Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.readline

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))
    xy = [list(map(int,input().split())) for _ in range(m)]

    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()}

        def __str__(self):
            return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


    uf = UnionFind(n)
    ans = 0
    for x,y in xy:
        uf.union(x-1,y-1)
    for v in uf.all_group_members().values():
        set1 = set()
        for i in v:
            set1.add(p[i]-1)
        ans += len(set(v)&set1)

    print(ans)

if __name__ == '__main__':
    main()


Fixed submission:
import sys
input = sys.stdin.readline

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))
    xy = [list(map(int,input().split())) for _ in range(m)]

    class UnionFind(object):
        def __init__(self, n=1):
            self.par = [i for i in range(n)]
            self.rank = [0 for _ in range(n)]
            self.size = [1 for _ in range(n)]

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

        def union(self, x, y):
            x = self.find(x)
            y = self.find(y)
            if x != y:
                if self.rank[x] < self.rank[y]:
                    x, y = y, x
                if self.rank[x] == self.rank[y]:
                    self.rank[x] += 1
                self.par[y] = x
                self.size[x] += self.size[y]

        def all_group_members(self):
            return_list = [list() for i in range(n)]
            for i in range(n):
              return_list[self.find(i)].append(i)
            return return_list

    uf = UnionFind(n)
    ans = 0
    for x,y in xy:
        uf.union(x-1,y-1)
    for v in uf.all_group_members():
        set1 = set()
        for i in v:
            set1.add(p[i]-1)
        ans += len(set(v)&set1)

    print(ans)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.readline

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))
    xy = [list(map(int,input().split())) for _ in range(m)]

    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()}

        def __str__(self):
            return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


    uf = UnionFind(n)
    ans = 0
    for x,y in xy:
        uf.union(x-1,y-1)
    for v in uf.all_group_members().values():
        li = []
        for i in v:
            li.append(p[i]-1)
        ans += len(set(v)&set(li))

    print(ans)

if __name__ == '__main__':
    main()


Fixed submission:
import sys
input = sys.stdin.readline

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))
    xy = [list(map(int,input().split())) for _ in range(m)]

    class UnionFind(object):
        def __init__(self, n=1):
            self.par = [i for i in range(n)]
            self.rank = [0 for _ in range(n)]
            self.size = [1 for _ in range(n)]

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

        def union(self, x, y):
            x = self.find(x)
            y = self.find(y)
            if x != y:
                if self.rank[x] < self.rank[y]:
                    x, y = y, x
                if self.rank[x] == self.rank[y]:
                    self.rank[x] += 1
                self.par[y] = x
                self.size[x] += self.size[y]

        def all_group_members(self):
            return_list = [list() for i in range(n)]
            for i in range(n):
              return_list[self.find(i)].append(i)
            return return_list

    uf = UnionFind(n)
    ans = 0
    for x,y in xy:
        uf.union(x-1,y-1)
    for v in uf.all_group_members():
        set1 = set()
        for i in v:
            set1.add(p[i]-1)
        ans += len(set(v)&set1)

    print(ans)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
n,m = map(int,input().split())
p = list(map(int,input().split()))
xy = [list(map(int,input().split())) for _ in range(m)]

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()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


uf = UnionFind(n)
ans = 0
for x,y in xy:
    uf.union(x-1,y-1)
for v in uf.all_group_members().values():
    li = []
    for i in v:
        if p[i]-1 in v:
            ans += 1

print(ans)


Fixed submission:
import sys
input = sys.stdin.readline

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))
    xy = [list(map(int,input().split())) for _ in range(m)]

    class UnionFind(object):
        def __init__(self, n=1):
            self.par = [i for i in range(n)]
            self.rank = [0 for _ in range(n)]
            self.size = [1 for _ in range(n)]

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

        def union(self, x, y):
            x = self.find(x)
            y = self.find(y)
            if x != y:
                if self.rank[x] < self.rank[y]:
                    x, y = y, x
                if self.rank[x] == self.rank[y]:
                    self.rank[x] += 1
                self.par[y] = x
                self.size[x] += self.size[y]

        def all_group_members(self):
            return_list = [list() for i in range(n)]
            for i in range(n):
              return_list[self.find(i)].append(i)
            return return_list

    uf = UnionFind(n)
    ans = 0
    for x,y in xy:
        uf.union(x-1,y-1)
    for v in uf.all_group_members():
        set1 = set()
        for i in v:
            set1.add(p[i]-1)
        ans += len(set(v)&set1)

    print(ans)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
n,m = map(int,input().split())
p = list(map(int,input().split()))
xy = [list(map(int,input().split())) for _ in range(m)]

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()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


uf = UnionFind(n)
ans = 0
for x,y in xy:
    uf.union(x-1,y-1)
for v in uf.all_group_members().values():
    li = []
    for i in v:
        li.append(p[i]-1)
    ans += len(set(v)&set(li))

print(ans)


Fixed submission:
import sys
input = sys.stdin.readline

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))
    xy = [list(map(int,input().split())) for _ in range(m)]

    class UnionFind(object):
        def __init__(self, n=1):
            self.par = [i for i in range(n)]
            self.rank = [0 for _ in range(n)]
            self.size = [1 for _ in range(n)]

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

        def union(self, x, y):
            x = self.find(x)
            y = self.find(y)
            if x != y:
                if self.rank[x] < self.rank[y]:
                    x, y = y, x
                if self.rank[x] == self.rank[y]:
                    self.rank[x] += 1
                self.par[y] = x
                self.size[x] += self.size[y]

        def all_group_members(self):
            return_list = [list() for i in range(n)]
            for i in range(n):
              return_list[self.find(i)].append(i)
            return return_list

    uf = UnionFind(n)
    ans = 0
    for x,y in xy:
        uf.union(x-1,y-1)
    for v in uf.all_group_members():
        set1 = set()
        for i in v:
            set1.add(p[i]-1)
        ans += len(set(v)&set1)

    print(ans)

if __name__ == '__main__':
    main()