#ifndef davele
#include "insects.h"
#endif // davele
#include <bits/stdc++.h>
//#define int long long
#define pii pair<int, int>
#define fi first
#define se second
#define vi vector <int>
#define pq priority_queue
#define MASK(i) (1ll<<(i))
#define BIT(x, i) (((x) >> (i)) & 1)
#define x0 ___x0
#define y0 ___y0
#define div ___div
#define next ___next
#define prev ___prev
#define left ___left
#define right ___right
#define pos pisosi
#define pb push_back
#define pf push_front
using namespace std;
//const int mod = ;
//void add (int &a, const int&b){
// a+=b;
// if (a>=mod) a-=mod;
//}
//
//void sub (int&a, const int&b){
// a-=b;
// if (a<0) a+=mod;
//}
//
//void mul (int&a, const int&b){
// a*=b;
// a%=mod;
//}
template<class X, class Y>
bool minimize(X &x, const Y&y){
if (x<=y) return false;
else{
x = y;
return true;
}
}
template<class X, class Y>
bool maximize (X &x, const Y&y){
if (x>=y) return false;
else{
x = y;
return true;
}
}
////////////////////////////////////////////////////////////////////////////
const int lim = 2e3, limit = lim+5;
int n, inMachine[limit], ini[limit], old[limit];
bool banned[limit], curbanned[limit];
#ifdef davele
int cnti, cnto, cntp;
int A[limit], ts[limit];
void move_inside( int i ){
cnti++;
// cerr<<"i "<<i<<"\n";
ts[A[i]]++;
}
void move_outside (int i){
cnto++;
// cerr<<"o "<<i<<"\n";
ts[A[i]]--;
}
int press_button(){
cntp++;
// cerr<<"p \n";
int ret = 1;
for (int i=0; i<=lim; i++) maximize (ret, ts[i]);
return ret;
}
#endif // davele
mt19937_64 rng (chrono::high_resolution_clock::now().time_since_epoch().count());
int min_cardinality (int N){
n = N;
vector <int> id;
for (int i=0; i<n; i++) id.pb(i);
//
int numDiff = 0;
for (int i=0; i<n; i++){
banned[i] = false;
move_inside(i);
if (press_button()>1){
move_outside(i);
inMachine[i] = false;
ini[i] = false;
}
else{
ini[i] = true;
numDiff++;
inMachine[i] = true;
}
}
// cerr<<numDiff<<"\n";
int numCur = numDiff;
//
int left = 2, right = N/numDiff, ret = 1;
int loop = 0;
while (left<=right){
loop ++;
int mid = (left+right)/2;
int num = numCur;
for (int i=0; i<n; i++) curbanned[i] = banned[i];
for (int i=0; i<n; i++) old[i] = inMachine[i];
shuffle (id.begin(), id.end(), rng);
for (int i = 0; i < n; i++){
int idx = id[i];
if (numCur == numDiff*mid) break;
if (inMachine[idx] || banned[idx]) continue;
move_inside(idx);
numCur++;
inMachine[idx] = true;
// cerr<<press_button()<<"\n";
if (press_button()>mid){
move_outside(idx);
numCur--;
inMachine[idx] = false;
curbanned[idx] = true;
}
}
// cerr<<mid<<" "<<numCur<<" "<<numDiff<<"\n";
if (numCur==(numDiff*mid)){
ret = mid;
left = mid+1;
}
else{
right = mid-1;
for (int i=0; i<n; i++){
if (inMachine[i] && !old[i]) if (left<=right) move_outside(i);
inMachine[i] = old[i];
}
for (int i=0; i<n; i++) banned[i] = curbanned[i];
numCur = num;
}
}
// cerr<<"loop "<<loop<<"\n";
return ret;
}
/*
signed main(){
freopen("insects.inp", "r", stdin);
freopen("insects.out", "w", stdout);
int n;
cin>>n;
for (int i=0; i<n; i++) cin>>A[i];
cout<<min_cardinality(n);
cerr<<"inside "<<cnti<<" outside "<<cnto<<" press "<<cntp<<"\n";
}
*/
