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.

<image>

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

<image>

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.awt.List;
import java.io.*;
import java.math.BigInteger;
import java.util.*;


/*
 * 
 * daiict
 *
 * 
 * 
 */

public class Solution {
	FastScanner in;
	PrintWriter out;

	static ArrayList[] adj;
	static ArrayList[] aadj;
	static int last;
	static int n;
	static int m;

	static long C[][];

	static int[] dp1;
	static int[] dp2;
	static int color[];
	static int visited[];
	static int[] arr;
	static long[] brr;
	static double ans;
	static int array[];
	static int start[];
	static int finish[];
	static int pref[];
	static int tree[];
	static int maxval = 32;
	
	static int fenwik[];

	static int ttt[];
	static int sum = 0;
	static String s;

	static int cc = 0;
	static long min = Long.MAX_VALUE;
	static int minva = Integer.MAX_VALUE;

	static ArrayList<Integer> segt[];

	// for dfs do not delete
	static int dir[][] = { { 1, 0 }, { 0, 1 }, { 0, -1 }, { -1, 0 } };

	static int[] seg;
	static long count = 1;
	static long mod = (long) 1e9 + 7;

	static int parent[];
	static int size[];

	static int[] l;
	static int[] r;
	static int[] next;
	static int[] cnt;
	static int[] block;

	static HashSet<String> set;
	static HashSet<String> set2;

	static int low[];
	static int disc[];
	static int time;
	static int acn[];

	static class Pair1 implements Comparable<Pair1> {
		int x;
		int y;

		Pair1(int l, int m) {

			this.x = l;
			this.y = m;

		}
		
		public void setX(int x){
			this.x = x;
		}
		public void setY(int y){
			this.y = y;
		}

		public int compareTo(Pair1 p) {

			if (this.y != p.y) {
				return (int) (this.x - p.x);
			}
			return 0;
		}

		public String toString() {
			return x + " " + y;
		}

		public boolean equals(Object o) {
			if (o instanceof Pair1) {
				Pair1 a = (Pair1) o;

				return this.x == a.x;
			}

			return false;
		}

		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode();
		}

	}

	public static int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}


	// public static void update(int x,int val){
	// while(x<=maxval){
	// tree[x] += val;
	// x = (x&-x);
	// }
	// }

	public static int read(int idx) {
		int sum = 0;

		while (idx >= 0) {
			sum += tree[idx];
			idx -= (idx & (-idx));
		}

		return sum;
	}

	public static int find(int i) {
		if (parent[i] != i) {
			return find(parent[i]);
		}

		return i;
	}

	public static void union(int a, int b) {
		int x = find(a);
		int y = find(b);

		if (x != y) {
			if (size[x] > size[y]) {
				size[x] += size[y];
				parent[y] = x;
			} else {
				size[y] += size[x];
				parent[x] = y;
			}
		}
	}
	
	void updateF(int pos, int v, int n){
		pos = pos + 1;
		while(pos < n) {
			fenwik[pos] += v;
			pos += ((pos)&(-pos));
		}
	}
	
	int getF(int pos, int n) {
		int sum = 0;
		pos++;
		while(pos>0) {
			sum += fenwik[pos];
			pos -= ((pos)&(-pos));
		}
		return sum;
	}
	
	int process(int sum, int n){
		int l = 0;
		int r = n;
		while(l+1<r){
			int mid = (l+r)/2;
			int got = getF(mid,1000010);
			if (got >= sum){
				r = mid;
			} else {
				l = mid;
			}
		}
		updateF(l,-1,1000010);
		return l;
	}
	
	void build(int n, int arr[]) { // build the tree
		for (int i = n - 1; i > 0; --i)
			arr[i] = arr[i << 1] + arr[i << 1 | 1];
	}

	public static void modify(int p, int val, int n, int arr[]) { // set value at position
														// p
		for (arr[p += n] = val; p > 1; p >>= 1)
			arr[p >> 1] = arr[p] + arr[p ^ 1];
	}

	int query(int l, int r, int n, int arr[]) { // sum on interval [l, r)
		int res = 0;
		for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
			if ((l & 1) == 1)
				res += arr[l++];
			if ((r & 1) == 1)
				res += arr[--r];
		}
		return res;
	}


	/* static */ void solve() throws NumberFormatException,InputMismatchException, IOException {
		    		    
		    		    	Scanner in = new Scanner(System.in);
		    		    	

