// includes
#include <bits/stdc++.h>
using namespace std;

// macros
#define pb emplace_back
#define mk make_pair
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define bit(n) (1LL<<(n))
// functions
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
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> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
//  types
using ll = long long int;
using P = pair<int, int>;
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1000000007;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
// io
struct fast_io{
  fast_io(){ios_base::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20);}
} fast_io_;

template <typename T>
struct edge {int to; T cap; int rev;};

template <typename T>
struct Graph{
  int n;
  vector<vector<edge<T>>> vec;
  vector<int> level;
  vector<int> iter;
  Graph(int n): n(n){
    vec.resize(n);
    level.resize(n);
    iter.resize(n);
  }
  void adde(int at, int to, T cap){
    vec[at].push_back((edge<T>){to, cap, (int)vec[to].size()});
    vec[to].push_back((edge<T>){at, 0, (int)vec[at].size() - 1});
  }
  void bfs(int s){
    fill(level.begin(), level.end(), -1);
    level[s] = 0;
    queue<int> q;
    q.push(s);
    while(!q.empty()){
      auto p = q.front(); q.pop();
      for(auto e: vec[p]){
        if(level[e.to] < 0 && e.cap > 0){
          level[e.to] = level[p] + 1;
          q.push(e.to);
        }
      }
    }
  }
  T dfs(int v, int t, T f){
    if(v == t)return f;
    int st = iter[v];
    for(int i = st; i < vec[v].size(); i++){
      iter[v] = i;
      auto& e = vec[v][i];
      if(level[v] < level[e.to] && e.cap > 0){
        auto d = dfs(e.to, t, min(f, e.cap));
        if(d > 0){
          e.cap -= d;
          vec[e.to][e.rev].cap += d;
          return d;
        }
      }
    }
    return 0;
  }
  T max_flow(int s, int t){
    T flow = 0;
    while(true){
      bfs(s);
      if(level[t] < 0)return flow;
      fill(iter.begin(), iter.end(), 0);
      T inf = numeric_limits<T>::max();
      T f = dfs(s, t, inf);
      while(f > 0){
        flow += f;
        f = dfs(s, t, inf);
      }
    }
  }
  T min_cut(int s, int t){
    return max_flow(s, t);
  }
};

using GraphI = Graph<int>;
using GraphL = Graph<long long>;

int main(int argc, char const* argv[])
{
  int n;
  cin >> n;
  vector<int> p(n), q(n);
  cin >> p >> q;

  vector<int> pi(n, -1), qi(n, -1);
  int l = 0, r = 0;
  rep(i, n){
    if(pi[i] != -1)continue;
    int curr = i;
    do{
      pi[curr] = l;
      curr = p[curr];
    }while(curr != i);
    l++;
  }
  rep(i, n){
    if(qi[i] != -1)continue;
    int curr = i;
    do{
      qi[curr] = r;
      curr = q[curr];
    }while(curr != i);
    r++;
  }
  GraphI g(2 + l + r);
  int ans = n;
  rep(i, n){
    if(p[i] == i && q[i] == i)ans--;
    else if(p[i] == i){
      g.adde(1 + l + qi[i], 1 + l + r, 1);
    }else if(q[i] == i){
      g.adde(0, 1 + pi[i], 1);
    }else{
      g.adde(1 + l + qi[i], 1 + pi[i], 1);
      if(p[i] == q[i]){
        g.adde(1 + pi[i], 1 + l + qi[i], 1);
      }
    }
  }
  cout << ans - g.min_cut(0, 1 + l + r) << endl;
  return 0;
}


Measured memory_bytes: 11776