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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

typedef long long int in;

in q(in l,in r)
{
	if(l==r)
	return 1e9;

	in e;

	cout<<"? "<<l<<" "<<r<<endl;
	cin>>e;

	return e;
}

int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);

	in n,ans;
	cin>>n;

	in i=q(1,n);

	if(i==1||(i!=1&&i!=q(1,i)))
	{
		in l=i,h=n,m;

		while(l<=h)
		{
			m=(l+h)/2;

			if(q(i,m)==i)
			{
				ans=m;
				h=m-1;
			}
			else
			l=m+1;
		}
	}
	else
	{
		in l=1,h=i,m;

		while(l<=h)
		{
			m=(l+h)/2;

			if(q(m,i)==i)
			{
				ans=m;
				l=m+1;
			}
			else
			h=m-1;
		}
	}
	
	cout<<"! "<<ans<<endl;
	
	return 0;
}