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;
#define ll long long
#define db double
#define ld long double
#define forr(i,a,n) for(int i=a;i<n;i++)
#define rep(i,n) forr(i,0,n)
#define repp(i,n) forr(i,1,n+1)
#define pb push_back
#define mp make_pair
#define vvi vector<vector<int> >
#define MAXN 0x3f3f3f3f
int ask(int l,int r){
	if(l==r)return 0;
	fflush(stdout);
	cout<<'?'<<' '<<l<<' '<<r<<endl;
	cin>>l;
	return l;
}
int main(){
	int n;
	cin>>n;
	int l=1,r=n,mid,pos;
	pos=ask(l,r);
	while(l<=r){
		if(l==r){
			cout<<'!'<<' '<<l;
			return 0;
		}
		mid=(l+r)/2;
		if(pos<=mid){
			if(mid<=1)l=mid+1;
			else if(ask(1,mid)==pos)r=mid;
				else l=mid+1;
		}
		else{
			if(mid+1>=n)r=mid;
			else if(ask(mid+1,n)==pos)l=mid+1;
				else r=mid;
		}
	}
	return 0;
}