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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] p = new int[n];
        for (int i=0; i<n; i++)
            p[i] = in.nextInt()-1;
        boolean[] b = new boolean[n];
        for (int i=0; i<n; i++) {
            b[i] = in.nextInt() == 1;
        }
        Set<Integer> nums = new HashSet<>();

        u = new int[n];
        for (int i=0; i<n; i++)
            u[i] = i;
        for (int i=0; i<n; i++) {
            int x = root(p[i]);
            u[i] = x;
        }
        for (int i=0; i<n; i++) {
            u[i] = root(i);
            nums.add(u[i]);
        }
        int tot = nums.size();
        int ans = tot == 1 ? 0 : tot;

        int sum = 0;
        for (int i=0; i<n; i++) if (b[i])
            sum++;
        if (sum%2 == 0)
            ans++;

        System.out.println(ans);
    }


    //union
    static int[] u;
    //u[root(i)] = j;
    private static int root (int i) {
        return u[i] == i ? i : (u[i] = root(u[i]));
    }


}
