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.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C {
	public static void main(String[] args) throws NumberFormatException, IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		int n = sc.nextInt();
		int p[] = new int[n];
		int b[] = new int[n];
		
		UnionFind uf = new UnionFind(n);
		
		for(int i = 0; i < n; i++) {
			p[i] = sc.nextInt();
			uf.unionSet(i, p[i] - 1);
		}
		
		int ones = 0;
		
		for(int i = 0; i < n; i++) {
			b[i] = sc.nextInt();
			if(b[i] == 1)
				ones++;
		}
		
		if(uf.numSets == 1)
			System.out.println((ones + 1) % 2);
		else
			System.out.println(uf.numSets + (ones + 1) % 2);
		
		out.flush();
		out.close();
	}
	
	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner(FileReader f) {
			br = new BufferedReader(f);
		}

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

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

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

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

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

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}
	}
	
	static class UnionFind {
		
		int[] p,rank,setSize;
		int numSets;
		
		public UnionFind(int N)
		{
			p = new int[N];
			rank = new int[N];
			setSize = new int[N];
			
			for(int i=0; i<N; i++)
				p[i] = i;
			
			numSets = N;
			Arrays.fill(setSize, 1);
		}
		
		public int findSet(int i)
		{
			if(p[i] == i)
				return i;
			
			int root = findSet(p[i]);
			p[i] = root; // Path compression
			return root;
		}
		
		public boolean isSameSet(int i, int j)
		{
			return findSet(i) == findSet(j);
		}
		
		public void unionSet(int i, int j)
		{
			int x = findSet(i);
			int y = findSet(j);
			if(x == y)
				return;
			
			if(rank[x] > rank[y]){
				p[y] = x;
				setSize[x] += setSize[y];
			}
			else{
				p[x] = y;
				setSize[y] += setSize[x];
			}
			
			if(rank[x] == rank[y])
				rank[y]++;
			
			numSets--;
		}
		
		public int numSets()
		{
			return numSets;
		}
		
		public int setSize(int i)
		{
			return setSize[findSet(i)];
		}
		
	}
	
}
