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 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 all_group_members(self):
        return [set(self.members(r)) for r in self.roots()]

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

def main():
    n, m = map(int, input().split())
    P = {i : int(p) - 1 for i, p in enumerate(input().split())}
    uf = UnionFind(n)
    for _ in range(m):
        x, y = map(lambda x:int(x) - 1, input().split())
        uf.union(x, y)
    ans = 0
    for g in uf.all_group_members():
        Q = set([P[p] for p in g])
        ans += len(g & Q)
    print(ans)

if __name__ == '__main__':
    main()


Fixed submission:
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 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 all_group_members(self):
        return [set(self.members(r)) for r in self.roots()]

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

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

def main():
    n, m = map(int, input().split())
    P = list(map(lambda x:int(x) - 1, input().split()))
    uf = UnionFind(n)
    for _ in range(m):
        x, y = map(lambda x:int(x) - 1, input().split())
        uf.union(x, y)
    ans = 0
    for i, p in enumerate(P):
        if uf.same(i, p):
            ans += 1
    print(ans)

if __name__ == '__main__':
    main()

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 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 all_group_members(self):
        return [set(self.members(r)) for r in self.roots()]

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

def main():
    n, m = map(int, input().split())
    P = list(map(lambda x:int(x) - 1, input().split()))
    uf = UnionFind(n)
    for _ in range(m):
        x, y = map(lambda x:int(x) - 1, input().split())
        uf.union(x, y)
    ans = 0
    for g in uf.all_group_members():
        Q = set([p for i, p in enumerate(P) if i in g])
        ans += len(g & Q)
    print(ans)

if __name__ == '__main__':
    main()


Fixed submission:
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 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 all_group_members(self):
        return [set(self.members(r)) for r in self.roots()]

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

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

def main():
    n, m = map(int, input().split())
    P = list(map(lambda x:int(x) - 1, input().split()))
    uf = UnionFind(n)
    for _ in range(m):
        x, y = map(lambda x:int(x) - 1, input().split())
        uf.union(x, y)
    ans = 0
    for i, p in enumerate(P):
        if uf.same(i, p):
            ans += 1
    print(ans)

if __name__ == '__main__':
    main()