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.*;
public class TestClass {
	
    static PrintWriter out = new PrintWriter(System.out);
    static ArrayList g[];
    static int v[];
    public static void main(String args[] ) throws Exception {

        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());
        String s1[] = in.readLine().split(" ");
        String s2[] = in.readLine().split(" ");
        int a[] = new int[n];
        int b[] = new int[n];
        int c=0,ans=0;
        for(int i=0;i<n;i++)
        {
        	a[i] = Integer.parseInt(s1[i])-1;
        	b[i] = Integer.parseInt(s2[i]);
        	c += b[i];
        }
        if(c%2==0)
        {
        	ans++;
        }
        v = new int[n];
        g = new ArrayList[n];
        for(int i=0;i<n;i++)
        {
        	g[i] = new ArrayList();
        }
        for(int i=0;i<n;i++)
        {
        	g[i].add(a[i]);
        }
        int q=0;
        for(int i=0;i<n;i++)
        {
        	if(v[i]==0)
        	{
        		q++;
        		//System.out.println(i);
        		dfs(i);
        	}
        }
        if(q!=1)
        {
        	ans += q;
        }
        out.println(ans);
        out.close();
   	}
    public static void dfs(int cur)
    {
    	v[cur] = 1;
    	for(int i=0;i<g[cur].size();i++)
    	{
    		int x = (int)g[cur].get(i);
    		if(v[x]==0)
    		{
    			dfs(x);
    		}
    	}
    }
    
}


	

  




