#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include "insects.h"
#define all(a) a.begin(), a.end()
using namespace std;
using namespace __gnu_pbds;
//int FRQ[10000];
//int a[10000];
//
//void move_inside(int i) {
// FRQ[a[i]]++;
// cout << "ADDED " << i << endl;
//}
//void move_outside(int i) {
// FRQ[a[i]]--;
// cout << "REMOVED " << i << endl;
//
//}
//int press_button() {
// cout << "ANSWER " << *max_element(FRQ, FRQ + 10000) << endl;
// return *max_element(FRQ, FRQ + 10000);
//}
int min_cardinality(int n) {
int frq[n+1]{}, a[n]{};
int val = 0;
for (int i = 0; i < n; i++) {
move_inside(i);
for (int j = 0; j < i; j++) {
move_inside(j);
if (press_button() == 2) {
a[i] = a[j];
move_outside(j);
break;
}
move_outside(j);
}
if (a[i] == 0) {
a[i] = ++val;
}
frq[a[i]] += 1;
move_outside(i);
}
int ans = n;
for (int i = 1; i <= n; i++) if (frq[i] > 0)
ans = min(ans, frq[i]);
return ans;
}
