#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
vector<int> ord, cand;
int vis[2000], act = 0;
void get_in(int u) {
u = ord[u];
if(vis[u]) return ;
act++;
vis[u] = 1;
move_inside(u);
}
void get_out(int u) {
u = ord[u];
if(!vis[u]) return ;
act--;
vis[u] = 0;
move_outside(u);
}
int min_cardinality(int n) {
ord = vector<int>(n);
iota(ord.begin(), ord.end(), 0);
shuffle(ord.begin(), ord.end(), rng);
int l=2, r=n, ans=1;
get_in(0);
for(int i=1; i<n; i++) {
get_in(i);
if(press_button() == 2) {
get_out(i);
cand.push_back(i);
}
}
int D = act;
r = n / D;
while(l <= r) {
int mid = (l + r) / 2;
vector<int> L, R;
for(int u : cand) {
if(act == mid * D) break;
get_in(u);
if(press_button() == mid + 1) {
get_out(u);
L.push_back(u);
continue;
}
R.push_back(u);
}
if(act == mid * D) {
ans = mid;
l = mid + 1;
cand = L;
} else {
r = mid - 1;
for(int u : R) get_out(u);
cand = R;
}
}
return ans;
}
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