#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
bool in[2011]; int sz[2011], mx[2011];
int p[2011];
int cnt = 0;
void move_in(int i){
i = p[i];
assert(!in[i]);
in[i] = true;
move_inside(i);
cnt++;
}
void move_out(int i){
i = p[i];
assert(in[i]);
in[i] = false;
move_outside(i);
cnt--;
}
int min_cardinality(int N) {
mt19937 rng(0);
for(int i = 0; i < N; i++) p[i] = i;
for(int i = 0; i < N; i++) swap(p[i], p[rng() % (i + 1)]);
fill(in, in + N, 0);
fill(sz, sz + N, 0);
for(int i = 0; i < N; i++){
move_in(i);
int c = press_button();
if(c >= 2) sz[i] = 2, move_out(i);
}
int K = cnt;
int L = 1, R = N / K;
fill(mx, mx + N, N + 1);
while(L != R){
int M = (L + R + 1) / 2;
for(int i = 0; i < N; i++){
if(mx[i] != N + 1 && mx[i] > M){
mx[i] = N + 1; move_out(i);
}
}
int prv = -1;
for(int i = 0; i < N; i++){
if(in[p[i]] || sz[i] > M) continue;
move_in(i);
int c = press_button(); mx[i] = c;
if(prv != -1 && c > prv) sz[i] = c;
if(c > M) move_out(i), mx[i] = N + 1;
prv = min(c, M);
}
if(cnt == M * K){
L = M;
}else{
R = cnt / K;
}
}
return L;
}
