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.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {

        new Main().solve();
    }

    int inf = 1000000000;
    int mod = 1000000007;
    double eps = 0.0000000001;

    PrintWriter out;

    int n;
    int m;

    void solve() throws IOException {

        Reader in;
        BufferedReader br;

        try {

            br = new BufferedReader( new FileReader("input.txt") );
            in = new Reader("input.txt");
            out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
        }
        catch (Exception e) {

            br = new BufferedReader( new InputStreamReader( System.in ) );
            in = new Reader();
            out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
        }


        int n = in.nextInt();

        int[] a = new int[n];
        int[] b = new int[n];

        for (int i = 0; i < n; i++)
            a[i] = in.nextInt()-1;

        int c = 0;

        for (int i = 0; i < n; i++) {
            b[i] = in.nextInt();
            if (b[i] == 1)
                c++;
        }

        boolean[] used = new boolean[n];

        int cyc = 0;

        for (int i = 0; i < n; i++) {

            if (used[i])
                continue;

            cyc++;
            int v = i;
            while (!used[v]) {
                used[v] = true;
                v = a[v];
            }
        }

        if (cyc == 1)
            cyc = 0;

        int ans = cyc;
        if (c%2 == 0)
            ans++;

        out.println(ans);
        out.flush();
        out.close();
    }

    long sum(int l, int r) {

        l--;

        if (l > r)
            return 0;

        long s1 = 1l*r*(r+1)/2;
        long s2 = 1l*l*(l+1)/2;

        return s1-s2;
    }

    class Pair implements Comparable<Pair>{

        int a;
        int b;

        Pair(int a, int b) {

            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair p) {

            return 0;
        }
    }

    class Item {

        int a;
        int b;
        int c;

        Item(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

    }

    class Reader {

        BufferedReader  br;
        StringTokenizer tok;

        Reader(String file) throws IOException {
            br = new BufferedReader( new FileReader(file) );
        }

        Reader() throws IOException {
            br = new BufferedReader( new InputStreamReader(System.in) );
        }

        String next() throws IOException {

            while (tok == null || !tok.hasMoreElements())
                tok = new StringTokenizer(br.readLine());
            return tok.nextToken();
        }

        int nextInt() throws NumberFormatException, IOException {
            return Integer.valueOf(next());
        }

        long nextLong() throws NumberFormatException, IOException {
            return Long.valueOf(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.valueOf(next());
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

    }

}