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.*;
import java.util.*;
import java.math.*;

public class Main32 {
	public static boolean flags[];
	public static int arr[], result;
	public static void main(String[] args) throws IOException
	{
		BufferedReader in;
		File file = new File("in");
		StringBuilder out = new StringBuilder("");
		if (file.exists()) {
			in = new BufferedReader(new FileReader(file));
		} else {
			in = new BufferedReader(new InputStreamReader(System.in));
		}
		String lines[];
		result = 0;
		int n = Integer.parseInt(in.readLine());
		arr = readInts(in.readLine());
		int arr2[] = readInts(in.readLine());
		flags  = new boolean[n+1];
		int sum = 0;
		for( int i = 1; i <= n; i++ )
		{
			if ( arr2[i-1] == 1 )
				sum++;
			if ( !flags[i] )
			{
				f(i);
			}
		}
		if ( result == 1) result--;
		if ( sum % 2 == 0) result++;
		System.out.println(result);
	}
	
	
	public static void f(int i)
	{
		if ( flags[i] ) 
		{
			result += 1;
			return;
		}
		flags[i] = true;
		f(arr[i-1]);
	}
	public static int[] readInts(String line)
	{
		String lines[] = line.split("\\s+");
		int result[] = new int[lines.length];
		for( int i = 0; i < lines.length ; i++ )
		{
			result[i] = Integer.parseInt(lines[i]);
		}
		return result;
	}
}
