#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
const int M = 2005;
int P[M], chk[M], mst[M], exc[M], cnt;
int IN(int x) { x = P[x];
if(chk[x]) return 0;
chk[x] = 1;
cnt++;
move_inside(x);
return 1;
}
int OUT(int x) { x = P[x];
if(!chk[x]) return 0;
chk[x] = 0;
cnt--;
move_outside(x);
return 1;
}
int GET() { return press_button(); }
int min_cardinality(int N) {
mt19937 mt(chrono::high_resolution_clock::now().time_since_epoch().count());
iota(P, P + N, 0);
//shuffle(P, P + N, mt);
IN(0);
for(int i = 1; i < N; i++) {
IN(i);
if(GET() != 1) OUT(i);
}
int K = cnt;
if(K == 1) return N;
for(int i = 0; i < N; i++) mst[i] = chk[i];
int L = 1, R = N / K, C = 1;
while(L < R) {
int M = (L + R) / 2;
for(int i = 0, j = 0; i < N; i++) if(!exc[i]) {
if(IN(i)) {
if(++j <= M + 1 - C) continue;
int cur = GET();
if(cur > M + 1) OUT(i);
else j = cur - C;
}
if(cnt == (M + 1) * K) break;
}
if(cnt == (M + 1) * K) {
for(int i = 0; i < N; i++) mst[i] = chk[i];
L = C = M + 1;
}
else {
for(int i = 0; i < N; i++) if(!mst[P[i]]) if(!OUT(i)) exc[i] = 1;
R = M;
}
}
return L;
}
