Problem: This is an interactive problem. In the interaction section below you will find the information about flushing the output.

The New Year tree of height h is a perfect binary tree with vertices numbered 1 through 2h - 1 in some order. In this problem we assume that h is at least 2. The drawing below shows one example New Year tree of height 3:

<image>

Polar bears love decorating the New Year tree and Limak is no exception. To decorate the tree, he must first find its root, i.e. a vertex with exactly two neighbours (assuming that h ≥ 2). It won't be easy because Limak is a little bear and he doesn't even see the whole tree. Can you help him?

There are t testcases. In each testcase, you should first read h from the input. Then you can ask at most 16 questions of format "? x" (without quotes), where x is an integer between 1 and 2h - 1, inclusive. As a reply you will get the list of neighbours of vertex x (more details in the "Interaction" section below). For example, for a tree on the drawing above after asking "? 1" you would get a response with 3 neighbours: 4, 5 and 7. Your goal is to find the index of the root y and print it in the format "! y". You will be able to read h for a next testcase only after printing the answer in a previous testcase and flushing the output.

Each tree is fixed from the beginning and it doesn't change during your questions.

Input

The first line of the input contains a single integer t (1 ≤ t ≤ 500) — the number of testcases.

At the beginning of each testcase you should read from the input a single integer h (2 ≤ h ≤ 7) — the height of the tree. You can't read the value of h in a next testcase until you answer a previous testcase.

Interaction

To ask a question about neighbours of vertex x, print "? x" (without quotes) on a separate line. Note, you must print an end-of-line character after the last character of the line and flush your output to get a response.

The response will consist of two lines. The first line will contain a single integer k (1 ≤ k ≤ 3) — the number of neighbours of vertex x. The second line will contain k distinct integers t1, ..., tk (1 ≤ t1 < ... < tk ≤ 2h - 1) — indices of neighbours of vertex x, gives in the increasing order.

After asking at most 16 questions you have to say y — the index of the root. Print "! y" (without quotes) and an end-of-line character, and flush the output.

Each tree is fixed from the beginning and it doesn't change during your questions.

You can get Idleness Limit Exceeded if you don't print anything or if you forget to flush the output.

To flush you can use (just printing a query/answer and end-of-line): 

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



In any moment if the program reads h = 0 or k = 0 it should immediately terminate normally (for example, calling exit(0)). It means that the system detected incorrect request/output from your program and printed 0 because if can't process your requests anymore. In this case you'll receive verdict "Wrong Answer", but if you ignore case h = 0 or k = 0 it could lead to "Runtime Error", "Time/Memory limit exceeded" or any other verdict because your program could read a trash from the closed input stream.

Hacking. To hack someone, use the following format:

The first line should contain a single integer t equal to 1 (only one testcase is allowed in hacks). The second line should contain a single integer h. Each of next 2h - 2 lines should contain two distinct integers ai and bi (1 ≤ ai, bi ≤ 2h - 1), denoting two nodes connected with an edge. The printed edges must form a perfect binary tree of height h.

Of course, contestant programs will not be able to see this input.

Examples

Input

1
3
3
4 5 7
2
1 2
1
2


Output

? 1
? 5
? 6
! 5


Input

2
2
1
3
2
1 2
2
1 2
4
3
3 12 13


Output

? 1
? 3
? 3
! 3
? 6
! 1

Note

In the first sample, a tree corresponds to the drawing from the statement.

In the second sample, there are two two testcases. A tree in the first testcase has height 2 and thus 3 vertices. A tree in the second testcase has height 4 and thus 15 vertices. You can see both trees on the drawing below.

<image>

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.Random;
import java.util.InputMismatchException;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.FileNotFoundException;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskF solver = new TaskF();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++) {
            solver.solve(i, in, out);
        }
        out.close();
    }

    static class TaskF {
        static boolean debug = false;
        Random rnd = new Random(112);
        InputReader in;
        OutputWriter out;
        int cntIter;
        boolean findAns;
        int h;
        IntArrayList[] gr;
        int[] parent;

        static {
            if (debug) {
                try {
                    FileOutputStream f = new FileOutputStream("file.txt");
                    System.setErr(new PrintStream(f));
                } catch (FileNotFoundException e) {
                    e.printStackTrace();
                }
            }
        }

        void f(String s) {
            if (debug) {
                System.err.println(s);
                System.err.flush();
            }
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            this.in = in;
            this.out = out;
            cntIter = 0;
            findAns = false;


            int vertex;
            int level;

            h = in.readInt();
//        h = 7;
            if (h == 0) {
                System.exit(0);
            }
            f("---------------------------------- testNumber : " + testNumber);

            vertex = 1 + rnd.nextInt((1 << h) - 1);
            gr = new IntArrayList[1 << h];

            getVertex(vertex, "first");
            if (findAns) {
                return;
            }

            if (gr[vertex].size() == 1) {
                level = h;
                f("FIND LIST: " + vertex);
            } else {
                IntArrayList l = new IntArrayList();
                IntArrayList r = new IntArrayList();

                f("goDOnw");
                dfsList(gr[vertex].get(0), vertex, l, 100500);
                if (findAns) {
                    return;
                }
                l.inPlaceReverse();

                f("goDOnw2");
                dfsList(gr[vertex].get(1), vertex, r, 100500);
                if (findAns) {
                    return;
                }

