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 = [x-1 for x in list(map(int, input().split()))]
key = dict()
for k,v in enumerate(p):
  key[v] = k
Union = UnionFind(n)
xy = [list(map(int, input().split())) for i in range(m)]
for x,y in xy:
  Union.union(x-1,y-1)
a = Union.all_group_members()
ans = 0
for i in a.values():
  x = set()
  for j in i:
    x.add(key[j])
  y = set(i)
  ans += len(x & y)
print(ans)


Fixed submission:
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
      
      
n,m = map(int, input().split())
p = [x-1 for x in list(map(int, input().split()))]
key = dict()
for k,v in enumerate(p):
  key[v] = k
Union = UnionFind(n)
xy = [list(map(int, input().split())) for i in range(m)]
for x,y in xy:
  Union.union(x-1,y-1)
a = Union.all_group_members()
ans = 0
for i in a:
  x = set()
  for j in i:
    x.add(key[j])
  y = set(i)
  ans += len(x & y)
print(ans)

Buggy python submission (verdict: Runtime Error):
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 = [x-1 for x in list(map(int, input().split()))]
key = dict()
for k,v in enumerate(p):
  key[v] = k
Union = UnionFind(n)
xy = [list(map(int, input().split())) for i in range(m)]
for x,y in range(xy):
  Union.union(x-1,y-1)
a = Union.all_group_members()
ans = 0
for i in a.values():
  x = set()
  for j in i:
    x.add(key[j])
  y = set(i)
  ans += len(x & y)
print(ans)

Fixed submission:
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
      
      
n,m = map(int, input().split())
p = [x-1 for x in list(map(int, input().split()))]
key = dict()
for k,v in enumerate(p):
  key[v] = k
Union = UnionFind(n)
xy = [list(map(int, input().split())) for i in range(m)]
for x,y in xy:
  Union.union(x-1,y-1)
a = Union.all_group_members()
ans = 0
for i in a:
  x = set()
  for j in i:
    x.add(key[j])
  y = set(i)
  ans += len(x & y)
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()}

      
n,m = map(int, input().split())
p = [x-1 for x in list(map(int, input().split()))]
key = dict()
for k,v in enumerate(p):
  key[v] = k
Union = UnionFind(n)
for i in range(m):
  x,y = map(int, input().split())
  Union.union(x-1,y-1)
a = Union.all_group_members()
ans = 0
for i in a.values():
  x = set()
  for j in i:
    x.add(key[j])
  y = set(i)
  ans += len(x & y)
print(ans)

Fixed submission:
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
      
      
n,m = map(int, input().split())
p = [x-1 for x in list(map(int, input().split()))]
key = dict()
for k,v in enumerate(p):
  key[v] = k
Union = UnionFind(n)
xy = [list(map(int, input().split())) for i in range(m)]
for x,y in xy:
  Union.union(x-1,y-1)
a = Union.all_group_members()
ans = 0
for i in a:
  x = set()
  for j in i:
    x.add(key[j])
  y = set(i)
  ans += len(x & y)
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()}

      
n,m = map(int, input().split())
p = [x-1 for x in list(map(int, input().split()))]
key = dict()
for k,v in enumerate(p):
  key[v] = k
Union = UnionFind(n)
for i in range(m):
  x,y = map(int, input().split())
  Union.union(x-1,y-1)
a = Union.all_group_members()
ans = 0
for i in a.values():
  x = set()
  for j in i:
    x.add(key[j])
  y = set(i)
  ans += len(x & y)
print(ans)

Fixed submission:
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
      
      
n,m = map(int, input().split())
p = [x-1 for x in list(map(int, input().split()))]
key = dict()
for k,v in enumerate(p):
  key[v] = k
Union = UnionFind(n)
xy = [list(map(int, input().split())) for i in range(m)]
for x,y in xy:
  Union.union(x-1,y-1)
a = Union.all_group_members()
ans = 0
for i in a:
  x = set()
  for j in i:
    x.add(key[j])
  y = set(i)
  ans += len(x & y)
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()}

      
n,m = map(int, input().split())
p = [x-1 for x in list(map(int, input().split()))]
key = dict()
for k,v in enumerate(p):
  key[v] = k
Union = UnionFind(n)
for i in range(m):
  x,y = map(int, input().split())
  Union.union(x-1,y-1)
a = Union.all_group_members()
ans = 0
for i in a.values():
  x = set()
  for j in i:
    x.add(key[j])
  y = set(i)
  ans += len(x & y)
print(ans)

Fixed submission:
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
      
      
n,m = map(int, input().split())
p = [x-1 for x in list(map(int, input().split()))]
key = dict()
for k,v in enumerate(p):
  key[v] = k
Union = UnionFind(n)
xy = [list(map(int, input().split())) for i in range(m)]
for x,y in xy:
  Union.union(x-1,y-1)
a = Union.all_group_members()
ans = 0
for i in a:
  x = set()
  for j in i:
    x.add(key[j])
  y = set(i)
  ans += len(x & y)
print(ans)