This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
pair<int, int> pii;
const int maxn = 1e5 + 100;
int n, d;
int used[maxn];
int f[maxn];
int mx[maxn];
void move_inside(int i);
void move_outside(int i);
int press_button();
void add(int i){
	used[i] = 1;
	move_inside(i);
}
void del(int i){
	used[i] = 0;
	move_outside(i);
}
void clear(){
	for(int i = 1; i <= n; i++){
		if(used[i]) del(i);
	}
}
int min_cardinality(int N){
	d = 0; n = N;
	for(int i = N - 1; i >= 0; i--){
		add(i); 
		if(press_button() == 1) f[i] = 1, d++;
		else del(i);
	} clear();
	int ans = n / d, x = 0;
	for(int l = 1, r = n / d - 1; l <= r;){
		int mid = (l + r) >> 1;
		if(x < mid){
			for(int i = 0; i < n; i++){
				if(used[i] || mx[i] > mid) continue;
				add(i);
				if(press_button() > mid){
					mx[i] = mid + 1;
					del(i);
				}
			}
		} else if(x > mid){
			for(int i = n - 1; i >= 0; i--){
				if(!used[i]) continue;
				if(press_button() <= mid) break;
				del(i);
			}
			for(int i = 0; i < n; i++){
				if(used[i] || mx[i] > mid) continue;
				add(i);
				if(press_button() > mid){
					mx[i] = mid + 1;
					del(i);
				}
			}
		} x = mid;
		bool ok = 0;
		for(int i = 0; i < n; i++){
			if(used[i] && f[i]) ok = 1;
		}
		if(!ok) l = mid + 1;
		else r = mid - 1, ans = mid;
	}
	return ans;
}
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