                IntArrayList all = new IntArrayList();
                all.addAll(l);
                all.add(vertex);
                all.addAll(r);

                level = h - all.size() / 2;
                vertex = all.get(all.size() / 2);

                f("goDOnw::all " + all);
                f("goDOnw::vertex " + vertex);
            }

            parent = new int[1 << h];
            Arrays.fill(parent, -1);

            for (int to : gr[vertex]) {
                if (gr[to] == null) {
                    parent[vertex] = to;
                    vertex = to;
                    break;
                }
            }
            --level;

            for (; ; --level) {

                if (level < 0) {
                    throw new RuntimeException();
                }

                getVertex(vertex, "level: " + level + " for(;;--level) lol");
                if (findAns) {
                    return;
                }

                if (level <= 3) {
                    IntArrayList arr = new IntArrayList();
                    for (int to : gr[vertex]) {
                        if (parent[to] == vertex) {
                            continue;
                        }
                        getVertex(to, "level <= 3 part I");
                        if (findAns) {
                            return;
                        }
                        parent[vertex] = to;
                        arr.add(to);
                    }

                    IntArrayList list2 = new IntArrayList();
                    for (int v : arr) {
                        getVertex(v, "level <= 3 part II");
                        if (findAns) {
                            return;
                        }
                        for (int to : gr[v]) {
                            if (parent[to] <= 0) {
                                list2.add(to);
                            }
                        }
                    }

                    for (int i = 0; i < 3; i++) {
                        getVertex(list2.get(i), "level <= 3 part III");
                        if (findAns) {
                            return;
                        }
                    }

                    out.printLine("! " + list2.get(3));
                    out.flush();
                    return;
                } else {
                    boolean wasGo = false;
                    for (int to : gr[vertex]) {
                        if (parent[to] == vertex) {
                            continue;
                        }
                        if (!wasGo) {
                            wasGo = true;
                            IntArrayList arr = new IntArrayList();
                            if (!dfsList(to, vertex, arr, h - level)) {
                                if (findAns) {
                                    return;
                                }
                                parent[vertex] = to;
                                vertex = to;
                                break;
                            }
                        } else {
                            parent[vertex] = to;
                            vertex = to;
                            break;
                        }
                    }
                }
            }
        }

        boolean dfsList(int v, int p, IntArrayList order, int maxDepth) {
            if (maxDepth == 0) {
                return false;
            }

            order.add(v);
            getVertex(v, "dfsList");
            if (findAns) {
                return false;
            }

            if (gr[v].size() == 1) {
                return true;
            }

            for (int j = 0; ; j++) {
                int to = gr[v].get(j);
                if (to != p) {
                    return dfsList(to, v, order, maxDepth - 1);
                }
            }
        }

        void getVertex(int v, String s) {
            if (gr[v] != null) {
                f("already find v: " + v + "   " + s);
                return;
            }

            ++cntIter;
            f(cntIter + ") getVertex: " + v + "       " + s);
            if (17 <= cntIter) {
                throw new RuntimeException("So many ex: " + cntIter);
            }

            out.printLine("? " + v);
            out.flush();
            IntArrayList arr = new IntArrayList();

            //
            int cnt = in.readInt();
            for (int i = 0; i < cnt; i++) {
                arr.add(in.readInt());
            }
            if (cnt == 0) {
                System.exit(0);
            }
        /**/

        /*/
        for (int x : new int[]{2 * v, 2 * v + 1, v / 2}) {
            if (1 <= x && x <= (1 << h) - 1) {
                arr.add(x);
            }
        }
        /**/

            for (int i = 0; i < arr.size(); i++) {
                arr.swap(i, rnd.nextInt(arr.size()));
            }

            gr[v] = arr;

            if (arr.size() == 2) {
                out.printLine("! " + v);
                out.flush();
                findAns = true;
            }
        }

