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 EdA {
	static long[] mods = {1000000007, 998244353, 1000000009};
	static long mod = mods[0];
	public static MyScanner sc;
    public static PrintWriter out;
    static int time = 0;
    static ArrayList<ArrayList<Integer>> a;//children
    static ArrayList<ArrayList<Integer>> b;//children
    static int[] l;
    static int[] r;
    static int ans = 0;
    static TreeSet<Pair> vertices;
	public static void main(String[] havish) throws Exception{
		// TODO Auto-generated method stub
 		sc = new MyScanner();
 		out = new PrintWriter(System.out);
 		int t = sc.nextInt();
 		while(t-->0) {
 	 		int n = sc.nextInt();
 	 		int[] pa = readArrayInt(n-1);
 	 		int[] pb = readArrayInt(n-1);
 	 		vertices = new TreeSet<>();
 	 		l = new int[n+1];
 	 		r = new int[n+1];
 	 		a = new ArrayList<>();
 	 		b = new ArrayList<>();
 	 		for(int j = 0;j<=n;j++){
 	 			a.add(new ArrayList<>());
 	 			b.add(new ArrayList<>());
 	 		}
 	 		for(int j = 2;j<=n;j++){
 	 			a.get(pa[j-2]).add(j);
 	 			b.get(pb[j-2]).add(j);
 	 		}
 	 		euler(1);
 	 		dfs(1);
 	 		out.println(ans);
 	 		ans = 0;
 	 		
 		}
 		
 		out.close();
 		
 	}
	public static void dfs(int v){
		Pair p = new Pair(v, l[v], r[v]);
		Pair s = vertices.lower(p);
		Pair t = vertices.higher(p);
		if ((s == null || s.endTime < p.startTime) && (t == null || p.endTime < t.startTime)){
			vertices.add(p);
		} else if (s != null && s.endTime > p.endTime) {
			vertices.remove(s);
			vertices.add(p);
		}
		int count = 0;
		for(int child : a.get(v)){
			dfs(child);
			count++;
		}
		if (count == 0){
			ans = Math.max(ans,  vertices.size());
		}
		if ((s == null || s.endTime < p.startTime) && (t == null || p.endTime < t.startTime)){
			vertices.remove(p);
		} else if (s != null && s.endTime > p.endTime) {
			vertices.add(s);
			vertices.remove(p);
		}
	}
	public static void euler(int v){
		l[v] = ++time;
		for(int child : b.get(v))
			euler(child);
		r[v] = ++time;
	}
	
	static class Pair implements Comparable<Pair>{
		private int index;
		private int startTime;
		private int endTime;
		public Pair(int index, int startTime, int endTime){
			this.index = index;
			this.startTime = startTime;
			this.endTime = endTime;
		}
		public int compareTo(Pair other){
			return Integer.compare(this.startTime, other.startTime);
		}
		
	}
	public static void sort(int[] array){
		ArrayList<Integer> copy = new ArrayList<>();
		for (int i : array)
			copy.add(i);
		Collections.sort(copy);
		for(int i = 0;i<array.length;i++)
			array[i] = copy.get(i);
	}
	static String[] readArrayString(int n){
		String[] array = new String[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.next();
		return array;
	}
	static int[] readArrayInt(int n){
    	int[] array = new int[n];
    	for(int j = 0;j<n;j++)
    		array[j] = sc.nextInt();
    	return array;
    }
	static int[] readArrayInt1(int n){
		int[] array = new int[n+1];
		for(int j = 1;j<=n;j++){
			array[j] = sc.nextInt();
		}
		return array;
	}
	static long[] readArrayLong(int n){
		long[] array = new long[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextLong();
		return array;
	}
	static double[] readArrayDouble(int n){
		double[] array = new double[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextDouble();
		return array;
	}
	static int minIndex(int[] array){
		int minValue = Integer.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(long[] array){
		long minValue = Long.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(double[] array){
		double minValue = Double.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static long power(long x, long y){
		if (y == 0)
			return 1;
		if (y%2 == 1)
			return (x*power(x, y-1))%mod;
		return power((x*x)%mod, y/2)%mod;
	}
	static void verdict(boolean a){
        out.println(a ? "YES" : "NO");
    }
    public 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;
        }
        
    }	
}

//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is