#include "insects.h"
#include "bits/stdc++.h"
using namespace std;
const int N = 2e3 + 5;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
map<vector<int>,int> Cache;
int vis[N], Kill[N] , D , tot = 0;
inline bool Add(int x){
if(vis[x] || Kill[x]) return 0;
vis[x]=1;
tot++;
move_inside(x);
return 1;
}
inline bool Rem(int x){
if(!vis[x] || Kill[x]) return 0;
vis[x]=0;
tot--;
move_outside(x);
return 1;
}
inline int Get(){
vector<int> v;
for(int i=0;i<N;i++) if(vis[i]) v.push_back(i);
if(Cache.count(v)) return Cache[v];
return Cache[v] = press_button();
}
int min_cardinality(int n){
vector<int> ar;
for(int i=0;i<n;i++) ar.push_back(i);
shuffle(ar.begin(),ar.end(),rng);
for(int i : ar){
Add(i);
if(i == 0 || Get() == 1) continue;
Rem(i);
}
for(int i : ar) if(vis[i]) Kill[i] = 1;
D = tot;
if(D > n / 2) return 1;
if(D == 1) return n;
int ans = 1, l = 2 , r = n / D;
while(l <= r){
shuffle(ar.begin(),ar.end(),rng);
int B = (l + r) / 2;
for(int i : ar) if(!Kill[i]) Rem(i);
vector<int> to_kill;
for(int i : ar){
if(vis[i] || Kill[i]) continue;
Add(i);
if(tot > B && Get() > B){
Rem(i);
to_kill.push_back(i);
}
}
if(tot == B * D){
l = B + 1;
ans = B;
r = min(r, B + (int) to_kill.size() / D);
if(to_kill.size() < D) return ans;
for(int i : ar) if(vis[i]) Kill[i] = 1;
}
else{
for(int x : to_kill) Kill[x] = 1;
r = min(tot / D, B - 1);
}
}
return ans;
}
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