Pavel cooks barbecue. There are n skewers, they lay on a brazier in a row, each on one of n positions. Pavel wants each skewer to be cooked some time in every of n positions in two directions: in the one it was directed originally and in the reversed direction.

Pavel has a plan: a permutation p and a sequence b1, b2, ..., bn, consisting of zeros and ones. Each second Pavel move skewer on position i to position pi, and if bi equals 1 then he reverses it. So he hope that every skewer will visit every position in both directions.

Unfortunately, not every pair of permutation p and sequence b suits Pavel. What is the minimum total number of elements in the given permutation p and the given sequence b he needs to change so that every skewer will visit each of 2n placements? Note that after changing the permutation should remain a permutation as well.

There is no problem for Pavel, if some skewer visits some of the placements several times before he ends to cook. In other words, a permutation p and a sequence b suit him if there is an integer k (k ≥ 2n), so that after k seconds each skewer visits each of the 2n placements.

It can be shown that some suitable pair of permutation p and sequence b exists for any n.

Input

The first line contain the integer n (1 ≤ n ≤ 2·105) — the number of skewers.

The second line contains a sequence of integers p1, p2, ..., pn (1 ≤ pi ≤ n) — the permutation, according to which Pavel wants to move the skewers.

The third line contains a sequence b1, b2, ..., bn consisting of zeros and ones, according to which Pavel wants to reverse the skewers.

Output

Print single integer — the minimum total number of elements in the given permutation p and the given sequence b he needs to change so that every skewer will visit each of 2n placements.

Examples

Input

4
4 3 2 1
0 1 1 1


Output

2


Input

3
2 3 1
0 0 0


Output

1

Note

In the first example Pavel can change the permutation to 4, 3, 1, 2.

In the second example Pavel can change any element of b to 1.
import java.util.*;
import java.math.*;
import java.io.*;
import java.text.*;

public class A {
    static class Node{
        int x;
        int id;

        public Node(int x,int id){
            this.x=x;
            this.id=id;

        }
    }
    //public static PrintWriter pw;
    public static PrintWriter pw = new PrintWriter(System.out);

    public static void solve() throws IOException {
//	pw=new PrintWriter(new FileWriter("C:\\Users\\shree\\Downloads\\small_output_in"));
        FastReader sc = new FastReader();
        int n=sc.I();
        graph=new Vector[n+1];
        for(int i=1;i<=n;i++) graph[i]=new Vector<>();
        for(int i=1;i<=n;i++){
            int x=sc.I();
            graph[i].add(x);

        }
        vis=new boolean [n+1];
        for(int i=1;i<=n;i++){
            if(!vis[i]){
                cc++;
                dfs(i);
            }
        }
        int b[]=new int[n+1];
        int sum=0;
        for(int i=1;i<=n;i++){
            b[i]=sc.I();
            sum+=b[i];
        }
        int ans=cc;
        if(cc==1) ans--;
        if(sum%2==0) ans++;
        pw.println(ans);
        pw.close();


    }
    static int cc=0;
    static Vector<Integer> graph[];
    static boolean vis[];
    static void dfs(int v){
        vis[v]=true;
        for(int u : graph[v]){
            if(!vis[u]) dfs(u);
        }
    }

    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                try {

                    solve();
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
        }, "1", 1 << 26).start();

    }

    static BufferedReader br;
    static long M = (long) 1e9 + 7;

    static class FastReader {

        StringTokenizer st;

        public FastReader() throws FileNotFoundException {
            //br=new BufferedReader(new FileReader("C:\\Users\\shree\\Downloads\\B-small-practice.in"));
            br = new BufferedReader(new InputStreamReader(System.in));

        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int I() {
            return Integer.parseInt(next());
        }

        long L() {
            return Long.parseLong(next());
        }

        double D() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public boolean hasNext() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                String s = br.readLine();
                if (s == null) {
                    return false;
                }
                st = new StringTokenizer(s);
            }
            return true;
        }

    }
}