		    		    	
		    		    	int t = in.nextInt();
		    		    	
		    		    	while(t-->0){
		    		    		int n = in.nextInt();
		    		    		adj = new ArrayList[n];
		    		    		for (int i = 0;i<n;i++){
		    		    			adj[i] = new ArrayList();
		    		    		}
		    		    		int tA = -1;
		    		    		int tB = -1;
		    		    		for (int i = 0;i<n-1;i++){
		    		    			int a = in.nextInt();
		    		    			int b = in.nextInt();
		    		    			tA = a;
		    		    			tB = b;
		    		    			adj[a-1].add(b-1);
		    		    			adj[b-1].add(a-1);
		    		    		}
		    		    		visited = new int[n];
		    		    		Map<Integer, ArrayList<Integer>> map = new HashMap(); 
		    		    		int max = 0;
		    		    		minva = Integer.MAX_VALUE;
		    		    		dddfffsss(0,map,n);
		    		    		ArrayList<Integer> get = map.get(minva);
		    		    		StringBuilder rs = new StringBuilder();
		    		    		if (get != null && get.size() == 1) {
		    		    			rs.append(tA + " " + tB);
		    		    			rs.append("\n");
		    		    			rs.append(tA + " " + tB);
		    		    		} else {
		    		    			String aa = findB(get.get(0),get.get(1));
		    		    			if (aa.equals("")) {
		    		    				aa = findB(get.get(1),get.get(0));
		    		    				rs.append((get.get(1)+1) + " " + aa);
		    		    				rs.append("\n");
		    		    				rs.append((get.get(0)+1) + " " + aa);
		    		    			} else {
		    		    				rs.append((get.get(0)+1) + " " + aa);
		    		    				rs.append("\n");
		    		    				rs.append((get.get(1)+1) + " " + aa);
		    		    			}
		    		    		}
		    		    		System.out.println(rs.toString());
		    		    	}
		    		    	
		    		    }
	
	public String findB(int i,int j){
		if (adj[i].size() > 1) {
			for (int k = 0;k<adj[i].size();k++){
				if (((int)(adj[i].get(k))) != j){
					return "" +((int)(adj[i].get(k)) + 1);
				}
			}
		}
		return "";
	}
	
	public int dddfffsss(int i,Map<Integer, ArrayList<Integer>> map,int n) {
		//System.out.println(i);
		if (visited[i] == 1) {
			return 0;
		}
		visited[i] = 1;
		int count = 1;
		int max = 0;
		for (int j = 0;j<adj[i].size();j++){
			int cur = (int) adj[i].get(j);
			int c = dddfffsss(cur,map,n);
			max = Math.max(max, c);
			count+=c;
		}
		int rem = n - count;
		max = Math.max(max, rem);
		if (max < minva) {
			minva = max;
		}
		ArrayList<Integer> get = map.get(max);
		if (get == null) {
			get = new ArrayList();
		}
		get.add(i);
		map.put(max, get);
		return count;
	}
	
	
	public int findSum(int i, int[] arr, int offset){
		
		int sum = 0;
		
		for(int j = 0;(1<<j)<=i;j++){
			//System.out.append(i + " " + j + " " + (i>>j));
			if (((i>>j)&1) == 1){
				//System.out.println(i + " " + j + " " + (i>>j));
				sum += arr[j+offset];
			}
		}
		
		return sum;
	}
	
	public static int c(int n){
		if(n == 1){
			return 1;
		}
		if(n == 2)
			return 5;
		
		return 4*(2*(n-2) - 1) + 4 + c(n-1);
		
	}

	public static long dfs(int i,ArrayList<Long> list,long n) {
		if (visited[i] == 1) {
			return 0;
		}

		visited[i] = 1;
		int count = 1;
		for (int j = 0; j < adj[i].size(); j++) {
			int next = (int) (adj[i].get(j));
			long nextC = dfs(next, list,n);
			if (nextC == 0) {
				continue;
			}
			long ans = (nextC * (n-nextC)%mod)%mod;
			list.add(ans);
			count += nextC;
		}
		return count;

	}

	public static void uu(int arr[], int i, int f) {
		if (i == 1) {
			return;
		}
		int next = i / 2;
		int x = 0;
		if (i % 2 == 0) {
			x = i + 1;
		} else {
			x = i - 1;
		}

		if (f == 1) {
			arr[next] = arr[i] ^ arr[x];
		} else {
			arr[next] = arr[i] | arr[x];
		}

		uu(arr, next, 1 - f);
	}

	public static void sbuild(int i, int l, int r) {
		// System.out.println(i + " ");
		if (l == r) {
			segt[i] = new ArrayList();
			segt[i].add(array[l - 1]);
			return;
		}

		int mid = (l + r) / 2;
		sbuild(2 * i, l, mid);
		sbuild(2 * i + 1, mid + 1, r);

		segt[i] = new ArrayList();
		merge(segt[2 * i], segt[2 * i + 1], segt[i]);
	}

	public static int squery(int i, int l, int r, int ql, int qr, int val) {

		if (l > qr || r < ql || l > r || ql > qr) {
			return 0;
		}

		if (l >= ql && r <= qr) {
			int x = lbw(segt[i], val);
			return x;
		}

		int mid = (l + r) / 2;

		return (squery(2 * i, l, mid, ql, qr, val) + squery(2 * i + 1, mid + 1, r, ql, qr, val));

