#include "prison.h"
#include <vector>
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
//~ #define ll int
typedef long double ld;
typedef pair<int, int> pi;
typedef vector<int> vi;
typedef vector<pi> vpi;
typedef pair<pi, ll> pii;
typedef set<ll> si;
typedef long double ld;
#define f first
#define s second
#define mp make_pair
#define FOR(i, s, e) for (int i = s; i <= int(e); ++i)
#define DEC(i, s, e) for (int i = s; i >= int(e); --i)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lbd(x, y) lower_bound(all(x), y)
#define ubd(x, y) upper_bound(all(x), y)
#define aFOR(i, x) for (auto i : x)
#define mem(x, i) memset(x, i, sizeof x)
#define fast ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0)
#define maxn 200010
#define INF (ll)1e18
#define MOD 998244353
typedef pair<vi, int> pvi;
typedef pair<int, pi> ipi;
typedef vector<pii> vpii;
#define DEBUG 0
typedef pair <pi,pi> pipi;
typedef vector <pipi> vpipi;
typedef pair <string, int> psi;
std::vector<std::vector<int>> devise_strategy(int N) {
vector <vi> ans;
// a = 0 : last B
// a = 1 : last A, off
// a = 2 : last A, on
int idx[2][20];
vpi states;
states.pb(pi(-1,-1));
FOR(a,0,1) FOR(k,0,12){
idx[a][k] = states.size();
states.pb({a,k});
}
vi v(N+1);
v[0] = 0; // query A first
FOR(i,1,N) v[i] = idx[bool(i&(1<<12))][12];
ans.pb(v);
FOR(i,1,states.size()-1){
int a = states[i].f, k = states[i].s;
vi res(N+1);
res[0] = (k % 2 == 0); // B if bit is even, currently a stores A
FOR(x,1,N){
if (k % 2 == 0){
if (bool(x&(1<<k)) != a){
if (a) res[x] = -2;
else res[x] = -1;
}else{
int a2 = bool(x&(1<<(k-1)));
int k2 = k-1;
//~ assert(k2 == -1 || idx[a2][k2] != 0);
res[x] = idx[a2][k2];
}
}else{
if (bool(x&(1<<k)) != a){
if (a) res[x] = -1;
else res[x] = -2;
}else{
int a2 = bool(x&(1<<(k-1)));
int k2 = k-1;
//~ assert(k2 == -1 || idx[a2][k2] != 0);
res[x] = idx[a2][k2];
}
}
}
//~ aFOR(j, res) assert(j <= 26);
ans.pb(res);
}
return ans;
}
