Problem: Soroush and Keshi each have a labeled and rooted tree on n vertices. Both of their trees are rooted from vertex 1.

Soroush and Keshi used to be at war. After endless decades of fighting, they finally became allies to prepare a Codeforces round. To celebrate this fortunate event, they decided to make a memorial graph on n vertices.

They add an edge between vertices u and v in the memorial graph if both of the following conditions hold: 

  * One of u or v is the ancestor of the other in Soroush's tree. 
  * Neither of u or v is the ancestor of the other in Keshi's tree. 



Here vertex u is considered ancestor of vertex v, if u lies on the path from 1 (the root) to the v.

Popping out of nowhere, Mashtali tried to find the maximum clique in the memorial graph for no reason. He failed because the graph was too big. 

Help Mashtali by finding the size of the maximum clique in the memorial graph.

As a reminder, clique is a subset of vertices of the graph, each two of which are connected by an edge.

Input

The first line contains an integer t (1≤ t≤ 3 ⋅ 10^5) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer n (2≤ n≤ 3 ⋅ 10^5).

The second line of each test case contains n-1 integers a_2, …, a_n (1 ≤ a_i < i), a_i being the parent of the vertex i in Soroush's tree.

The third line of each test case contains n-1 integers b_2, …, b_n (1 ≤ b_i < i), b_i being the parent of the vertex i in Keshi's tree.

It is guaranteed that the given graphs are trees.

It is guaranteed that the sum of n over all test cases doesn't exceed 3 ⋅ 10^5.

Output

For each test case print a single integer — the size of the maximum clique in the memorial graph.

Example

Input


4
4
1 2 3
1 2 3
5
1 2 3 4
1 1 1 1
6
1 1 1 1 2
1 2 1 2 2
7
1 1 3 4 4 5
1 2 1 4 2 5


Output


1
4
1
3

Note

In the first and third test cases, you can pick any vertex.

In the second test case, one of the maximum cliques is \{2, 3, 4, 5\}.

In the fourth test case, one of the maximum cliques is \{3, 4, 6\}.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class C3 {

	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int T = sc.nextInt();
		while(T-->0) {
			n = sc.nextInt();
			g1 = new LinkedList[n];
			for(int i = 0; i < n; i++) {
				g1[i] = new LinkedList<>();
			}
			for(int i = 1; i < n; i++) {
				int u = sc.nextInt()-1;
				g1[u].add(i);
			}
			g2 = new ArrayList[n];
			for(int i = 0; i < n; i++) {
				g2[i] = new ArrayList<>();
			}
			for(int i = 1; i < n; i++) {
				int u = sc.nextInt()-1;
				g2[u].add(i);
			}
			t = 0;
			op = new int[n];
			cl = new int[n];
			build(0);	
			res = 0; curr = 0;
			starr = new int[2*n];
			stset = new TreeSet<>();
			dfs(0);
			System.out.println(res);
		}

	}
	static int[] starr;
	static TreeSet<Integer> stset;
	static int n;
	static LinkedList<Integer>[] g1;
	static ArrayList<Integer>[] g2;
	static int t;
	static int res, curr;
	static int[] op, cl;
	static void build(int u) {
		op[u] = t; t++;
		for(int v: g2[u]) {
			build(v);
		}
		cl[u] = t; t++;
	}
	static void dfs(int u) {
		starr[op[u]] = 1;
		starr[cl[u]] = -1;
		stset.add(op[u]);
		stset.add(cl[u]);
//		System.out.println(st);
		boolean add = false;
		if(u == 0) {
			add = true;
		}
		else {
			//add if parent is not leaf
			//this happens if and only if rightmost nonzero value to the left is 1
			// and if leftmost nonzero value to the right is -1
			int posl = stset.lower(op[u]);
			int posr = stset.higher(cl[u]);
			if(starr[posl] != 1 || starr[posr] != -1) add = true;
		}
		if(add) {
			curr++;
			res = Math.max(curr, res);
		}
		for(int v: g1[u]) {
			dfs(v);
		}
		if(add) {
			curr--;
		}
		starr[op[u]] = 0;
		starr[cl[u]] = 0;
		stset.remove(op[u]);
		stset.remove(cl[u]);
	}
	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		public FastScanner() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch(IOException e) {
				throw new RuntimeException(e);
			}
		}
	}

}