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.ArrayList;
import java.util.Stack;
import java.util.StringTokenizer;

public class C {

    static ArrayList<Integer>[] adjList;
    static int V, counter, SCC, dfs_num[], dfs_low[];
    static boolean[] inSCC;
    static Stack<Integer> stack;


    static void tarjanSCC()	 	//O(V + E)
    {
        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
            while(true)
            {
                int v = stack.pop();
                inSCC[v] = true;
                if(v == u)
                    break;
            }
            SCC++;
        }


    }
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        V = sc.nextInt();


        adjList = new ArrayList[V];
        for (int i = 0 ; i < V ; ++ i) adjList[i] = new ArrayList<>();
        counter = 0;
        SCC = 0;
        dfs_num = new int[V];
        dfs_low = new int[V];
        inSCC = new boolean[V];
        stack = new Stack<>();
        for (int i = 0; i < V; i++) adjList[i].add(sc.nextInt() - 1);

        int ones = 0;
        for (int i = 0; i < V ; i++) ones += (sc.nextInt() == 1 ? 1 : 0);

        tarjanSCC();

        int a = SCC == 1 ? 0 : SCC;
        System.out.println(a + (ones % 2 == 0 ? 1 : 0));
        out.flush();
        out.close();
    }

























    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }
        public Scanner (FileReader f) { br = new BufferedReader(f);}

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }
}