Problem: Fishing Prince loves trees, and he especially loves trees with only one centroid. The tree is a connected graph without cycles.

A vertex is a centroid of a tree only when you cut this vertex (remove it and remove all edges from this vertex), the size of the largest connected component of the remaining graph is the smallest possible.

For example, the centroid of the following tree is 2, because when you cut it, the size of the largest connected component of the remaining graph is 2 and it can't be smaller.

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However, in some trees, there might be more than one centroid, for example:

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Both vertex 1 and vertex 2 are centroids because the size of the largest connected component is 3 after cutting each of them.

Now Fishing Prince has a tree. He should cut one edge of the tree (it means to remove the edge). After that, he should add one edge. The resulting graph after these two operations should be a tree. He can add the edge that he cut.

He wants the centroid of the resulting tree to be unique. Help him and find any possible way to make the operations. It can be proved, that at least one such way always exists.

Input

The input consists of multiple test cases. The first line contains an integer t (1≤ t≤ 10^4) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer n (3≤ n≤ 10^5) — the number of vertices.

Each of the next n-1 lines contains two integers x, y (1≤ x,y≤ n). It means, that there exists an edge connecting vertices x and y.

It's guaranteed that the given graph is a tree.

It's guaranteed that the sum of n for all test cases does not exceed 10^5.

Output

For each test case, print two lines.

In the first line print two integers x_1, y_1 (1 ≤ x_1, y_1 ≤ n), which means you cut the edge between vertices x_1 and y_1. There should exist edge connecting vertices x_1 and y_1.

In the second line print two integers x_2, y_2 (1 ≤ x_2, y_2 ≤ n), which means you add the edge between vertices x_2 and y_2.

The graph after these two operations should be a tree.

If there are multiple solutions you can print any.

Example

Input


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


Output


1 2
1 2
1 3
2 3

Note

Note that you can add the same edge that you cut.

In the first test case, after cutting and adding the same edge, the vertex 2 is still the only centroid.

In the second test case, the vertex 2 becomes the only centroid after cutting the edge between vertices 1 and 3 and adding the edge between vertices 2 and 3.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.util.concurrent.TimeUnit;

public class c1405 implements Runnable{
	
    public static void main(String[] args) {
    	try{
            new Thread(null, new c1405(), "process", 1<<26).start();
        }
        catch(Exception e){
            System.out.println(e);
        }
    }
	public void run() {
		FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		//PrintWriter out = new PrintWriter("file.out");
		Task solver = new Task();
		int t = scan.nextInt();
		//int t = 1;
		for(int i = 1; i <= t; i++) solver.solve(i, scan, out);
		out.close();
	}

	static class Task {
		static final int oo = Integer.MAX_VALUE;
		static final long OO = Long.MAX_VALUE;

		static List<List<Integer>> adj = new ArrayList<>();
		static int[] size;
		static int[] parent;
		public void solve(int testNumber, FastReader sc, PrintWriter out) {
			int N = sc.nextInt();
			adj.clear();
			size = new int[N+1];
			parent = new int[N+1];
			for(int i = 0; i<= N; i++) {
				adj.add(new ArrayList<>());
				
			}
			for(int i= 1; i < N; i++) {
				int x = sc.nextInt();
				int y = sc.nextInt();
				adj.get(x).add(y);
				adj.get(y).add(x);
			}
			
			dfs(1, 0);
			
			int min = Integer.MAX_VALUE;
			int max = 0;
			for(int each: adj.get(1)) {
				max = Math.max(max, size[each]);
			}
			min = Math.min(min, max);
			
			
			for(int i = 2; i <= N; i++) {
				max = 0;
				int sum = 0;
				for(int each: adj.get(i)) {
					if(each != parent[i]) {
						max = Math.max(max, size[each]);
						sum += size[each];
					}
				}
				max = Math.max(max, N - sum - 1);
				min = Math.min(min, max);
			}
			
			List<Integer> unique = new ArrayList<>();
			max = 0;
			for(int each: adj.get(1)) {
				max = Math.max(max, size[each]);
			}
			if(max == min)
				unique.add(1);
			
			
			for(int i = 2; i <= N; i++) {
				max = 0;
				int sum = 0;
				for(int each: adj.get(i)) {
					if(each != parent[i]) {
						max = Math.max(max, size[each]);
						sum += size[each];
					}
				}
				max = Math.max(max, N - sum - 1);
				if(max == min)
					unique.add(i);
			}
			
