#include <bits/stdc++.h>
using namespace std;
#define ld long double
#define mp make_pair
#define pb push_back
#define pii pair<int,int>
#define fi first
#define se second
/*草，以后一定要拿金牌啊!!! 注意数值范围拿分数哦*/
#include "insects.h"
const int S=1e5+5;
mt19937 rand1(time(0));
int l,r,cnt,cnt1,a[S],n;
bool vs[S],vs1[S];
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) {
n=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)>>1;
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;
}
