#include "insects.h"
#include<bits/stdc++.h>
using namespace std;
int min_cardinality(int N) {
if (N <= 1000) {
int ans = N;
int d = 0;
vector<int> allIdx(N);
for (int i = 0; i < N; i++){
allIdx[i] = i;
}
for (int i = 0; i < allIdx.size(); i++){
move_inside(allIdx[i]);
int count = press_button();
if (count > 1){
move_outside(allIdx[i]);
}
else{
allIdx.erase(allIdx.begin() + i);
i--;
d++;
}
}
int curAmount = d;
for (int m = 2; m <= N; m++){
for (int i = 0; i < allIdx.size(); i++){
move_inside(allIdx[i]);
int count = press_button();
if (count > m){
move_outside(allIdx[i]);
}
else{
allIdx.erase(allIdx.begin() + i);
i--;
curAmount++;
if (curAmount == d * m) break;
}
}
if (d * m > curAmount){
return m - 1;
}
}
return N;
}
vector<int> temp;
int d = 0;
for (int i = 0; i < N; i++){
move_inside(i);
int count = press_button();
if (count > 1){
move_outside(i);
}
else{
temp.push_back(i);
d++;
}
}
for (int i = 0; i < temp.size(); i++){
move_outside(temp[i]);
}
int ans = N;
int oriN = N;
vector<int> newUse(N);
for (int i = 0; i < N; i++){
newUse[i] = i;
}
while(1){
int B = N / d;
vector<int> all;
for (int i = 0; i < newUse.size(); i++){
move_inside(newUse[i]);
int count = press_button();
if (count > B){
move_outside(newUse[i]);
}
else{
all.push_back(newUse[i]);
if (all.size() == B * d) break;
}
}
if (all.size() == B * d){
return B;
}
N = all.size();
for (int i = 0; i < all.size(); i++){
move_outside(all[i]);
}
newUse = all;
}
return 1;
}
#ifdef LOCAL
#include "insects.h"
#include <cassert>
#include <cstdio>
#include <algorithm>
#include <map>
#include <set>
#include <string>
#include <vector>
static constexpr int kMaxQueries = 40000;
static int N;
// Insect types are compressed to colors in the range [0, N).
static std::vector<int> color;
static std::vector<bool> in_box;
static std::vector<int> color_occurrences;
static std::multiset<int> max_occurrences;
static std::vector<int> op_counter(3, 0);
static inline void protocol_violation(std::string message) {
printf("Protocol Violation: %s\n", message.c_str());
exit(0);
}
void move_inside(int i) {
if (i < 0 || i >= N) {
protocol_violation("invalid parameter");
}
++op_counter[0];
if (op_counter[0] > kMaxQueries) {
protocol_violation("too many calls");
}
if (!in_box[i]) {
in_box[i] = true;
max_occurrences.erase(max_occurrences.find(color_occurrences[color[i]]));
++color_occurrences[color[i]];
max_occurrences.insert(color_occurrences[color[i]]);
}
}
void move_outside(int i) {
if (i < 0 || i >= N) {
protocol_violation("invalid parameter");
}
++op_counter[1];
if (op_counter[1] > kMaxQueries) {
protocol_violation("too many calls");
}
if (in_box[i]) {
in_box[i] = false;
max_occurrences.erase(max_occurrences.find(color_occurrences[color[i]]));
--color_occurrences[color[i]];
max_occurrences.insert(color_occurrences[color[i]]);
}
}
int press_button() {
++op_counter[2];
if (op_counter[2] > kMaxQueries) {
protocol_violation("too many calls");
}
return *(max_occurrences.rbegin());
}
int main() {
assert(1 == scanf("%d", &N));
color.resize(N);
in_box.assign(N, false);
std::map<int, int> type_to_color;
for (int i = 0; i < N; ++i) {
int Ti;
assert(1 == scanf("%d", &Ti));
if (type_to_color.find(Ti) == type_to_color.end()) {
int new_color = type_to_color.size();
type_to_color[Ti] = new_color;
max_occurrences.insert(0);
}
color[i] = type_to_color[Ti];
}
color_occurrences.assign(type_to_color.size(), 0);
int answer = min_cardinality(N);
int Q = *std::max_element(op_counter.begin(), op_counter.end());
printf("%d\n", answer);
printf("%d\n", Q);
return 0;
}
#endif
