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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.Arrays;
import java.math.BigInteger;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
public class Main{
  public static class InputReader {
    BufferedReader reader;
    StringTokenizer tokenizer;
    
    public InputReader (InputStream stream){
      reader = new BufferedReader(new InputStreamReader(stream));
    }
    
    public String next(){
      while(tokenizer == null || !tokenizer.hasMoreTokens()){
        try{
          String line = reader.readLine();
          if(line == null){
            return "0";
          }
          tokenizer = new StringTokenizer(line);
        } catch(IOException ioe){
          throw new RuntimeException(ioe);
        }
      }
      return tokenizer.nextToken();
    }
    
    public int nextInt(){
      return Integer.parseInt(next());
    }
    
    public double nextDouble(){
      return Double.parseDouble(next());
    }
    
    public Long nextLong(){
      return Long.parseLong(next());
    }
    
    public BigInteger nextBigInteger(){
      return new BigInteger(next());
    }
    
    public String nextLine(){
      String line = "";
      try{
        while(line.equals("")){
          line = reader.readLine();
        }
      } catch(IOException ioe){
        throw new RuntimeException(ioe);
      }
      return line;
    }
  }
 
  public static int solve(int n, int[] perm, int[] sw){
    int[] visited = new int[n+1];
    int color = 1;
    for(int i=1;i<=n;++i){
      if(visited[i] > 0){
        continue;
      }
      while(visited[i] == 0){
        visited[i] = color;
        i = perm[i];
        
      }
      color ++;
    }
    color--;
//     System.out.printf("%d\n", color);
    int swCount = 1;
    for(int i=0; i<n; ++i){
      swCount ^= sw[i];
    }
    return (color == 1 ? 0 : color) + swCount;
  }
 
 public static void main(String[] args){
    InputReader reader = new InputReader(System.in);
    PrintWriter pw = new PrintWriter(System.out);
    int n = reader.nextInt();
    int[] t = new int[n+1];
    for(int i=1; i<=n; ++i){
      t[i] = reader.nextInt();
    }
    int[] s = new int[n];
    for(int i=0; i<n; ++i){
      s[i] = reader.nextInt();
    }
    pw.printf("%d\n", solve(n,t,s));
    pw.flush();
    pw.close();
    
  }
}