#include "insects.h"
#include "bits/stdc++.h"
using namespace std;
mt19937 rng(time(0));
int rand(int l, int r) {
int x = rng(); x = abs(x);
return x % (r - l + 1) + l;
}
int min_cardinality(int n) {
vector<int> ord(n);
iota(ord.begin(), ord.end(), 0);
for (int i = 1; i < n; i++) swap(ord[i], ord[rand(0, i)]);
vector<bool> vis(n);
vector<int> pos = {0};
move_inside(0);
for (int i = 1; i < n; i++) {
move_inside(i);
int x = press_button();
if (x > 1) {
move_outside(i);
} else {
pos.emplace_back(i);
}
}
for (int x: pos) vis[x] = true;
int sq = sqrt(n);
if (pos.size() <= sq) {
int ans = 1e9;
for (int t = 0; t < pos.size(); t++) {
int old = 1;
vector<int> added;
for (int i: ord) {
if (vis[i]) continue;
move_inside(i);
int nw = press_button();
if (nw == old) {
move_outside(i);
} else {
added.emplace_back(i);
vis[i] = true;
old = nw;
}
}
for (int x: added) move_outside(x);
ans = min(ans, old);
if (ans == 1) break;
}
return ans;
}
if (pos.size() == 1) return n;
if (pos.size() == n) return 1;
for (int cnt = 2; ; cnt++) {
for (int i: ord) {
if (vis[i]) continue;
move_inside(i);
int now = press_button();
if (now > cnt) {
move_outside(i);
} else {
vis[i] = true;
}
}
// cout << '\t' << cnt << endl;
// for (int i = 0; i < n; i++) cout << vis[i];
// cout << endl;
if (count(vis.begin(), vis.end(), true) != cnt * pos.size()) return cnt - 1;
if (count(vis.begin(), vis.end(), true) == n) return cnt;
}
}
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