Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}


n, m = map(int, input().split())
p_list = list(map(int, input().split()))
q_list = []
for item in p_list:
    q_list.append(item-1)

uni = UnionFind(n)

for i in range(m):
    x, y = map(int, input().split())
    uni.union(x-1, y-1)

ret = 0

tmp_dict = uni.all_group_members()

for item in tmp_dict:
    t_list = tmp_dict[item]
    tmp = set()
    for var in t_list:
        tmp.add(q_list[var])
    ret += len(tmp & set(t_list))

print(ret)


Fixed submission:
class UnionFind():
    def __init__(self, n):
        self.parents = list(range(n))
        self.rank = [0] * n

    def find(self, x):
        if self.parents[x] == x:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.rank[x] < self.rank[y]:
            self.parents[x] = y
        else:
            self.parents[y] = x
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1


n, m = map(int, input().split())
p_list = list(map(int, input().split()))
q_list = list(map(lambda x: x - 1, p_list))

uni = UnionFind(n)

for i in range(m):
    x, y = map(int, input().split())
    uni.union(x-1, y-1)

ret = 0

tmp_dict = dict()

for i in range(n):
    parent = uni.find(i)
    if parent in tmp_dict:
        tmp_dict[parent].append(i)
    else:
        tmp_dict[parent] = [i]

for item in tmp_dict:
    t_list = tmp_dict[item]
    tmp = set()
    for var in t_list:
        tmp.add(q_list[var])
    ret += len(tmp & set(t_list))

print(ret)

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}


n, m = map(int, input().split())
p_list = list(map(int, input().split()))
q_list = []
for item in p_list:
    q_list.append(item-1)

uni = UnionFind(n)

for i in range(m):
    x, y = map(int, input().split())
    uni.union(x-1, y-1)

ret = 0

tmp_dict = uni.all_group_members()

for item in tmp_dict:
    t_list = tmp_dict[item]
    tmp = []
    for var in t_list:
        tmp.append(q_list[var])
    ret += len(set(tmp) & set(t_list))

print(ret)


Fixed submission:
class UnionFind():
    def __init__(self, n):
        self.parents = list(range(n))
        self.rank = [0] * n

    def find(self, x):
        if self.parents[x] == x:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.rank[x] < self.rank[y]:
            self.parents[x] = y
        else:
            self.parents[y] = x
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1


n, m = map(int, input().split())
p_list = list(map(int, input().split()))
q_list = list(map(lambda x: x - 1, p_list))

uni = UnionFind(n)

for i in range(m):
    x, y = map(int, input().split())
    uni.union(x-1, y-1)

ret = 0

tmp_dict = dict()

for i in range(n):
    parent = uni.find(i)
    if parent in tmp_dict:
        tmp_dict[parent].append(i)
    else:
        tmp_dict[parent] = [i]

for item in tmp_dict:
    t_list = tmp_dict[item]
    tmp = set()
    for var in t_list:
        tmp.add(q_list[var])
    ret += len(tmp & set(t_list))

print(ret)

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}


n, m = map(int, input().split())
p_list = list(map(int, input().split()))
q_list = []
for item in p_list:
    q_list.append(item-1)

uni = UnionFind(n)

for i in range(m):
    x, y = map(int, input().split())
    uni.union(x-1, y-1)

ret = 0

for item in uni.all_group_members():
    t_list = uni.all_group_members()[item]
    tmp = []
    for var in t_list:
        tmp.append(q_list[var])
    ret += len(set(tmp) & set(t_list))

print(ret)


Fixed submission:
class UnionFind():
    def __init__(self, n):
        self.parents = list(range(n))
        self.rank = [0] * n

    def find(self, x):
        if self.parents[x] == x:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.rank[x] < self.rank[y]:
            self.parents[x] = y
        else:
            self.parents[y] = x
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1


n, m = map(int, input().split())
p_list = list(map(int, input().split()))
q_list = list(map(lambda x: x - 1, p_list))

uni = UnionFind(n)

for i in range(m):
    x, y = map(int, input().split())
    uni.union(x-1, y-1)

ret = 0

tmp_dict = dict()

for i in range(n):
    parent = uni.find(i)
    if parent in tmp_dict:
        tmp_dict[parent].append(i)
    else:
        tmp_dict[parent] = [i]

for item in tmp_dict:
    t_list = tmp_dict[item]
    tmp = set()
    for var in t_list:
        tmp.add(q_list[var])
    ret += len(tmp & set(t_list))

print(ret)