#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define mp make_pair
#define pii pair<int, int>
#define fi first
#define se second
int min_cardinality(int n){
vector<int> ord;
for (int i=1; i<n; ++i)ord.pb(i);
mt19937 gen(67);
shuffle(ord.begin(), ord.end(), gen);
int uq=1;
move_inside(0);
vector<bool> got(n, 0), ban(n, 0);
got[0]=1;
for (int i:ord){
move_inside(i);
got[i]=1;
if (press_button()==2)move_outside(i), got[i]=0;
else ++uq;
}
int low=1, high=n/uq+1;
while (low+1<high){
int mid=(low+high)/2, c=0, b=0;
vector<bool> toomuch(n, 0), added(n, 0);
for (int i:ord)if (got[i])++c;
for (int i:ord)if (!ban[i])++b;
if (b<uq*mid){
high=mid;
continue;
}
int extra=max(0, mid-low);
for (int i:ord)if (!got[i]&&!ban[i]){
move_inside(i);
got[i]=1;
added[i]=1;
if (extra)--extra, ++c;
else{
int res=press_button();
if (res>mid)move_outside(i), got[i]=0, added[i]=0, toomuch[i]=1;
else ++c, extra=mid-res;
}
if (c==uq*mid)break;
}
if (c==uq*mid)low=mid;
else{
high=mid;
for (int i:ord)if (added[i])move_outside(i), got[i]=0;
for (int i:ord)if (toomuch[i])ban[i]=1;
}
}
return low;
}
