#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define f0r(i, n) for (auto i = 0; i < (n); ++i)
#define fnr(i, n, k) for (auto i = (n); i < (k); ++i)
#define all(v) (v).begin(), (v).end()
#define pb push_back
#define F first
#define S second
#define ctn(x) cout << x << '\n'
#define forl(a, l) for (auto a : l)
#define ctl(l) for (auto &a : (l)) cout << a << ' '; cout << endl;
#define lb(v, x) (lower_bound(all(v), x) - begin(v))
#define ub(v, x) (upper_bound(all(v), x) - begin(v))
#define pq priority_queue
template <class T>
using V = vector<T>;
using ll = long long;
using vi = V<int>;
using vl = V<ll>;
using pi = pair<int, int>;
using ti = tuple<int, int, int>;
using Adj = V<vi>;
using vvi = V<vi>;
#include "insects.h"
int cnt = 0;
vi in;
V<vi> ts;
int exe(int k, int N) {
vi dn;
f0r(i, N) if (!in[i]) {
move_inside(i);
if (press_button() > k) move_outside(i);
else {
cnt += in[i] = 1;
dn.pb(i);
}
}
ts.pb(dn);
return cnt;
}
int min_cardinality(int N) {
in.assign(N, 0);
cnt = 0;
int D = exe(1, N);
int lo = 2, hi = N, ans = 1;
while (lo <= hi) {
int m = (lo + hi)/2;
if (exe(m, N) == D*m) {
lo = m+1;
ans = m;
} else {
hi = m-1;
if (hi < lo) break;
forl(i, ts.back()) if (in[i]) {
in[i] = 0;
move_outside(i);
cnt -= 1;
}
ts.pop_back();
}
}
return ans;
}
