#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
const int MAXN=1e5+5;
mt19937 rand1(time(0));
int l,r,cnt,cnt1,a[MAXN];bool vs[MAXN],vs1[MAXN];
void ins(int x) {++cnt1;move_inside(x-1);}
void dlt(int x) {--cnt1;move_outside(x-1);}
int qry() {return press_button();}
int min_cardinality(int n)
{
	for(int i=1;i<=n;++i) {ins(i);if(qry()>1) dlt(i);else vs[i]=1,++cnt;}
	if(cnt==1) return n;l=2;r=n/cnt;
	while(l<=r)
	{
		int mid=(l+r)/2;for(int i=1;i<=n;++i) vs1[i]=0,a[i]=i;
		shuffle(a+1,a+n+1,rand1);
		for(int i=1;i<=n;++i) if(!vs[a[i]])
		{
			if(cnt*mid<=cnt1) break;ins(a[i]);
			if(qry()>mid) dlt(a[i]);else vs1[a[i]]=1;
		}
		if(cnt*mid<=cnt1) {l=mid+1;for(int i=1;i<=n;++i) if(vs1[i]) vs[i]=1;}
		else {r=cnt1/cnt;for(int i=1;i<=n;++i) if(vs1[i]) dlt(i);else vs[i]=1;}
	}return r;
}