#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using i64 = long long;
void __print(int x) { cerr << x; } void __print(long x) { cerr << x; } void __print(long long x) { cerr << x; } void __print(unsigned x) { cerr << x; } void __print(unsigned long x) { cerr << x; } void __print(unsigned long long x) { cerr << x; } void __print(float x) { cerr << x; } void __print(double x) { cerr << x; } void __print(long double x) { cerr << x; } void __print(char x) { cerr << '\'' << x << '\''; } void __print(const char* x) { cerr << '"' << x << '"'; } void __print(const string& x) { cerr << '"' << x << '"'; } void __print(bool x) { cerr << (x ? "true" : "false"); } template<typename T, typename V> void __print(const pair<T, V>& x) { cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}'; } template<typename T> void __print(const T& x) { int f = 0; cerr << '{'; for (auto& i : x) cerr << (f++ ? "," : ""), __print(i); cerr << "}"; } void _print() { cerr << "]\n"; } template <typename T, typename... V> void _print(T t, V... v) { __print(t); if (sizeof...(v)) cerr << ", "; _print(v...); }
#define dbg(x...) cerr << "[" << #x << "] = ["; _print(x)
#define ln "\n"
#define fastIO() ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#define all(x) (x).begin(), (x).end()
#define rep(i,a,b) for(int i=a; i<=b; ++i)
#define ar array
int Bit(int mask, int b) { return (mask >> b) & 1; }
const ll base = 311, MOD = 998244353, M = 1e9 + 7, INF = 1e18;
int min_cardinality(int N) {
set<int> T;
auto add = [&](int x) { T.insert(x); move_inside(x); };
auto del = [&](int x) { T.erase(x); move_outside(x); };
for (int i = 0; i < N; ++i) {
add(i);
if (press_button() > 1)
del(i);
}
int n_species = T.size();
map<int, set<int>> states;
states[1] = T;
states[N] = set<int>();
for (int i = 0; i < N; ++i) states[N].insert(i);
int lo = 2, hi = N / n_species, res = 1;
while (lo <= hi) {
int md = (lo + hi) / 2;
vector<int> just_added;
auto it = states.lower_bound(md)->second;
for (int i : it) if (!T.count(i)) {
add(i);
if (press_button() > md)
del(i);
else
just_added.push_back(i);
}
int x = T.size();
states[md] = T;
if (x >= n_species * md) {
res = md;
lo = md + 1;
}
else {
for (int i : just_added)
del(i);
hi = md - 1;
}
}
return res;
}