//			if(unique.size() > 2) {
//				parent[N+10] = 0;
//				// throw an error for my unproven theory
//			}
			
			if(unique.size() == 1) {
				out.println("1 " + adj.get(1).get(0));
				out.println("1 " + adj.get(1).get(0));
				return;
			}
			
			if(unique.get(0) == parent[unique.get(1)]) {
				unique.add(unique.remove(0));
			}
			int a = unique.get(0);
			int b = unique.get(1);
			
//			if(parent[a] != b && parent[b] != a) {
//				parent[N+10] = 0; // my theory is wrong
//			}
			int diff = 0;
			for(int each: adj.get(a)) {
				if(each != b)
					diff = each;
			}
//			if(diff == 0) {
//				while(true) {} // if there is no child this also doesn't work, throw a different error
//			}
			out.println(diff + " " + a);
			out.println(diff + " " + b);
			
			// wrong answer means I have cut and added the wrong edges
		}
		
		public static void dfs(int node, int par) {
			int sum = 0;
			parent[node] = par;
			for(int each: adj.get(node)) {
				if(each != par) {
					dfs(each, node);
					sum += size[each];
				}
			}
			sum++;
			size[node] = sum;
		}
		
	}
	
	static long modDivide(long a, long b, long MOD) {
		a %= MOD;
		return (binpow(b, MOD-2, MOD) * a) % MOD;
	}
	static long binpow(long a, long b, long m) {
		a %= m;
		long res = 1;
		while (b > 0) {
			if ((b & 1) == 1)
				res = res * a % m;
			a = a * a % m;
			b >>= 1;
		}
		return res;
	}
	static int[] reverse(int a[]) 
    { 
        int[] b = new int[a.length]; 
        for (int i = 0, j = a.length; i < a.length; i++, j--) { 
            b[j - 1] = a[i]; 
        } 
        
        return b;
    }
	static long[] reverse(long a[]) 
    { 
        long[] b = new long[a.length]; 
        for (int i = 0, j = a.length; i < a.length; i++, j--) { 
            b[j - 1] = a[i]; 
        } 
        
        return b;
    }
	static void sort(int[] x){
		shuffle(x);
		Arrays.sort(x);
	}
	static void sort(long[] x){
		shuffle(x);
		Arrays.sort(x);
	}
	static class tup implements Comparable<tup>, Comparator<tup>{
		int a, b;
		tup(int a,int b){
			this.a=a;
			this.b=b;
		}
		public tup() {
		}
		@Override
		public int compareTo(tup o){
			return Integer.compare(b,o.b);
		}
		@Override
		public int compare(tup o1, tup o2) {
			return Integer.compare(o1.b, o2.b);
		}
		
		@Override
	    public int hashCode() {
			return Objects.hash(a, b);
	    }
 
	    @Override
	    public boolean equals(Object obj) {
	    	if (this == obj)
                return true;
	    	if (obj == null)
                return false;
	    	if (getClass() != obj.getClass())
                return false;
	    	tup other = (tup) obj;
	    	return a==other.a && b==other.b;
	    }
	    
	    @Override
	    public String toString() {
	    	return a + " " + b;
	    }
	}
	
	static void shuffle(int[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			int temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
	}

	static void shuffle(long[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			long temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public FastReader(String s) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(new File(s)));
		}

		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;
		}
		
		int[] readArray(int size) {
			int[] a = new int[size];
			for(int i = 0; i < size; i++) {
				a[i] = nextInt();
			}
			return a;
		}
		
		long[] readLongArray(int size) {
			long[] a = new long[size];
			for(int i = 0; i < size; i++) {
				a[i] = nextLong();
			}
			return a;
		}
	}
	
	static void dbg(int[] arr) {
		System.out.println(Arrays.toString(arr));
	}
	static void dbg(long[] arr) {
		System.out.println(Arrays.toString(arr));
	}
	static void dbg(boolean[] arr) {
		System.out.println(Arrays.toString(arr));
	}

	static void dbg(Object... args) {
        for (Object arg : args)
            System.out.print(arg + " ");
        System.out.println();
    }
}