#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 998244353;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};

template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}

class Stack {
private:
  const int N, H;
  vector< int > node;

public:
  Stack(const int N, const int H) : N(N), H(H), node(N + H) { clear(); }

  inline bool empty(const int h) const { return node[N + h] == N + h; }

  inline int top(const int h) const { return node[N + h]; }

  inline void pop(const int h) { node[N + h] = node[node[N + h]]; }

  inline void push(const int h, const int u) { node[u] = node[N + h], node[N + h] = u; }

  inline void clear() { iota(node.begin() + N, node.end(), N); }
};

class List {
public:
  struct node {
    int prev, next;
  };
  const int N, H;
  vector< node > dat;

  List(const int N, const int H) : N(N), H(H), dat(N + H) { clear(); }

  inline bool empty(const int h) const { return (dat[N + h].next == N + h); }

  inline bool more_one(const int h) const { return dat[N + h].prev != dat[N + h].next; }

  inline void insert(const int h, const int u) {
    dat[u].prev = dat[N + h].prev, dat[u].next = N + h;
    dat[dat[N + h].prev].next = u, dat[N + h].prev = u;
  }

  inline void erase(const int u) {
    dat[dat[u].prev].next = dat[u].next, dat[dat[u].next].prev = dat[u].prev;
  }

  inline void clear() {
    for(int i = N; i < N + H; ++i) dat[i].prev = dat[i].next = i;
  }
};

template< typename flow_t >
struct PushRelabel {
  struct edge {
    int to;
    flow_t cap;
    int rev;
    bool isrev;
    int idx;
  };

  vector< vector< edge > > graph;
  vector< int > potential, cur_edge;
  vector< flow_t > excess;
  int V, height, checker;
  List all_ver;
  Stack act_ver;

  PushRelabel(int V)
      : V(V), height(-1), checker(0), excess(V, flow_t(0)), potential(V, 0), cur_edge(V), all_ver(V, V), act_ver(V, V), graph(V) {}

  void add_edge(int from, int to, flow_t cap, int idx = -1) {
    graph[from].emplace_back((edge) {to, cap, (int) graph[to].size(), false, idx});
    graph[to].emplace_back((edge) {from, 0, (int) graph[from].size() - 1, true, idx});
  }

  int calc_active(int t) {
    height = -1;
    for(int i = 0; i < V; i++) {
      if(potential[i] < V) {
        cur_edge[i] = 0;
        height = max(height, potential[i]);
        all_ver.insert(potential[i], i);
        if(excess[i] > 0 && i != t)
          act_ver.push(potential[i], i);
      } else {
        potential[i] = V + 1;
      }
    }
    return height;
  }

  void bfs(int t) {
    for(int i = 0; i < V; i++) {
      potential[i] = max(potential[i], V);
    }
    potential[t] = 0;
    queue< int > que;
    que.emplace(t);
    while(!que.empty()) {
      int p = que.front();
      que.pop();
      for(auto &e : graph[p]) {
        if(potential[e.to] == V && graph[e.to][e.rev].cap > 0) {
          potential[e.to] = potential[p] + 1;
          que.emplace(e.to);
        }
      }
    }
  }

  int init(int s, int t) {
    potential[s] = V + 1;
    bfs(t);
    for(auto &e : graph[s]) {
      if(potential[e.to] < V) {
        graph[e.to][e.rev].cap = e.cap;
        excess[s] -= e.cap;
        excess[e.to] += e.cap;
      }
      e.cap = 0;
    }
    return calc_active(t);
  }

  bool push(int u, int t, edge &e) {
    flow_t f = min(e.cap, excess[u]);
    int v = e.to;
    e.cap -= f, excess[u] -= f;
    graph[v][e.rev].cap += f, excess[v] += f;
    if(excess[v] == f && v != t)
      act_ver.push(potential[v], v);
    return excess[u] == 0;
  }

  int discharge(int u, int t) {
    for(int &i = cur_edge[u]; i < graph[u].size(); i++) {
      auto &e = graph[u][i];
      if(potential[u] == potential[e.to] + 1 && e.cap > 0) {
        if(push(u, t, e))
          return potential[u];
      }
    }
    return relabel(u);
  }

  int global_relabel(int t) {
    bfs(t);
    all_ver.clear(), act_ver.clear();
    return calc_active(t);
  }

  void gap_relabel(const int u) {
    for(int i = potential[u]; i <= height; ++i) {
      for(int id = all_ver.dat[V + i].next; id < V; id = all_ver.dat[id].next) {
        potential[id] = V + 1;
      }
      all_ver.dat[V + i].prev = all_ver.dat[V + i].next = V + i;
    }
  }

  int relabel(const int u) {
    ++checker;
    int prv = potential[u], cur = V;
    for(int i = 0; i < (int) graph[u].size(); ++i) {
      const edge &e = graph[u][i];
      if(cur > potential[e.to] + 1 && e.cap > 0) {
        cur_edge[u] = i;
        cur = potential[e.to] + 1;
      }
    }
    if(all_ver.more_one(prv)) {
      all_ver.erase(u);
      if((potential[u] = cur) == V)
        return potential[u] = V + 1, prv;
      act_ver.push(cur, u);
      all_ver.insert(cur, u);
      height = max(height, cur);
    } else {
      gap_relabel(u);
      return height = prv - 1;
    }
    return cur;
  }

  flow_t max_flow(int s, int t) {
    int level = init(s, t);
    while(level >= 0) {
      if(act_ver.empty(level)) {
        --level;
        continue;
      }
      int u = act_ver.top(level);
      act_ver.pop(level);
      level = discharge(u, t);
      if(checker * 2 >= V) {
        level = global_relabel(t);
        checker = 0;
      }
    }
    return excess[t];
  }
};

struct UnionFind {
  vector< int > data;

  UnionFind(int sz) {
    data.assign(sz, -1);
  }

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if(x == y) return (false);
    if(data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }

  int find(int k) {
    if(data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }

  int size(int k) {
    return (-data[find(k)]);
  }
};

int main() {
  int N;
  cin >> N;
  vector< int > P(N), Q(N);
  cin >> P >> Q;
  UnionFind uf1(N), uf2(N);
  for(int i = 0; i < N; i++) uf1.unite(P[i], i);
  for(int i = 0; i < N; i++) uf2.unite(Q[i], i);


  int dame = 0;
  unordered_map< int, int > mp[400002];
  PushRelabel< int > flow(N + N + 2);
  int S = N + N, T = N + N + 1;
  for(int i = 0; i < N; i++) {
    if(i == P[i] && P[i] == Q[i]) {
      ++dame;
    } else if(i == P[i]) {
      mp[S][uf2.find(Q[i]) + N] += 1;
    } else if(i == Q[i]) {
      mp[uf1.find(P[i])][T] += 1;
    } else if(P[i] != Q[i]) {
      mp[uf1.find(P[i])][uf2.find(Q[i]) + N] += 1;
    } else {
      mp[uf1.find(P[i])][uf2.find(Q[i]) + N] += 1;
      mp[uf2.find(Q[i]) + N][uf1.find(P[i])] += 1;
    }
  }
  for(int i = 0; i < T; i++) {
    for(auto &p : mp[i]) flow.add_edge(i, p.first, p.second);
  }
  cout << N - (flow.max_flow(S, T) + dame) << endl;
}


Measured memory_bytes: 47872