Intersection of Permutations
You 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.
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 $$$[5, 1, 3, 2, 4, 6]$$$.
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:  $$$1~l_a~r_a~l_b~r_b$$$ ($$$1 \le l_a \le r_a \le n$$$, $$$1 \le l_b \le r_b \le n$$$);  $$$2~x~y$$$ ($$$1 \le x, y \le n$$$, $$$x \ne y$$$). 
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 $$$b$$$.
import sys, os, io
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

def make_tree(n):
    tree = [[0] * (n + 1) for _ in range(n // l)]
    return tree

def get_sum(i, j):
    s = 0
    treej = tree[j]
    while i > 0:
        s += treej[i]
        i -= i & -i
    return s

def get_sum_segment(s, t, j):
    ans = get_sum(t, j) - get_sum(s - 1, j)
    return ans

def add(i, j, x):
    while i <= n:
        tree[j][i] += x
        i += i & -i

def make_tree2(n):
    tree2 = [[0] * (n + 1) for _ in range(n // l2)]
    return tree2

def get_sum2(i, j):
    s = 0
    treej = tree2[j]
    while i > 0:
        s += treej[i]
        i -= i & -i
    return s

def get_sum_segment2(s, t, j):
    ans = get_sum2(t, j) - get_sum2(s - 1, j)
    return ans

def add2(i, j, x):
    while i <= n:
        tree2[j][i] += x
        i += i & -i
(n, m) = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
(l, l2) = (2000, 20000)
(a0, b0) = ([0] * (n + 1), [0] * (n + 1))
for i in range(n):
    a0[a[i]] = i + 1
    b0[b[i]] = i + 1
x = [0] * (n + 1)
for i in range(1, n + 1):
    x[a0[i]] = b0[i]
n0 = n
while (len(x) - 1) % l2:
    x.append(0)
    n0 += 1
y = [0] * (n + 1)
for i in range(1, n + 1):
    y[x[i]] = i
tree = make_tree(n0)
tree2 = make_tree2(n0)
for i in range(1, n + 1):
    add(x[i], (i - 1) // l, 1)
    add2(x[i], (i - 1) // l2, 1)
ans = []
for _ in range(m):
    t = list(map(int, input().split()))
    if t[0] == 1:
        (la, ra, lb, rb) = (t[1], t[2], t[3], t[4])
        ans0 = 0
        while la <= ra and (not la % l == 1):
            if lb <= x[la] <= rb:
                ans0 += 1
            la += 1
        while la <= ra and (not ra % l == 0):
            if lb <= x[ra] <= rb:
                ans0 += 1
            ra -= 1
        while la < ra:
            if (la - 1) % l2 == 0 and la + l2 <= ra + l:
                ans0 += get_sum_segment2(lb, rb, (la - 1) // l2)
                la += l2
            else:
                ans0 += get_sum_segment(lb, rb, (la - 1) // l)
                la += l
        ans.append(ans0)
    else:
        (u, v) = (t[1], t[2])
        (yu, yv) = (y[u], y[v])
        if not (yu - 1) // l == (yv - 1) // l:
            add(x[yu], (yu - 1) // l, -1)
            add(x[yv], (yv - 1) // l, -1)
            add(x[yu], (yv - 1) // l, 1)
            add(x[yv], (yu - 1) // l, 1)
            if not (yu - 1) // l2 == (yv - 1) // l2:
                add2(x[yu], (yu - 1) // l2, -1)
                add2(x[yv], (yv - 1) // l2, -1)
                add2(x[yu], (yv - 1) // l2, 1)
                add2(x[yv], (yu - 1) // l2, 1)
        (y[u], y[v]) = (yv, yu)
        (x[yu], x[yv]) = (x[yv], x[yu])
sys.stdout.write('\n'.join(map(str, ans)))
import sys
import random
input = sys.stdin.readline
rd = random.randint(10 ** 9, 2 * 10 ** 9)

class BIT:

    def __init__(self, n):
        self.n = n
        self.tree = [0] * (n + 1)

    def update(self, index, val):
        while index <= self.n:
            self.tree[index] += val
            index += index & -index

    def query(self, r):
        res = 0
        while r > 0:
            res += self.tree[r]
            r -= r & -r
        return res

