#include <bits/stdc++.h>
#define ll long long
#define sz(x) int(x.size())
#define forn(i, n) for (i = 0; i < n; i++)
#define all(x) x.begin(), x.end()
#define pb push_back
#define mp make_pair
#define fr first
#define se second
using namespace std;
void move_inside(int i);
void move_outside(int i);
int press_button();
vector<bool> vis, en;
map<vector<bool>, ll> memo;
ll n;
void mi(ll x)
{
en[x] = 1;
}
void mo(ll x)
{
en[x] = 0;
}
ll pBtn()
{
if (memo.find(en) != memo.end())
return memo[en];
for (int i = 0; i < n; ++i)
{
if (en[i] == vis[i])
continue;
if (en[i])
move_inside(i);
else
move_outside(i);
}
vis = en;
return memo[en] = press_button();
}
int min_cardinality(int N)
{
ll i, act = 0;
n = N;
vis.resize(N, 0);
en.resize(N, 0);
vector<ll> in, out, ins;
for (i = 0; i < n; i++)
ins.pb(i);
for (auto k : ins)
{
mi(k);
if (pBtn() > 1)
{
mo(k);
out.pb(k);
}
else
{
in.pb(k);
act++;
}
}
ll l = 2, r = n / act, piv, pos = 1, tot = act;
ins = out;
while (l <= r)
{
piv = (l + r) / 2;
in.resize(0);
out.resize(0);
for (auto k : ins)
{
mi(k);
if (pBtn() > piv)
{
mo(k);
out.pb(k);
}
else
{
in.pb(k);
act++;
}
}
if (act == tot * piv)
{
l = piv + 1;
pos = piv;
ins = out;
}
else
{
r = piv - 1;
for (auto k : in)
{
mo(k);
act--;
}
ins = in;
}
}
return int(pos);
}
