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

#define ll long long int
#define LD long double

const int N = 100010;

int inf = 1e9;
int mod = 1e9 + 7;

template <typename T>
class flow_graph {
 public:
  static constexpr T eps = (T) 1e-9;

  struct edge {
    int from;
    int to;
    T c;
    T f;
  };

  vector<vector<int>> g;
  vector<edge> edges;
  int n;
  int st;
  int fin;
  T flow;

  flow_graph(int _n, int _st, int _fin) : n(_n), st(_st), fin(_fin) {
    assert(0 <= st && st < n && 0 <= fin && fin < n && st != fin);
    g.resize(n);
    flow = 0;
  }

  void clear_flow() {
    for (const edge &e : edges) {
      e.f = 0;
    }
    flow = 0;
  }

  int add(int from, int to, T forward_cap, T backward_cap) {
    assert(0 <= from && from < n && 0 <= to && to < n);
    int id = (int) edges.size();
    g[from].push_back(id);
    edges.push_back({from, to, forward_cap, 0});
    g[to].push_back(id + 1);
    edges.push_back({to, from, backward_cap, 0});
    return id;
  }
};

template <typename T>
class dinic {
 public:
  flow_graph<T> &g;

  vector<int> ptr;
  vector<int> d;
  vector<int> q;

  dinic(flow_graph<T> &_g) : g(_g) {
    ptr.resize(g.n);
    d.resize(g.n);
    q.resize(g.n);
  }

  bool expath() {
    fill(d.begin(), d.end(), -1);
    q[0] = g.fin;
    d[g.fin] = 0;
    int beg = 0, end = 1;
    while (beg < end) {
      int i = q[beg++];
      for (int id : g.g[i]) {
        const auto &e = g.edges[id];
        const auto &back = g.edges[id ^ 1];
        if (back.c - back.f > g.eps && d[e.to] == -1) {
          d[e.to] = d[i] + 1;
          if (e.to == g.st) {
            return true;
          }
          q[end++] = e.to;
        }
      }
    }
    return false;
  }

  T dfs(int v, T w) {
    if (v == g.fin) {
      return w;
    }
    int &j = ptr[v];
    while (j >= 0) {
      int id = g.g[v][j];
      const auto &e = g.edges[id];
      if (e.c - e.f > g.eps && d[e.to] == d[v] - 1) {
        T t = dfs(e.to, min(e.c - e.f, w));
        if (t > g.eps) {
          g.edges[id].f += t;
          g.edges[id ^ 1].f -= t;
          return t;
        }
      }
      j--;
    }
    return 0;
  }

  T max_flow() {
    while (expath()) {
      for (int i = 0; i < g.n; i++) {
        ptr[i] = (int) g.g[i].size() - 1;
      }
      T big_add = 0;
      while (true) {
        T add = dfs(g.st, numeric_limits<T>::max());
        if (add <= g.eps) {
          break;
        }
        big_add += add;
      }
      if (big_add <= g.eps) {
        break;
      }
      g.flow += big_add;
    }
    return g.flow;
  }

  vector<bool> min_cut() {
    max_flow();
    vector<bool> ret(g.n);
    for (int i = 0; i < g.n; i++) {
      ret[i] = (d[i] != -1);
    }
    return ret;
  }
};


signed main()
{
    //freopen("IN.txt", "r", stdin);
    //freopen("OUT.txt", "w", stdout);


    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);


    int n; cin >> n;
    int p[n + 1], q[n + 1];
    for(int i = 0; i < n; i++) {
        cin >> p[i];
    }
    for(int i = 0; i < n; i++) {
        cin >> q[i];
    }

    int group = 0;

    int G[n + 1];
    memset(G, -1, sizeof(G));

    for(int i = 0; i < n; i++) {
        if(G[p[i]] != -1) {
            continue;
        }
        int x = p[i];
        bool key = true;
        while(x != p[i] || key) {
            G[x] = group;
            x = p[x];
            key = false;
        }
        group++;
    }

    int F[n + 1];
    memset(F, -1, sizeof(F));

    for(int i = 0; i < n; i++) {
        if(F[q[i]] != -1) {
            continue;
        }
        int x = q[i];
        bool key = true;
        while(x != q[i] || key) {
            F[x] = group;
            x = q[x];
            key = false;
        }
        group++;
    }

    int s = group, t = group + 1; group += 2;

    flow_graph<int> graph(group, s, t);

    int ans = n;

    for(int i = 0; i < n; i++) {
        if(i == p[i] && i == q[i]) {
            ans--;
        }
        else if(i == p[i]) {
            graph.add(F[q[i]], t, 1, 0);
        }
        else if(i == q[i]) {
            graph.add(s, G[p[i]], 1, 0);
        }
        else {
            graph.add(F[q[i]], G[p[i]], 1, 0);
            if(p[i] == q[i]) {
                graph.add(G[p[i]], F[q[i]], 1, 0);
            }
        }
    }

    dinic<int> d(graph);

    ans -= d.max_flow();

    cout << ans << "\n";

    return 0;
}


Measured memory_bytes: 14956