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()}

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


n,m = map(int,input().split())
pl = list(map(int,input().split()))
uf = UnionFind(n)
for _ in range(m):
   x,y = map(int,input().split())
   uf.union(x-1,y-1)
ans = 0
for member in uf.all_group_members().values():
   a = [pl[i]-1 for i in member]
   ans += len(set(a) & set(member))

print(ans)

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 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())


n,m = map(int,input().split())
pl = list(map(int,input().split()))
uf = UnionFind(n)
for _ in range(m):
   x,y = map(int,input().split())
   uf.union(x-1,y-1)
ans = 0
for idx,p in enumerate(pl):
   ans += uf.same(p-1,idx)
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 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())


n,m = map(int,input().split())
pl = list(map(int,input().split()))
uf = UnionFind(n)
for _ in range(m):
   x,y = map(int,input().split())
   uf.union(x-1,y-1)
ans = 0
for member in uf.all_group_members().values():
   a = [pl[i]-1 for i in member]
   ans += len(set(a) & set(member))

print(ans)

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 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())


n,m = map(int,input().split())
pl = list(map(int,input().split()))
uf = UnionFind(n)
for _ in range(m):
   x,y = map(int,input().split())
   uf.union(x-1,y-1)
ans = 0
for idx,p in enumerate(pl):
   ans += uf.same(p-1,idx)
print(ans)