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:

<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:
	/*
	TO LEARN
	1-segment trees
	2-euler tour
	3-fenwick tree and interval tree
	*/
	/*
	TO SOLVE 
	uva 1103
	codeforces 722 kavi on pairing duty
	*/
	/*
	bit manipulation shit
	1-Computer Systems: A Programmer's Perspective
	2-hacker's delight
	3-(02-03-bits-ints)
	4-machine-basics
	5-Bits Manipulation tutorialspoint
	*/
	/*
	TO WATCH
	1-what is bitmasking by kartik arora youtube

	*/
	            import java.util.*;
			    import java.math.*;
			    import java.io.*; 
			    import java.util.stream.Collectors;

			       public class A{
			     
			  static InputStream inputStream = System.in;
	            static FastScanner scan=new FastScanner();
			     public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
static StringBuilder s;
static Set<Integer>edges[];
static int parent[];
static int count[];
static int n;
static int cent;
static ArrayList<Integer>arr=new ArrayList<Integer>();
static void dfs(int x,int par)
{
	count[x]=1;
	for(int v:edges[x])
	{
		if(par==v)
			continue;
		parent[v]=x;
		dfs(v,x);
		count[x]+=count[v];
	}
}
static int get_cent()
{
	int cent=Integer.MAX_VALUE;
	for(int i=0;i<n;i++)
	{
		int cnt=0;
		int cur=Integer.MIN_VALUE;
		for(int x:edges[i])
		{
			if(parent[i]!=x)
			{
				//if(i==2)
				//	out.println("FUCK "+count[x]);
				cur=Math.max(cur,count[x]);
				cnt+=count[x];
			}
		}
		
		cur=Math.max(cur,n-1-cnt);
		//if(i==2)
			//out.println("CUR "+cnt);
		cent=Math.min(cent,cur);
	}
	return cent;
}
static int how_many()
{
	int res=0;
	for(int i=0;i<n;i++)
	{
		int cnt=0;
		int cur=Integer.MIN_VALUE;
		for(int x:edges[i])
		{
			if(parent[i]!=x)
			{
				cur=Math.max(cur,count[x]);
				cnt+=count[x];
			}
		}
		cur=Math.max(cur,n-1-cnt);
		if(cur==cent){
			arr.add(i);
			res++;
		}
	}
	return res;
}
		public static void main(String[] args)  throws Exception 
	      {
		
			//	scan=new FastScanner("help.in");
			//out = new PrintWriter("lifeguards.out");
			 
			 /*
			 currently doing 
			 1-digit dp
			 2-ds like fenwick and interval tree and sparse table 
			 */
			 /*
			 READING 
			 1-Everything About Dynamic Programming codeforces
			 2-DYNAMIC PROGRAMMING: FROM NOVICE TO ADVANCED topcoder
			 3-Introduction to DP with Bitmasking codefoces
			 4-Bit Manipulation hackerearth
			 5-read more about mobious and inculsion-exclusion 
			 */
			


			    int tt=1;
			tt=scan.nextInt();

		 outer:while(tt-->0)
			    {
			    	n=scan.nextInt();

			    	count=new int[n];
			    	edges=new HashSet[n];
			    	for(int i=0;i<n;i++)
			    		edges[i]=new HashSet();
			    	parent=new int[n];
			    	Arrays.fill(parent,-1);
			    	int st=-1,en=-1;
			    	for(int i=0;i<n-1;i++)
			    	{
			    		int x=scan.nextInt()-1,y=scan.nextInt()-1;
			    		st=x+1;
			    		en=y+1;
			    		edges[x].add(y);
			    		edges[y].add(x);
			    	}
			    	arr=new ArrayList();
			    	dfs(0,-1);
			    	cent=get_cent();
			    	int res=how_many();
			    	if(res==1)
			    	{
			    		out.println(st+" "+en);
			    		out.println(st+" "+en);
			    		continue outer;
			    	}
			    	//out.println(arr);
			    	for(int i=0;i<n;i++)
			    	{
			    		if(arr.get(0)!=i&&arr.get(1)!=i&&edges[arr.get(0)].contains(i)&&!edges[arr.get(1)].contains(i))
			    		{
			    			out.println((arr.get(0)+1)+" "+(i+1));
			    			out.println((i+1)+" "+(arr.get(1)+1));
			    			continue outer;
			    		}
			    	}
			    	//out.println(arr);
			    	//out.println(cent+" "+res);

			    	
	}
	   out.close();
}
	  	 
	 		  
			   
			
			static class special{
				long x1,y1,x2,y2;
				//int id;
				special(long x1,long y1,long x2,long y2)
				{
					this.x1=x1;
					this.y1=y1;
					this.x2=x2;
					this.y2=y2;
					//this.id=id;
				}
				@Override
				    public int hashCode() {
			                int hash = 7;
    hash = 31 * hash + (int) x1;
    hash = 31 * hash + (int)x2;
    hash = 31 * hash + (int)y1;
    hash = 31 * hash + (int)y2;
    return hash;
			            }
			              @Override
			            public boolean equals(Object o){
			                if (o == this) return true;
			                if (o.getClass() != getClass()) return false;
			                special t = (special)o;
			                return t.x1 == x1 && t.y1 == y1&&t.x2==x2&&t.y2==y2;
			            }
			}

