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.util.*;

public class Main {

    private FastScanner scanner = new FastScanner();

    public static void main(String[] args) {
        new Main().solve();
    }

    private void solve() {

        int n = scanner.nextInt();

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

        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
        }

        int cnt[] = new int[2];
        for (int i = 0; i < n; i++) {
            b[i] = scanner.nextInt();
            cnt[b[i]] ++;
        }


        int c = 0;
        for (int i = 0; i < n; i++) {
            if (used[i] != 0) {
                continue;
            }
            used[i] = 1;
            c ++;

            int t = a[i] - 1;
            while (t != i) {
                used[t] = 1;
                t = a[t] - 1;
            }
        }

        if (c == 1) {
            c = 0;
        }

        if (cnt[1] % 2 != 1) {
            c++;
        }
        System.out.print(c);


    }



    int diff(int a, int b) {
        StringBuilder sa = new StringBuilder(String.valueOf(a));
        for (int i = 0; i < 3 - sa.length() + 1; i++) {
            sa.insert(0, '0');
        }

        StringBuilder sb = new StringBuilder(String.valueOf(b));
        for (int i = 0; i < 3 - sb.length() + 1; i++) {
            sb.insert(0, '0');
        }
        int ans = 0;

        for (int i = 0; i < 3; i++) {
            if (sa.charAt(i) != sb.charAt(i) ) {
                ans ++;
            }
        }
        return ans;
    }


    public static final <T> void swap(T[] a, int i, int j) {
        T t = a[i];
        a[i] = a[j];
        a[j] = t;
    }

    class Pair implements Comparable<Pair> {
        int a, i;

        public Pair(int a, int i) {
            this.a = a;
            this.i = i;
        }

        @Override
        public int compareTo(Pair o) {
            return this.a - o.a;
        }
    }

    long gcd(long a, long b) {
        if (b != 0) {
            return gcd(b, a % b);
        }
        return a;
    }

    long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    class FastScanner {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public FastScanner() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}