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.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.BitSet;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        Scanner in = new Main().new Scanner(inputStream);
        Main solver = new Main();
        solver.runn(in);
    }

    long MOD = 1000000007L;

    public void runn(Scanner in) {
        int n = in.ni();
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = in.ni() - 1;
        BitSet vst = new BitSet(n);
        int count = 0;
        for (int i = 0; i < n; i++) {
            if (!vst.get(i)) {
                int j = i;
                while (!vst.get(j)) {
                    vst.set(j);
                    j = arr[j];
                }
                count++;
            }
        }
        if (count == 1)
            count = 0;
        int c = 0;
        for (int i = 0; i < n; i++)
            if (in.ni() == 1)
                c++;
        if (c % 2 == 0)
            count++;
        System.out.println(count);
    }

    class Scanner {
        BufferedReader br;
        StringTokenizer in;

        public Scanner(InputStream inputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
        }

        public String next() {
            return hasMoreTokens() ? in.nextToken() : null;
        }

        public String rl() {
            try {
                return br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
                return null;
            }
        }

        boolean hasMoreTokens() {
            while (in == null || !in.hasMoreTokens()) {
                String s = rl();
                if (s == null)
                    return false;
                in = new StringTokenizer(s);
            }
            return true;
        }

        public String nextString() {
            return next();
        }

        public int ni() {
            return Integer.parseInt(nextString());
        }

        public double nd() {
            return Double.parseDouble(nextString());
        }

        public long nl() {
            return Long.parseLong(nextString());
        }

        public int[] nia(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public long[] nla(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

    }

    int stoi(String a) {
        return Integer.parseInt(a);
    }

    void debug(int[] arr) {
        System.out.println(Arrays.toString(arr));
    }

    void debug(long[] arr) {
        System.out.println(Arrays.toString(arr));
    }

    void debug(int[][] arr) {
        for (int i = 0; i < arr.length; i++) {
            for (int j = 0; j < arr[i].length; j++)
                System.out.print(arr[i][j] + "\t");
            System.out.println();
        }
    }

    class Pair implements Comparable<Pair> {
        int a;
        int b;

        public Pair(int x, int y) {
            a = x;
            b = y;
        }

        public int compareTo(Pair other) {
            if (a == other.a)
                return Integer.compare(b, other.b);
            else
                return Integer.compare(a, other.a);
        }

        public int hashCode() {
            return a * 100007 + b;
        }

        public boolean equals(Object other) {
            Pair o = (Pair) other;
            return a == o.a && b == o.b;
        }
    }
}