    }

    static class IntArrayList extends IntAbstractStream implements IntList {
        private int size;
        private int[] data;

        public IntArrayList() {
            this(3);
        }

        public IntArrayList(int capacity) {
            data = new int[capacity];
        }

        public IntArrayList(IntCollection c) {
            this(c.size());
            addAll(c);
        }

        public IntArrayList(IntStream c) {
            this();
            if (c instanceof IntCollection) {
                ensureCapacity(((IntCollection) c).size());
            }
            addAll(c);
        }

        public IntArrayList(IntArrayList c) {
            size = c.size();
            data = c.data.clone();
        }

        public IntArrayList(int[] arr) {
            size = arr.length;
            data = arr.clone();
        }

        public int size() {
            return size;
        }

        public int get(int at) {
            if (at >= size) {
                throw new IndexOutOfBoundsException("at = " + at + ", size = " + size);
            }
            return data[at];
        }

        private void ensureCapacity(int capacity) {
            if (data.length >= capacity) {
                return;
            }
            capacity = Math.max(2 * data.length, capacity);
            data = Arrays.copyOf(data, capacity);
        }

        public void addAt(int index, int value) {
            ensureCapacity(size + 1);
            if ((index > size) || (index < 0)) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != size) {
                System.arraycopy(data, index, data, index + 1, size - index);
            }
            data[index] = value;
            size++;
        }

        public void removeAt(int index) {
            if ((index >= size) || (index < 0)) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != (size - 1)) {
                System.arraycopy(data, index + 1, data, index, size - index - 1);
            }
            size--;
        }

        public void set(int index, int value) {
            if (index >= size) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            data[index] = value;
        }

    }

    static interface IntList extends IntReversableCollection {
        public abstract int get(int index);

        public abstract void set(int index, int value);

        public abstract void addAt(int index, int value);

        public abstract void removeAt(int index);

        default public void swap(int first, int second) {
            if (first == second) {
                return;
            }
            int temp = get(first);
            set(first, get(second));
            set(second, temp);
        }

        default public IntIterator intIterator() {
            return new IntIterator() {
                private int at;
                private boolean removed;

                public int value() {
                    if (removed) {
                        throw new IllegalStateException();
                    }
                    return get(at);
                }

                public boolean advance() {
                    at++;
                    removed = false;
                    return isValid();
                }

                public boolean isValid() {
                    return !removed && (at < size());
                }

                public void remove() {
                    removeAt(at);
                    at--;
                    removed = true;
                }
            };
        }


        default public void add(int value) {
            addAt(size(), value);
        }

        default public void inPlaceReverse() {
            for (int i = 0, j = size() - 1; i < j; i++, j--) {
                swap(i, j);
            }
        }

    }

    static interface IntCollection extends IntStream {
        public int size();

        default public void add(int value) {
            throw new UnsupportedOperationException();
        }

        default public IntCollection addAll(IntStream values) {
            for (IntIterator it = values.intIterator(); it.isValid(); it.advance()) {
                add(it.value());
            }
            return this;
        }

    }

    static abstract class IntAbstractStream implements IntStream {

        public String toString() {
            StringBuilder builder = new StringBuilder();
            boolean first = true;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                if (first) {
                    first = false;
                } else {
                    builder.append(' ');
                }
                builder.append(it.value());
            }
            return builder.toString();
        }


        public boolean equals(Object o) {
            if (!(o instanceof IntStream)) {
                return false;
            }
            IntStream c = (IntStream) o;
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                if (it.value() != jt.value()) {
                    return false;
                }
                it.advance();
                jt.advance();
            }
            return !it.isValid() && !jt.isValid();
        }


        public int hashCode() {
            int result = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                result *= 31;
                result += it.value();
            }
            return result;
        }

    }

    static interface IntReversableCollection extends IntCollection {
    }

    static interface IntStream extends Iterable<Integer>, Comparable<IntStream> {
        public IntIterator intIterator();

        default public Iterator<Integer> iterator() {
            return new Iterator<Integer>() {
                private IntIterator it = intIterator();

                public boolean hasNext() {
                    return it.isValid();
                }

                public Integer next() {
                    int result = it.value();
                    it.advance();
                    return result;
                }
            };
        }

        default public int compareTo(IntStream c) {
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                int i = it.value();
                int j = jt.value();
                if (i < j) {
                    return -1;
                } else if (i > j) {
                    return 1;
                }
                it.advance();
                jt.advance();
            }
            if (it.isValid()) {
                return 1;
            }
            if (jt.isValid()) {
                return -1;
            }
            return 0;
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.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 readInt() {
            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 readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return (c == ' ') || (c == '\n') || (c == '\r') || (c == '\t') || (c == -1);
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static interface IntIterator {
        public int value() throws NoSuchElementException;

        public boolean advance();

        public boolean isValid();

    }

    static 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();
        }

    }
}