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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
   static Scanner sc=new Scanner(System.in);
    static int ask(int l,int r) {
        if(l==r)
        return -1;
        System.out.println("? "+" "+l+" "+r);
        
       int x=sc.nextInt();
	return x;
    }
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		int n=sc.nextInt();
		int secmaxpos=ask(1,n);
		if(ask(1,secmaxpos)==secmaxpos) {
		    int low=1;
		    int high=secmaxpos;
		    while(low<high) {
		        int mid=(low+high+1)/2;
		        if(ask(mid,n)==secmaxpos)
		        low=mid;
		        else 
		        high=mid-1;
		    }
		    System.out.println("! "+" "+low);
		}
		else {
		    int low=secmaxpos;
		    int high=n;
		    while(low<high) {
		        int mid=(low+high)/2;
		        if(ask(1,mid)==secmaxpos)
		        high=mid;
		        else 
		        low=mid+1;
		    }
		    System.out.println("! "+" "+low);
		}
	}
}