#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define replr(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define reprl(i, a, b) for (int i = int(a); i >= int(b); --i)
#define rep(i, n) for (int i = 0; i < int(n); ++i)
#define mkp(a, b) make_pair(a, b)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<PII> VPI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<VPI> VVPI;
typedef pair<ll, ll> PLL;
typedef vector<ll> VL;
typedef vector<PLL> VPL;
typedef vector<VL> VVL;
typedef vector<VVL> VVVL;
typedef vector<VPL> VVPL;
template<class T> T setmax(T& a, T b) {if (a < b) return a = b; return a;}
template<class T> T setmin(T& a, T b) {if (a < b) return a; return a = b;}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<class T>
using indset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#include "insects.h"
mt19937 rng;
VI rngind;
void movein(int i) {
move_inside(rngind[i]);
}
void moveout(int i) {
move_outside(rngind[i]);
}
int n, D;
int solution1() {
VI vis(n);
int ans = 2e9;
replr(i, 0, n-1) if (!vis[i]) {
vis[i] = true;
movein(i);
int cnt = 1;
replr(j, i+1, n-1) if (!vis[j]) {
movein(j);
if (press_button() == 2) {
vis[j] = true;
cnt++;
}
moveout(j);
}
setmin(ans, cnt);
moveout(i);
}
return ans;
}
int solution2() {
VI vis(n);
int k = -1;
int ans = 0;
replr(i, 0, n-1) if (!vis[i]) {
vis[i] = true;
movein(i);
VI a;
a.pb(i);
replr(j, i+1, n-1) if (!vis[j]) {
movein(j);
if (press_button() == 2) {
moveout(j);
} else {
vis[j] = true;
a.pb(j);
}
}
for (int i : a) moveout(i);
if (k == -1) {
k = a.size();
} else if (a.size() != k) break;
ans++;
}
return ans;
}
int min_cardinality(int N) {
rng = mt19937(chrono::steady_clock().now().time_since_epoch().count());
n = N;
rngind = VI(n);
rep(i, n) rngind[i] = i;
/*shuffle(all(rngind), rng);*/
rep(i, n) movein(i);
D = press_button();
rep(i, n) moveout(i);
if (D < sqrt(n)) return solution1();
return solution2();
return -1;
}
