Problem: This is an interactive problem.

After getting AC after 13 Time Limit Exceeded verdicts on a geometry problem, Kuroni went to an Italian restaurant to celebrate this holy achievement. Unfortunately, the excess sauce disoriented him, and he's now lost!

The United States of America can be modeled as a tree (why though) with n vertices. The tree is rooted at vertex r, wherein lies Kuroni's hotel.

Kuroni has a phone app designed to help him in such emergency cases. To use the app, he has to input two vertices u and v, and it'll return a vertex w, which is the lowest common ancestor of those two vertices.

However, since the phone's battery has been almost drained out from live-streaming Kuroni's celebration party, he could only use the app at most ⌊ n/2 ⌋ times. After that, the phone would die and there will be nothing left to help our dear friend! :(

As the night is cold and dark, Kuroni needs to get back, so that he can reunite with his comfy bed and pillow(s). Can you help him figure out his hotel's location?

Interaction

The interaction starts with reading a single integer n (2 ≤ n ≤ 1000), the number of vertices of the tree.

Then you will read n-1 lines, the i-th of them has two integers x_i and y_i (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i), denoting there is an edge connecting vertices x_i and y_i. It is guaranteed that the edges will form a tree.

Then you can make queries of type "? u v" (1 ≤ u, v ≤ n) to find the lowest common ancestor of vertex u and v.

After the query, read the result w as an integer.

In case your query is invalid or you asked more than ⌊ n/2 ⌋ queries, the program will print -1 and will finish interaction. You will receive a Wrong answer verdict. Make sure to exit immediately to avoid getting other verdicts.

When you find out the vertex r, print "! r" and quit after that. This query does not count towards the ⌊ n/2 ⌋ limit.

Note that the tree is fixed beforehand and will not change during the queries, i.e. the interactor is not adaptive.

After printing any query do not forget to print end of line and flush the output. Otherwise, you might get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++;
  * System.out.flush() in Java;
  * flush(output) in Pascal;
  * stdout.flush() in Python;
  * see the documentation for other languages.



Hacks

To hack, use the following format:

The first line should contain two integers n and r (2 ≤ n ≤ 1000, 1 ≤ r ≤ n), denoting the number of vertices and the vertex with Kuroni's hotel.

The i-th of the next n-1 lines should contain two integers x_i and y_i (1 ≤ x_i, y_i ≤ n) — denoting there is an edge connecting vertex x_i and y_i.

The edges presented should form a tree.

Example

Input


6
1 4
4 2
5 3
6 3
2 3

3

4

4



Output








? 5 6

? 3 1

? 1 2

! 4

Note

Note that the example interaction contains extra empty lines so that it's easier to read. The real interaction doesn't contain any empty lines and you shouldn't print any extra empty lines as well.

The image below demonstrates the tree in the sample test:

