#include <bits/stdc++.h>
using namespace std;
void move_inside(int i);
void move_outside(int i);
int press_button();
int p[2222], sz[2222];
bool asked[2222][2222];
int root(int a){
return p[a] == a?a:(p[a]=root(p[a]));
}
void merge(int a, int b, int n){
a = root(a), b = root(b);
if(a != b){
p[a] = b;
sz[b] += sz[a];
for(int i=1;i<=n;i++){
asked[b][i] |= asked[a][i];
asked[i][b] |= asked[i][a];
}
}
}
int min_cardinality(int n){
for(int i=1;i<=n;i++) p[i] = i, sz[i] = 1;
for(int i=1;i<=n;i++) asked[i][i] = 1;
set<int> cur;
for(int i=1;i<=n;i++) cur.insert(i);
while(!cur.empty()){
int u = *cur.begin();
cur.erase(cur.begin());
move_inside(u-1);
int cnt = 1;
for(int i=1;i<=n;i++){
int ru = root(u), rv = root(i);
if(asked[ru][rv]) continue;
move_inside(i-1);
int r = press_button();
if(r == 2){
asked[ru][rv] = 1;
asked[rv][ru] = 1;
merge(u, i, n);
cnt++;
cur.erase(cur.find(i));
}
else{
asked[ru][rv] = 1;
asked[rv][ru] = 1;
}
move_outside(i-1);
}
if(cnt == 1 || cnt == n) return cnt;
move_outside(u-1);
}
int ans = 1e9;
for(int i=1;i<=n;i++){
int r = root(i);
ans = min(ans, sz[r]);
}
return ans;
}
