Problem: The only difference between the easy and the hard version is the limit to the number of queries.

This is an interactive problem.

There is an array a of n different numbers. In one query you can ask the position of the second maximum element in a subsegment a[l..r]. Find the position of the maximum element in the array in no more than 20 queries.

A subsegment a[l..r] is all the elements a_l, a_{l + 1}, ..., a_r. After asking this subsegment you will be given the position of the second maximum from this subsegment in the whole array.

Input

The first line contains a single integer n (2 ≤ n ≤ 10^5) — the number of elements in the array.

Interaction

You can ask queries by printing "? l r" (1 ≤ l < r ≤ n). The answer is the index of the second maximum of all elements a_l, a_{l + 1}, ..., a_r. Array a is fixed beforehand and can't be changed in time of interaction.

You can output the answer by printing "! p", where p is the index of the maximum element in the array.

You can ask no more than 20 queries. Printing the answer doesn't count as a query.

After printing a query do not forget to output end of line and flush the output. Otherwise, you will 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 documentation for other languages 



Hacks

To make a hack, use the following test format.

In the first line output a single integer n (2 ≤ n ≤ 10^5). In the second line output a permutation of n integers 1 to n. The position of n in the permutation is the position of the maximum

Example

Input


5

3

4



Output


? 1 5

? 4 5

! 1

Note

In the sample suppose a is [5, 1, 4, 2, 3]. So after asking the [1..5] subsegment 4 is second to max value, and it's position is 3. After asking the [4..5] subsegment 2 is second to max value and it's position in the whole array is 4.

Note that there are other arrays a that would produce the same interaction, and the answer for them might be different. Example output is given in purpose of understanding the interaction.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastReader in = new FastReader(inputStream);
            PrintWriter out = new PrintWriter(outputStream);
            C1GuessingTheGreatestEasyVersion solver = new C1GuessingTheGreatestEasyVersion();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class C1GuessingTheGreatestEasyVersion {
        FastReader s;
        PrintWriter w;

        public void solve(int testNumber, FastReader s, PrintWriter w) {
            int n = s.nextInt();
            this.s = s;
            this.w = w;
            int min = query(1, n);
            int mid = 1 + n >> 1;
            if (n == 2) {
                if (min == 1) w.println("! 2");
                else w.println("! 1");
                w.flush();
                return;
            }
            int l = 1, r;
            if (min == n) {
                r = min - 1;
                while (l <= r) {
                    mid = l + r >> 1;
                    int res = query(min - mid, min);
                    if (res == min) r = mid - 1;
                    else l = mid + 1;
                }
                ++r;
                w.println("! " + (min - r));
            } else if (min == 1) {
                r = n - min;
                while (l <= r) {
                    mid = l + r >> 1;
                    int res = query(min, min + mid);
                    if (res == min) r = mid - 1;
                    else l = mid + 1;
                }
                ++r;
                w.println("! " + (min + r));
            } else {
                int minot = query(1, min);
                if (minot == min) {
                    r = min - 1;
                    while (l <= r) {
                        mid = l + r >> 1;
                        int res = query(min - mid, min);
                        if (res == min) r = mid - 1;
                        else l = mid + 1;
                    }
                    ++r;
                    w.println("! " + (min - r));
                } else {
                    r = n - min;
                    while (l <= r) {
                        mid = l + r >> 1;
                        int res = query(min, min + mid);
                        if (res == min) r = mid - 1;
                        else l = mid + 1;
                    }
                    ++r;
                    w.println("! " + (min + r));
                }
            }
            w.flush();
        }

        int query(int l, int r) {
            w.println("? " + l + " " + r);
            w.flush();
            return s.nextInt();
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(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 nextInt() {

            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 boolean isSpaceChar(int c) {

            if (filter != null)
                return filter.isSpaceChar(c);

            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

        }

    }
}