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 java.io.PrintWriter;
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Map.Entry;
import java.util.Arrays;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;
public class C {
	public static void main(String[] args)throws Throwable {
		MyScanner sc=new MyScanner();
		PrintWriter pw=new PrintWriter(System.out,true);
		
		int n=sc.nextInt();
		int [] a=new int [n];
		int [] b=new int [n];
		for(int i=0;i<n;i++)
			a[i]=sc.nextInt();
		int c=0;
		for(int i=0;i<n;i++){
			b[i]=sc.nextInt();
			if(b[i]==1)
				c++;
		}
		int ans=0;
		if(c%2==0)
			ans++;
		V=n;
		adjList=new ArrayList[n];
		dfs_low=new int [V];
		dfs_num=new int [V];
		stack=new Stack<Integer>();
		inSCC=new boolean[V];
		
		for(int i=0;i<n;i++){
			adjList[i]=new ArrayList<Integer>();
			adjList[i].add(a[i]-1);
		}
		tarjanSCC();
		if(SCC>1)
			ans+=SCC;
		pw.println(ans);
		pw.flush();
		pw.close();
	}
	
	static ArrayList<Integer>[] adjList;
	static int V, counter, SCC, dfs_num[], dfs_low[];
	static boolean[] inSCC;
	static Stack<Integer> stack;
		
	
	static void tarjanSCC()
	{
		for(int i = 0; i < V; ++i)
			if(dfs_num[i] == 0)
				tarjanSCC(i);
	}
	
	static void tarjanSCC(int u)
	{
		dfs_num[u] = dfs_low[u] = ++counter;
		stack.push(u);
		
		for(int v: adjList[u])
		{
			if(dfs_num[v] == 0)
				tarjanSCC(v);
			if(!inSCC[v])
				dfs_low[u] = Math.min(dfs_low[u], dfs_low[v]);	
		}
		if(dfs_num[u] == dfs_low[u])
		{
			//SCC found
			SCC++;
			while(true)
			{
				int v = stack.pop();
				inSCC[v] = true;
				if(v == u)
					break;
			}
		}	
	}
	
	static class MyScanner {
	      BufferedReader br;
	      StringTokenizer st;
	 
	      public MyScanner() {
	         br = new BufferedReader(new InputStreamReader(System.in));
	      }
	 
	      String next() {
	          while (st == null || !st.hasMoreElements()) {
	              try {
	                  st = new StringTokenizer(br.readLine());
	              } catch (IOException e) {
	                  e.printStackTrace();
	              }
	          }
	          return st.nextToken();
	      }
	 
	      int nextInt() {
	          return Integer.parseInt(next());
	      }
	 
	      long nextLong() {
	          return Long.parseLong(next());
	      }
	 
	      double nextDouble() {
	          return Double.parseDouble(next());
	      }
	 
	      String nextLine(){
	          String str = "";
		  try {
		     str = br.readLine();
		  } catch (IOException e) {
		     e.printStackTrace();
		  }
		  return str;
	      }

	   }
}
