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.io.*;

public class C {
    BufferedReader br;
    PrintWriter out;
    StringTokenizer stok;

    String nextToken() throws IOException {
        while (stok == null || !stok.hasMoreTokens()) {
            String s = br.readLine();
            if (s == null) {
                return null;
            }
            stok = new StringTokenizer(s);
        }
        return stok.nextToken();
    }

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

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

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    char nextChar() throws IOException {
        return (char) (br.read());
    }

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

    boolean[] used;
    int[] a;
    int cycle;
    void dfs(int v) {
        cycle++;
        used[v] = true;
        if (!used[a[v]]) {
            dfs(a[v]);
        }
    }

    private void solve() throws IOException {
        int n = nextInt();
        a = new int[n];
        int[] b = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt() - 1;
        }
        for (int i = 0; i < n; i++) {
            b[i] = nextInt();
        }
        used = new boolean[n];
        int ans = -1;
        for (int i = 0; i < n; i++) {
            if (!used[i]) {
                cycle = 0;
                dfs(i);
                ans++;
            }
        }
        if (ans > 0) ans++;
        boolean p0 = false, p1 = false;
        int k = 0;
        for (int i = 0; i < n; i++) {
//            if (b[i] == 0) p0 = true;
//            if (b[i] == 1) p1 = true;
            k += b[i];
        }
//        if ((p0 && !p1) || (!p0 && p1)) {
        if (k % 2 == 0){
            ans++;
        }
        out.println(ans);
    }

    void run() throws IOException {
        // br = new BufferedReader(new FileReader("input.txt"));
        // out = new PrintWriter("output.txt");
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        br.close();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        // Locale.setDefault(Locale.US);
        new C().run();
    }
}