    def query_lr(self, left, right):
        return self.query(right) - self.query(left - 1)
(n, m) = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
d1 = {a[i]: i + 1 for i in range(n)}
tree = BIT(n)
queries = []
ans = [-1] * m
for i in range(n):
    queries.append([2, 1, d1[b[i]], i + 1])
for i in range(m):
    q = list(map(int, input().split()))
    if q[0] == 1:
        (x1, x2, y1, y2) = q[1:]
        queries.append([1, x1, x2, y1 - 1, -1, i])
        queries.append([1, x1, x2, y2, 1, i])
        ans[i] = 0
    else:
        (x, y) = q[1:]
        (bx, by) = (b[x - 1], b[y - 1])
        queries.append([2, -1, d1[bx], x])
        queries.append([2, -1, d1[by], y])
        queries.append([2, 1, d1[by], x])
        queries.append([2, 1, d1[bx], y])
        (b[x - 1], b[y - 1]) = (b[y - 1], b[x - 1])
idx = list(range(len(queries)))

def cdq(l, r):
    if l == r:
        return
    mid = l + r >> 1
    cdq(l, mid)
    cdq(mid + 1, r)
    left = l
    for right in range(mid + 1, r + 1):
        if queries[idx[right]][0] == 1:
            (x1, x2, y, val, i) = queries[idx[right]][1:]
            while left <= mid:
                if queries[idx[left]][0] == 1:
                    left += 1
                elif queries[idx[left]][3] <= y:
                    tree.update(queries[idx[left]][2], queries[idx[left]][1])
                    left += 1
                else:
                    break
            ans[i] += val * tree.query_lr(x1, x2)
    for mm in range(l, left):
        if queries[idx[mm]][0] == 2:
            tree.update(queries[idx[mm]][2], -queries[idx[mm]][1])
    tmp = []
    left = l
    right = mid + 1
    while left <= mid and right <= r:
        if queries[idx[left]][3] <= queries[idx[right]][3]:
            tmp.append(idx[left])
            left += 1
        else:
            tmp.append(idx[right])
            right += 1
    while left <= mid:
        tmp.append(idx[left])
        left += 1
    while right <= r:
        tmp.append(idx[right])
        right += 1
    for i in range(l, r + 1):
        idx[i] = tmp[i - l]
cdq(0, len(queries) - 1)
for i in ans:
    if i != -1:
        print(i)
import sys
import random
input = sys.stdin.readline
rd = random.randint(10 ** 9, 2 * 10 ** 9)

class BIT:

    def __init__(self, n):
        self.n = n
        self.tree = [0] * (n + 1)

    def update(self, index, val):
        while index <= self.n:
            self.tree[index] += val
            index += index & -index

    def query(self, r):
        res = 0
        while r > 0:
            res += self.tree[r]
            r -= r & -r
        return res

    def query_lr(self, left, right):
        return self.query(right) - self.query(left - 1)
(n, m) = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
d1 = {a[i]: i + 1 for i in range(n)}
tree = BIT(n)
queries = []
ans = [-1] * m
for i in range(n):
    queries.append([2, 1, d1[b[i]], i + 1])
for i in range(m):
    q = list(map(int, input().split()))
    if q[0] == 1:
        (x1, x2, y1, y2) = q[1:]
        queries.append([1, x1, x2, y1 - 1, -1, i])
        queries.append([1, x1, x2, y2, 1, i])
        ans[i] = 0
    else:
        (x, y) = q[1:]
        (bx, by) = (b[x - 1], b[y - 1])
        queries.append([2, -1, d1[bx], x])
        queries.append([2, -1, d1[by], y])
        queries.append([2, 1, d1[by], x])
        queries.append([2, 1, d1[bx], y])
        (b[x - 1], b[y - 1]) = (b[y - 1], b[x - 1])
idx = list(range(len(queries)))

def cdq(l, r):
    if l == r:
        return
    mid = l + r >> 1
    cdq(l, mid)
    cdq(mid + 1, r)
    left = l
    for right in range(mid + 1, r + 1):
        if queries[idx[right]][0] == 1:
            (x1, x2, y, val, i) = queries[idx[right]][1:]
            while left <= mid:
                if queries[idx[left]][0] == 1:
                    left += 1
                elif queries[idx[left]][3] <= y:
                    tree.update(queries[idx[left]][2], queries[idx[left]][1])
                    left += 1
                else:
                    break
            ans[i] += val * tree.query_lr(x1, x2)
    for mm in range(l, left):
        if queries[idx[mm]][0] == 2:
            tree.update(queries[idx[mm]][2], -queries[idx[mm]][1])
    tmp = []
    left = l
    right = mid + 1
    while left <= mid and right <= r:
        if queries[idx[left]][3] <= queries[idx[right]][3]:
            tmp.append(idx[left])
            left += 1
        else:
            tmp.append(idx[right])
            right += 1
    while left <= mid:
        tmp.append(idx[left])
        left += 1
    while right <= r:
        tmp.append(idx[right])
        right += 1
    for i in range(l, r + 1):
        idx[i] = tmp[i - l]
cdq(0, len(queries) - 1)
for i in ans:
    if i != -1:
        print(i)