$a$$$ exactly once.

The third line contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_i \le n$$$) — permutation $$$b$$$. It is guaranteed that each value from $$$1$$$ to $$$n$$$ appears in $$$b$$$ exactly once.

Each of the next $$$m$$$ lines contains the description of a certain query. These are either:

- $$$1~l_a~r_a~l_b~r_b$$$ ($$$1 \le l_a \le r_a \le n$$$, $$$1 \le l_b \le r_b \le n$$$);
- $$$2~x~y$$$ ($$$1 \le x, y \le n$$$, $$$x \ne y$$$).

Output

Print the answers for the queries of the first type, each answer in the new line — the number of values which appear in both segment $$$[l_a; r_a]$$$ of positions in permutation $$$a$$$ and segment $$$[l_b; r_b]$$$ of positions in permutation $$$b$$$.

Example

Input

6 7 5 1 4 2 3 6 2 5 3 1 4 6 1 1 2 4 5 2 2 4 1 1 2 4 5 1 2 3 3 5 1 1 6 1 2 2 4 1 1 4 4 1 3

Output

1 1 1 2 0

Note

Consider the first query of the first example. Values on positions $$$[1; 2]$$$ of $$$a$$$ are $$$[5, 1]$$$ and values on positions $$$[4; 5]$$$ of $$$b$$$ are $$$[1, 4]$$$. Only value $$$1$$$ appears in both segments.

After the first swap (the second query) permutation $$$b$$$ becomes $$$[2, 1, 3, 5, 4, 6]$$$.

After the second swap (the sixth query) permutation $$$b$$$ becomes $$$[5, 1, 3, 2, 4, 6]$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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