	}

	public static int lbw(ArrayList<Integer> list, int value) {

		// System.out.println(list);
		// System.out.println(value + " ff ");

		int low = 0;
		int high = list.size();

		while (low != high) {
			int mid = (low + high) / 2;
			if (list.get(mid) <= value) {
				low = mid + 1;
			} else {
				high = mid;
			}
		}
		if (low == list.size()) {
			return list.size();
		}
		return low;
	}

	public static void merge(ArrayList<Integer> l1, ArrayList<Integer> l2, ArrayList<Integer> ans) {
		int i = 0;
		int j = 0;

		while (i < l1.size() && j < l2.size()) {
			if (l1.get(i) > l2.get(j)) {
				ans.add(l2.get(j));
				j++;
			} else {
				ans.add(l1.get(i));
				i++;
			}
		}

		while (i < l1.size()) {
			ans.add(l1.get(i));
			i++;
		}

		while (j < l2.size()) {
			ans.add(l2.get(j));
			j++;
		}
	}

	public static void dfs(int i, int p) {
		start[i] = time;
		array[time] = arr[i];
		time++;
		for (int j = 0; j < adj[i].size(); j++) {
			if ((int) adj[i].get(j) != p) {
				dfs((int) adj[i].get(j), i);
			}
		}

		finish[i] = time;

	}

	static void call(int i) {

		// System.out.println(i);

		visited[i] = 1;
		time++;
		disc[i] = time;
		low[i] = time;

		for (int j = 0; j < adj[i].size(); j++) {
			if (visited[(int) adj[i].get(j)] == 0) {
				acn[(int) adj[i].get(j)] = i;
				call((int) adj[i].get(j));

				low[i] = Math.min(low[i], low[(int) adj[i].get(j)]);

				if (low[(int) adj[i].get(j)] > disc[i]) {
					int temp = (int) adj[i].get(j);
					union(temp, i);
					System.out.println(temp + " " + i);
				}
			} else if ((int) adj[i].get(j) != acn[i]) {
				low[i] = Math.min(low[i], disc[(int) adj[i].get(j)]);
			}
		}

	}

	static void update(int idx, int b) {
		int j = block[idx];
		arr[idx] = b;

		for (int i = r[j]; i >= l[j]; i--) {
			int k = (int) (i + arr[i]);
			if (k >= n) {
				next[i] = i;
				cnt[i] = 1;
				continue;
			}
			if (block[k] > block[i]) {
				next[i] = k;
				cnt[i] = 1;
			} else {
				next[i] = next[k];
				cnt[i] = cnt[k] + 1;
			}
		}

	}

	static void get(int idx) {
		if (next[idx] == idx) {
			last = idx;
			ans = 1;
			return;
		}
		int c = 0;
		while (true) {
			int j = next[idx];
			if (block[j] == block[idx]) {
				c += cnt[idx];
				last = next[idx];
				break;
			} else {
				c += cnt[idx];
				idx = next[idx];
			}
		}

		ans = c;
	}

	static private String Frac(double x) {
		if (x < 0) {
			return "-" + Frac(-x);
		}
		double tolerance = 1.0E-18;
		double h1 = 1;
		double h2 = 0;
		double k1 = 0;
		double k2 = 1;
		double b = x;
		do {
			double a = Math.floor(b);
			double aux = h1;
			h1 = a * h1 + h2;
			h2 = aux;
			aux = k1;
			k1 = a * k1 + k2;
			k2 = aux;
			b = 1 / (b - a);
		} while (Math.abs(x - h1 / k1) > x * tolerance);

		return h1 + " " + k1;
	}

	public static long invcount(int arr[]) {
		if (arr.length < 2) {
			return 0;
		}

		int mid = (arr.length + 1) / 2;

		int left[] = Arrays.copyOfRange(arr, 0, mid);
		int right[] = Arrays.copyOfRange(arr, mid, arr.length);

		return invcount(left) + invcount(right) + merge(arr, left, right);

