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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Locale;
import java.util.StringTokenizer;

public class C implements Runnable {

    private void solve() throws Exception {
        int n = nextInt();
        int[] p = new int[n];
        for (int i = 0; i < n; i++) {
            p[i] = nextInt() - 1;
        }
        int sum = 0;
        for (int i = 0; i < n; i++) {
            sum += nextInt();
        }
        boolean[] was = new boolean[n];
        Arrays.fill(was, false);
        int ans = 0;
        for (int i = 0; i < n; i++) {
            if (!was[i]) {
                ans++;
                int current = i;
                do {
                    was[current] = true;
                    current = p[current];
                } while (current != i);
            }
        }
        if (ans == 1) {
            ans = 0;
        }
        ans += 1 - (sum % 2);
        out.println(ans);
    }

    private BufferedReader in;
    private StringTokenizer tokenizer = new StringTokenizer("");
    private PrintWriter out;

    private String nextToken() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(in.readLine());
        }
        return tokenizer.nextToken();
    }

    private int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    private long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    @Override
    public void run() {
        Locale.setDefault(Locale.US);
        this.in = new BufferedReader(new InputStreamReader(System.in));
        this.out = new PrintWriter(System.out);
        try {
//            int t = nextInt();
//            for (int c = 0; c < t; c++) {
                solve();
//                out.println();
//            }
        } catch (Exception e) {
            e.printStackTrace();
        } finally {
            out.close();
        }
    }

    public static void main(String[] args) {
        new Thread(new C()).start();
    }

}