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 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 all_group_members(self):
        return {r: self.members(r) for r in self.roots()}
      
n,m = map(int,input().split())
P = list(map(int,input().split()))

uf = UnionFind(n)

for i in range(m):
  a,b = map(int,input().split())
  uf.union(a-1,b-1)
values = uf.all_group_members().values()

ans = 0
for vs in values:
  s = set(P[v]-1 for v in vs)
  ans += len(s & (set(vs)))

print(ans)  

Fixed submission:
## TLE
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 same(self, x, y):
        return self.find(x) == self.find(y)
      
n,m = map(int,input().split())
P = list(map(int,input().split()))

uf = UnionFind(n)

for i in range(m):
  a,b = map(int,input().split())
  uf.union(a-1,b-1)

ans = 0  
for i in range(n):
  if uf.same(P[i]-1,i):
    ans += 1

print(ans)

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 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 all_group_members(self):
        return {r: self.members(r) for r in self.roots()}
      
n,m = map(int,input().split())
P = list(map(int,input().split()))

uf = UnionFind(n)

for i in range(m):
  a,b = map(int,input().split())
  uf.union(a-1,b-1)
values = uf.all_group_members().values()

ans = 0
for vs in values:
  s = set(P[v]-1 for v in vs)
  ans += len(s & (set(vs)))

print(ans)  

Fixed submission:
## TLE
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 same(self, x, y):
        return self.find(x) == self.find(y)
      
n,m = map(int,input().split())
P = list(map(int,input().split()))

uf = UnionFind(n)

for i in range(m):
  a,b = map(int,input().split())
  uf.union(a-1,b-1)

ans = 0  
for i in range(n):
  if uf.same(P[i]-1,i):
    ans += 1

print(ans)