#include <bits/stdc++.h>

#include "insects.h"

using namespace std;

#define ll long long
#define flt double
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

const ll inf = 1e18;
mt19937 rnd(234);

int n;

int solve_slow() {
    vector<int> biba(n);
    int clrs = 0;
    for (int i = 0; i < n; i += 1) {
        move_inside(i);
        int x = press_button();
        if (x >= 2) {
            move_outside(i);
            biba[i] = 0;
        } else {
            biba[i] = 1;
            clrs += 1;
        }
    }
    int l = 1;
    int r = n / clrs + 1;
    while (l + 1 < r) {
        int m = (l + r) / 2;
        vector<int> to_dl;
        int cnt = clrs;
        for (int i = 0; i < n; i += 1) {
            if (biba[i] == 1) {
                continue;
            }
            move_inside(i);
            int x = press_button();
            if (x > m) {
                move_outside(i);
            } else {
                to_dl.push_back(i);
                cnt += 1;
            }
        }
        for (auto x : to_dl) {
            move_outside(x);
        }
        if (cnt == clrs * m) {
            l = m;
        } else {
            r = m;
        }
    }
    return l;
}

int min_cardinality(int N) {
    n = N;
    int rs = solve_slow();
    return rs;
}