#include <bits/stdc++.h>
#include "insects.h"
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define ALL(v) (v).begin(), (v).end()
#define MASK(i) (1LL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
// mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng(1);
ll rngesus(ll l, ll r){return ((ull) rng()) % (r - l + 1) + l;}
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll LASTBIT(ll mask){return mask & (-mask);}
ll pop_cnt(ll mask){return __builtin_popcountll(mask);}
ll ctz(ll mask){return __builtin_ctzll(mask);}
ll clz(ll mask){return __builtin_clzll(mask);}
ll logOf(ll mask){return 63 - clz(mask);}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b){a = b; return true;}
return false;
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b){a = b; return true;}
return false;
}
template <class T>
void printArr(T& a, string separator = " ", string finish = "\n", ostream& out = cout){
for(auto i: a) out << i << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
// namespace Grader{
// int n;
// vector<int> a;
// set<int> S;
// int o_cnt[3];
// void move_inside(int i){
// o_cnt[0]++;
// S.insert(i);
// }
// void move_outside(int i){
// o_cnt[1]++;
// S.erase(i);
// }
// int press_button(){
// o_cnt[2]++;
// map<int, int> mp;
// int ans = 0;
// for(int i: S) {
// maximize(ans, ++mp[a[i]]);
// }
// return ans;
// }
int BS(int l, int r, int d_cnt, vector<int> &S, vector<int> space){
if (l == r) return l;
int mid = (l + r + 1) >> 1;
vector<int> left, right;
for(int i: space){
if (S.size() == d_cnt * mid) {
right.push_back(i);
continue;
}
move_inside(i);
S.push_back(i);
if (press_button() > mid) {
move_outside(i);
right.push_back(i);
S.pop_back();
}
else left.push_back(i);
}
if (S.size() == d_cnt * mid){
return BS(mid, r, d_cnt, S, right);
}
else{
for(int i: left) {
move_outside(i);
S.pop_back();
}
return BS(l, mid - 1, d_cnt, S, left);
}
return 0;
}
int min_cardinality(int n){
//find number of distinct dud
vector<int> S;
for(int i = 0; i<n; ++i){
move_inside(i);
S.push_back(i);
if (i > 0 && press_button() > 1) {
move_outside(i);
S.pop_back();
}
}
int d_cnt = S.size();
sort(ALL(S));
if (d_cnt == 1) return n;
vector<int> space;
for(int i= 0; i<n; ++i) if (!binary_search(ALL(S), i)) space.push_back(i);
shuffle(ALL(space), rng);
return BS(1, n / d_cnt, d_cnt, S, space);
}
// pair<bool, int> solve(int _n){
// n = _n;
// a.resize(n);
// S.clear();
// memset(o_cnt, 0, sizeof o_cnt);
// for(int i = 0; i<n; ++i) a[i] = rngesus(1, 10);
// int ans = min_cardinality(n);
// map<int, int> mp;
// for(int i: a) mp[i]++;
// int mi = 1e9;
// for(auto i: mp) minimize(mi, i.second);
// return make_pair(mi == ans, max({o_cnt[0], o_cnt[1], o_cnt[2]}));
// }
// }
// int main(void){
// ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
// int n = 2000;
// pair<bool, int> verdict = Grader::solve(n);
// if (verdict.first) cout << "AC\n";
// else cout << "WA\n";
// cout << "Operation cnt: " << verdict.second << "\n";
// return 0;
// }