			   
			     static long binexp(long a,long n)
			    {
			        if(n==0)
			            return 1;
			        long res=binexp(a,n/2);
			        if(n%2==1)
			            return res*res*a;
			        else 
			            return res*res;
			    }
			     
			    static long powMod(long base, long exp, long mod) {
			           if (base == 0 || base == 1) return base;
			           if (exp == 0) return 1;
			           if (exp == 1) return (base % mod+mod)%mod;
			           long R = (powMod(base, exp/2, mod) % mod+mod)%mod;
			           R *= R;
			           R %= mod;
			           if ((exp & 1) == 1) {
			               return (base * R % mod+mod)%mod;
			           }
			           else return (R %mod+mod)%mod;
			       }
			    static double dis(double x1,double y1,double x2,double y2)
			    {
			        return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
			    }
			    static long mod(long x,long y)
			        {
			            if(x<0)
			                x=x+(-x/y+1)*y;
			            return x%y;
			        }
			     public static  long pow(long b, long e) {
			                long r = 1;
			                while (e > 0) {
			                    if (e % 2 == 1) r = r * b ;
			                    b = b * b;
			                    e >>= 1;
			                }
			                return r;
			            }
			    private static void sort(long[] arr) {
			            List<Long> list = new ArrayList<>();
			            for (long object : arr) list.add(object);
			            Collections.sort(list);
			        //Collections.reverse(list);
			            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
			        }
			    private static void sort2(long[] arr) {
			            List<Long> list = new ArrayList<>();
			            for (Long object : arr) list.add(object);
			            Collections.sort(list);
			        Collections.reverse(list);
			            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
			        }
			     static class FastScanner
	{
	    private int BS = 1 << 16;
	    private char NC = (char) 0;
	    private byte[] buf = new byte[BS];
	    private int bId = 0, size = 0;
	    private char c = NC;
	    private double cnt = 1;
	    private BufferedInputStream in;
	 
	    public FastScanner() {
	        in = new BufferedInputStream(System.in, BS);
	    }
	 
	    public FastScanner(String s) {
	        try {
	            in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
	        } catch (Exception e) {
	            in = new BufferedInputStream(System.in, BS);
	        }
	    }
	 
	    private char getChar() {
	        while (bId == size) {
	            try {
	                size = in.read(buf);
	            } catch (Exception e) {
	                return NC;
	            }
	            if (size == -1) return NC;
	            bId = 0;
	        }
	        return (char) buf[bId++];
	    }
	 
	    public int nextInt() {
	        return (int) nextLong();
	    }
	 
	    public int[] nextInts(int N) {
	        int[] res = new int[N];
	        for (int i = 0; i < N; i++) {
	            res[i] = (int) nextLong();
	        }
	        return res;
	    }
	 
	    public long[] nextLongs(int N) {
	        long[] res = new long[N];
	        for (int i = 0; i < N; i++) {
	            res[i] = nextLong();
	        }
	        return res;
	    }
	 
	    public long nextLong() {
	        cnt = 1;
	        boolean neg = false;
	        if (c == NC) c = getChar();
	        for (; (c < '0' || c > '9'); c = getChar()) {
	            if (c == '-') neg = true;
	        }
	        long res = 0;
	        for (; c >= '0' && c <= '9'; c = getChar()) {
	            res = (res << 3) + (res << 1) + c - '0';
	            cnt *= 10;
	        }
	        return neg ? -res : res;
	    }
	 
	    public double nextDouble() {
	        double cur = nextLong();
	        return c != '.' ? cur : cur + nextLong() / cnt;
	    }
	 
	    public double[] nextDoubles(int N) {
	        double[] res = new double[N];
	        for (int i = 0; i < N; i++) {
	            res[i] = nextDouble();
	        }
	        return res;
	    }
	 
	    public String next() {
	        StringBuilder res = new StringBuilder();
	        while (c <= 32) c = getChar();
	        while (c > 32) {
	            res.append(c);
	            c = getChar();
	        }
	        return res.toString();
	    }
	 
	    public String nextLine() {
	        StringBuilder res = new StringBuilder();
	        while (c <= 32) c = getChar();
	        while (c != '\n') {
	            res.append(c);
	            c = getChar();
	        }
	        return res.toString();
	    }
	 
	    public boolean hasNext() {
	        if (c > 32) return true;
	        while (true) {
	            c = getChar();
	            if (c == NC) return false;
	            else if (c > 32) return true;
	        }
	    }
	}

			     static class Pair implements Comparable<Pair>{
			            public long x, y,z;
			            public Pair(long x1, long y1,long z1) {
			                x=x1;
			                y=y1;
			                z=z1;
			            }
			             public Pair(long x1, long y1) {
			                x=x1;
			                y=y1;
			    
			            }
			            
			            @Override
			            public int hashCode() {
			                return (int)(x + 31 * y);
			            }
			            public String toString() {
			                return x + " " + y+" "+z;
			            }
			            @Override
			            public boolean equals(Object o){
			                if (o == this) return true;
			                if (o.getClass() != getClass()) return false;
			                Pair t = (Pair)o;
			                return t.x == x && t.y == y&&t.z==z;
			            }
			    public int compareTo(Pair o)
			    {
			    
			    	return (int)(x-o.x);
			     
			        }
			     
			    }
			    
			    }