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.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class P760C {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < arr.length; i++) {
			arr[i] = scan.nextInt()-1;
		}
		int total = 0;
		for (int i = 0; i < arr.length; i++) {
			if (scan.nextInt() == 1)
				total++;
		}
		int min = 0;
		if (total % 2 == 0)
			min++;
		int groups = 0;
		boolean[] vis = new boolean[n];
		for (int i = 0; i < arr.length; i++) {
			if (vis[i])
				continue;
			groups++;
			Queue<Integer> q = new LinkedList<>();
			q.add(i);
			while (!q.isEmpty())
			{
				int x = q.poll();
				vis[x] = true;
				if (!vis[arr[x]])
					q.add(arr[x]);
			}
		}
		if (groups > 1)
			min += groups;
		System.out.println(min);
	}
}
