#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ari2 = array<int, 2>;
using ari3 = array<int, 3>;
using arl2 = array<ll, 2>;
using arl3 = array<ll, 3>;
template <class T> using vt = vector<T>;
#define all(x) begin(x), end(x)
#define size(x) (int((x).size()))
#define REP(a,b,c,d) for(int a=(b);(d)>0?a<=(c):a>=(c);a+=(d))
#define FOR(a,b,c) REP(a,b,c,1)
#define ROF(a,b,c) REP(a,b,c,-1)
int min_cardinality(int N) {
vt<int> A, B;
move_inside(0);
A.push_back(0);
FOR(i, 1, N-1) {
move_inside(i);
if (press_button() == 1) {
A.push_back(i);
} else {
move_outside(i);
B.push_back(i);
}
}
if (size(A) > double(N) / 4.0) {
int ret = 1;
const int bef = size(A);
while (true) {
for (const auto &i : A)
move_outside(i);
const vt<int> C = B;
A.clear();
B.clear();
for (const auto &i : C) {
move_inside(i);
if (!size(A) || press_button() == 1) {
A.push_back(i);
} else {
B.push_back(i);
move_outside(i);
}
}
if (size(A) != bef)
break;
ret++;
}
return ret;
}
int ret = N;
const auto dnc = [&](auto &&self, const vt<int> &Q, const vt<int> &R, bool in) -> void {
if (size(Q) == 1) {
ret = min(ret, size(R) + 1);
return;
}
if (in) {
FOR(i, size(Q)/2, size(Q)-1)
move_outside(Q[i]);
} else {
FOR(i, size(Q)/2, size(Q)-1)
move_inside(Q[i]);
}
vt<int> lft, rht;
for (const auto &i : R) {
move_inside(i);
const int v = press_button();
(v > 1 && in || v == 1 && !in ? lft : rht).push_back(i);
move_outside(i);
}
self(self, vt<int>(Q.begin(), Q.begin() + size(Q) / 2), lft, in);
self(self, vt<int>(Q.begin() + size(Q) / 2, Q.end()), rht, !in);
};
dnc(dnc, A, B, true);
return ret;
}
