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.*;
import java.util.Arrays;
 
public class codeforces { 
	
	static int ask(int l,int r)throws IOException {
		if(l==r) {
			return -1;
		}
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        
		int out1;
		System.out.println("? "+l+" "+r);
    	System.out.flush();
    	out1=Integer.parseInt(br.readLine());
    	return out1;
	}
	public static void main(String[] args)throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        int l=1;
        int r=n;
        int pos=ask(1,n);
        if(ask(1,pos)==pos) {
        	l=1;
        	r=pos;
        	while(l<r) {
        		int mid=(l+r+1)/2;
        		if(ask(mid,n)==pos) {
        			l=mid;
        		}
        		else {
        			r=mid-1;
        		}
        	}
        	System.out.println("! "+l);
        }
        else {
        	l=pos;
        	r=n;
        	while(l<r) {
        		int mid=(l+r)/2;
        		if(ask(pos,mid)==pos) {
        			r=mid;
        		}
        		else {
        			l=mid+1;
        			
        		}
        	}
        	System.out.println("! "+l);
        }
       
 
	}
 
}