#include <bits/stdc++.h>
using namespace std;
using i32 = int;
using i64 = long long;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<VV<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
}
#define OVERRIDE4(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, l, r) for (i32 i = (i32)(l); i < (i32)(r); ++i)
#define REP(...) OVERRIDE4(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, l, r) for (i32 i = (i32)(r)-1; i >= (i32)(l); --i)
#define PER(...) OVERRIDE4(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32) size(x)
void dbg(i32 x) { cerr << x; }
void dbg(i64 x) { cerr << x; }
template <typename T, typename U>
void dbg(pair<T, U> p) {
cerr << '(';
dbg(p.first);
cerr << ", ";
dbg(p.second);
cerr << ')';
}
template <typename T>
void dbg(V<T> arr) {
cerr << '[';
REP(i, LEN(arr)) {
if (i) {
cerr << ", ";
}
dbg(arr[i]);
}
cerr << ']';
}
void debug() { cerr << '\n'; }
template <typename Head, typename... Tail>
void debug(Head head, Tail... tail) {
dbg(head);
cerr << ", ";
debug(tail...);
}
#ifdef DEBUGF
#define DBG(...) \
do { \
cerr << #__VA_ARGS__ << " : "; \
debug(__VA_ARGS__); \
} while (false)
#else
#define DBG(...) (void)0
#endif
#include "insects.h"
i32 min_cardinality(i32 n) {
i32 kind = 0;
V<i32> rem;
REP(i, n) {
move_inside(i);
if (press_button() == 1) {
++kind;
rem.push_back(i);
} else {
move_outside(i);
}
}
for (i32 ele : rem) {
move_outside(ele);
}
rem.clear();
auto judge = [&](i32 th) -> bool {
REP(i, n) {
move_inside(i);
if (press_button() <= th) {
rem.push_back(i);
} else {
move_outside(i);
}
}
bool ans = (LEN(rem) == (i64)th * kind);
for (i32 ele : rem) {
move_outside(ele);
}
rem.clear();
return ans;
};
i32 ok = 1, ng = n + 1;
while (ng - ok > 1) {
i32 mid = (ok + ng) / 2;
(judge(mid) ? ok : ng) = mid;
}
return ok;
}