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;
public class Main7
{
	static class Pair
	{
		int x;
		int y;
		Pair(int x ,int y)
		{
			this.x=x;
			this.y=y;
		}
	}
	static int mod=1000000007;
	public static int[] sort(int[] a)
	{
		int n=a.length;
		ArrayList<Integer> ar=new ArrayList<>();
		for(int i=0;i<a.length;i++)
		{
			ar.add(a[i]);
		}
		Collections.sort(ar);
		for(int i=0;i<n;i++)
		{
			a[i]=ar.get(i);
		}
		return a;
	}
	public static long pow(long a, long b)
    {
        long result=1;
        while(b>0)
        {
            if (b % 2 != 0)
            {
                result=(result*a)%mod;
                b--;
            } 
            a=(a*a)%mod;
            b /= 2;
        }   
        return result;
    }
	static class StudentComparator implements Comparator<Integer>
	{ 
		public int compare(Integer s1, Integer s2)
		{ 
			if (graph.get(s1).size()<graph.get(s2).size()) 
				return -1; 
			else if (graph.get(s1).size()> graph.get(s2).size()) 
				return 1; 
			return 0; 
		} 
	} 
	static ArrayList<ArrayList<Integer>> graph;
	static public void main(String args[])throws IOException
	{
		int tt=1;
		StringBuilder sb=new StringBuilder();
		while(tt-->0)
		{
			int n=i();
			int[] x=new int[n-1];
			int[] y=new int[n-1];
			graph=new ArrayList<>();
			for(int i=0;i<=n;i++)
				graph.add(new ArrayList<>());
			for(int i=0;i<n-1;i++)
			{
				x[i]=i();
				y[i]=i();
				graph.get(x[i]).add(y[i]);
				graph.get(y[i]).add(x[i]);
			}
			TreeSet<Integer> ts=new TreeSet<>();
			PriorityQueue<Integer> q=new PriorityQueue<>(new StudentComparator());
			for(int i=1;i<=n;i++)
				q.add(i);
			int fin=-1;
			while(q.isEmpty()==false && q.size()>1)
			{
				int first=0,second=0;
				first=q.poll();
				second=q.poll();
				int num1=first;
				int num2=second;
				pln("? "+first+" "+second);
				System.out.flush();
				int lca=i();
				if(lca==num1)
				{
					Queue<Integer> queue=new LinkedList<>();
					boolean[] visited=new boolean[n+1];
					queue.add(num2);
					ArrayList<Integer> ar2=new ArrayList<>();
					while(queue.isEmpty()==false)
					{
						int num4=queue.poll();
						ArrayList<Integer> ar=graph.get(num4);
						ar2.add(num4);
						for(int j=0;j<ar.size();j++)
						{
							int num5=ar.get(j);
							if(num5!=num1 && visited[num5]==false)
							{
								queue.add(num5);
								visited[num5]=true;
							}
						}
					}
					for(int i=0;i<ar2.size();i++)
					{
						q.remove(new Integer(ar2.get(i)));
					}
					if(q.contains(num1)==false)
						q.add(num1);
				}
				else if(lca==num2)
				{
					Queue<Integer> queue=new LinkedList<>();
					boolean[] visited=new boolean[n+1];
					queue.add(num1);
					ArrayList<Integer> ar2=new ArrayList<>();
					while(queue.isEmpty()==false)
					{
						int num4=queue.poll();
						ArrayList<Integer> ar=graph.get(num4);
						ar2.add(num4);
						for(int j=0;j<ar.size();j++)
						{
							int num5=ar.get(j);
							if(num5!=num2 && visited[num5]==false)
							{
								queue.add(num5);
								visited[num5]=true;
							}
						}
					}
					for(int i=0;i<ar2.size();i++)
					{
						q.remove(new Integer(ar2.get(i)));
					}
					if(q.contains(num2)==false)
						q.add(num2);
				}
				else if(lca!=num1 && lca!=num2)
				{
					Queue<Integer> queue=new LinkedList<>();
					boolean[] visited=new boolean[n+1];
					queue.add(num1);
					ArrayList<Integer> ar2=new ArrayList<>();
					while(queue.isEmpty()==false)
					{
						int num4=queue.poll();
						ArrayList<Integer> ar=graph.get(num4);
						ar2.add(num4);
						for(int j=0;j<ar.size();j++)
						{
							int num5=ar.get(j);
							if(num5!=lca && visited[num5]==false)
							{
								queue.add(num5);
								visited[num5]=true;
							}
						}
					}
					for(int i=0;i<ar2.size();i++)
					{
						q.remove(new Integer(ar2.get(i)));
					}
					visited=new boolean[n+1];
					ar2=new ArrayList<>();
					queue.add(num2);
					while(queue.isEmpty()==false)
					{
						int num4=queue.poll();
						ArrayList<Integer> ar=graph.get(num4);
						ar2.add(num4);
						for(int j=0;j<ar.size();j++)
						{
							int num5=ar.get(j);
							if(num5!=lca && visited[num5]==false)
							{
								queue.add(num5);
								visited[num5]=true;
							}
						}
					}
					for(int i=0;i<ar2.size();i++)
					{
						q.remove(new Integer(ar2.get(i)));
					}
					if(q.contains(lca)==false)
						q.add(lca);
				}
			}
			pln("! "+q.poll());
		}
		System.out.print(sb.toString());
	}
			/**/
	static InputReader in=new InputReader(System.in);
	static OutputWriter out=new OutputWriter(System.out);
	public static long l()
	{
		String s=in.String();
		return Long.parseLong(s);
	}
	public static void pln(String value)
	{
		System.out.println(value);
	}
	public static int i()
	{
		return in.Int();
	}
	public static String s()
	{
		return in.String();
	}
}
	class InputReader 
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
	 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
	 
		public int read() {
			if (numChars== -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
	 
		public int Int() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
	 
		public String String() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
	 
		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	 
		public String next() {
			return String();
		}
	 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
	 
	class OutputWriter {
		private final PrintWriter writer;
	 
		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}
	 
		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}
	 
		public void print(Object...objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}
	 
		public void printLine(Object...objects) {
			print(objects);
			writer.println();
		}
	 
		public void close() {
			writer.close();
		}
	 
		public void flush() {
			writer.flush();
		}
	 
		}
	 
		class IOUtils {
	 
		public static int[] readIntArray(InputReader in, int size) {
			int[] array = new int[size];
			for (int i = 0; i < size; i++)
				array[i] = in.Int();
			return array;
		}
	 
	}