	}

	public static long merge(int arr[], int left[], int right[]) {
		long count = 0;

		int i = 0;
		int j = 0;

		while (i < left.length || j < right.length) {

			if (i == left.length) {
				arr[i + j] = right[j];
				j++;
			} else if (j == right.length) {
				arr[j + i] = left[i];
				i++;
			} else {
				if (left[i] <= right[j]) {
					arr[i + j] = left[i];
					i++;
				} else {
					arr[i + j] = right[j];
					j++;
					count += left.length - i;
				}
			}

		}

		return count;
	}

	/**
	 * 
	 * @param div
	 * @param left
	 * @param right
	 * @param value
	 * @return the smallest index i which a[i] >= value in range [left, right)
	 *         if exists, otherwise return -1
	 */
	int ff(int[] div, int left, int right, int value) {
		int low = left;
		int high = right;

		if (value > div[right - 1]) {
			return left;
		}

		while (low != high) {
			int mid = (low + high) / 2;
			if (div[mid] < value) {
				low = mid + 1;
			} else {
				high = mid;
			}
		}
		if (low == right) {
			return low;
		}
		return low;
	}

	/**
	 * 
	 * @param div
	 * @param left
	 * @param right
	 * @param value
	 * @return greatest index i which a[i] <= value in range [left, right) if
	 *         exists, otherwise return a number out of [left, right)
	 */
	int ffff(int[] div, int left, int right, int value) {

		if (value < div[left]) {
			return right - 1;
		}

		while (left != right) {
			int mid = (left + right) >> 1;
			if (div[mid] <= value) {
				left = mid + 1;
			} else {
				right = mid;
			}
		}
		if (left < 0) {
			left *= -1;
		}
		return --left;
	}

	public static String reverse(String s) {

		String ans = "";

		for (int i = s.length() - 1; i >= 0; i--) {
			ans += s.charAt(i);
		}

		return ans;

	}

	public static long sum(long x) {
		return x < 10 ? x : x % 10 + sum(x / 10);
	}

	public static long gcd(long x, long y) {
		if (x == 0)
			return y;
		else
			return gcd(y % x, x);
	}

	static long inv(long x, long mod) {
		long r, y;
		for (r = 1, y = mod - 2; y != 0; x = x * x % mod, y >>= 1) {
			if ((y & 1) == 1)
				r = r * x % mod;

		}
		return r;
	}

	public static long pow(long x, long y, long n) {
		if (y == 0)
			return 1 % n;
		if (y % 2 == 0) {
			long z = pow(x, y / 2, n);
			return (z * z) % n;
		}
		return ((x % n) * pow(x, y - 1, n)) % n;
	}

	public static boolean isPrime(long a) {
		// Corner cases
		if (a <= 1)
			return false;
		if (a <= 3)
			return true;

		// This is checked so that we can skip
		// middle five numbers in below loop
		if (a % 2 == 0 || a % 3 == 0)
			return false;

		for (long i = 5; i * i <= a; i = i + 6)
			if (a % i == 0 || a % (i + 2) == 0)
				return false;

		return true;
	}

	void run() throws NumberFormatException, InputMismatchException, IOException {
		in = new FastScanner();
		out = new PrintWriter(System.out);

		solve();

		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

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

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(in.br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

		double nextDouble() {
			return Double.parseDouble(next());
		}
	}

	public static void main(String[] args) throws NumberFormatException, InputMismatchException, IOException {
		// new Thread(null ,new Runnable(){
		// public void run(){
		// try{
		//
		// test();
		//
		// } catch(Exception e){
		// e.printStackTrace();
		// }
		// }
		// },"1",1<<26).start();
		// }
		// static StringBuilder sb;
		// public static void test() throws IOException{
		// sb=new StringBuilder();
		// int t=1;
		// while(t-->0){
		//
		// solve();
		//
		// }
		//

		new Solution().run();
	}

}

class Pair {
	int x;
	int y;

	public Pair(int i, int j) {
		this.x = i;
		this.y = j;

	}

}

class MyComp implements Comparator<String> {

	int c = 0;

	MyComp(int d) {
		c = d;
	}

	@Override
	public int compare(String a, String b) {

		// < == -1

		String arr[] = a.split(" ");
		String brr[] = b.split(" ");

		return arr[c].compareTo(brr[c]);

	}

}

class MyComp2 implements Comparator<Pair> {

	@Override
	public int compare(Pair a, Pair b) {

		// < == -1

		if (a.y != b.y) {
			return a.x - b.x;
		} else {
			return 0;
		}

	}

}