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 static java.util.Arrays.stream;

public class ProblemC4 {
    BufferedReader rd;

    ProblemC4() throws IOException {
        rd = new BufferedReader(new InputStreamReader(System.in));
        compute();
    }

    private void compute() throws IOException {
        rd.readLine();
        int[] p = intarr();
        int[] b = intarr();
        out(solve(p, b));
    }

    private int solve(int[] p, int[] b) {
        if(p.length == 1) {
            return 1-b[0];
        }
        int pc = 0;
        int n = p.length;
        for(int i=0;i<n;i++) {
            p[i]--;
        }
        boolean[] v = new boolean[n];
        for(int i=0;i<n;i++) {
            if(!v[i]) {
                pc++;
                int j = i;
                v[i] = true;
                while(!v[p[j]]) {
                    v[p[j]] = true;
                    j = p[j];
                }
            }
        }
        int sum = stream(b).sum();
        int res;
        if(pc == 1) {
            res = 0;
        } else {
            res = pc;
        }
        return res + (1 - (sum%2));
    }

    private int[] intarr() throws IOException {
        return intarr(rd.readLine());
    }

    private int[] intarr(String s) {
        String[] q = split(s);
        int n = q.length;
        int[] a = new int[n];
        for(int i=0;i<n;i++) {
            a[i] = Integer.parseInt(q[i]);
        }
        return a;
    }

    private String[] split(String s) {
        if(s == null) {
            return new String[0];
        }
        int n = s.length();
        int start = -1;
        int end = 0;
        int sp = 0;
        boolean lastWhitespace = true;
        for(int i=0;i<n;i++) {
            char c = s.charAt(i);
            if(isWhitespace(c)) {
                lastWhitespace = true;
            } else {
                if(lastWhitespace) {
                    sp++;
                }
                if(start == -1) {
                    start = i;
                }
                end = i;
                lastWhitespace = false;
            }
        }
        if(start == -1) {
            return new String[0];
        }
        String[] res = new String[sp];
        int last = start;
        int x = 0;
        lastWhitespace = true;
        for(int i=start;i<=end;i++) {
            char c = s.charAt(i);
            boolean w = isWhitespace(c);
            if(w && !lastWhitespace) {
                res[x++] = s.substring(last,i);
            } else if(!w && lastWhitespace) {
                last = i;
            }
            lastWhitespace = w;
        }
        res[x] = s.substring(last,end+1);
        return res;
    }

    private boolean isWhitespace(char c) {
        return c==' ' || c=='\t';
    }

    private static void out(Object x) {
        System.out.println(x);
    }

    public static void main(String[] args) throws IOException {
        new ProblemC4();
    }
}
