/*************************************
* author: marvinthang *
* created: 25.08.2022 20:38:19 *
*************************************/
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define div ___div
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define FULL(i) (MASK(i) - 1)
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#define file(name) if (fopen (name".inp", "r")) { freopen (name".inp", "r", stdin); freopen (name".out", "w", stdout); }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class T> print_op(vector <T>) { out << '{'; for (size_t i = 0; i + 1 < u.size(); ++i) out << u[i] << ", "; if (!u.empty()) out << u.back(); return out << '}'; }
template <class U, class V> scan_op(pair <U, V>) { return in >> u.fi >> u.se; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.fi << ", " << u.se << ')'; }
const double PI = 3.1415926535897932384626433832795; // acos(-1.0); atan(-1.0);
const int dir[] = {1, 0, -1, 0, 1, 1, -1, -1, 1}; // {2, 1, -2, -1, -2, 1, 2, -1, 2};
const int NUM_BIT = 13;
const int NUM_STATE = NUM_BIT * 2 + 1;
pair <int, int> decode(int code) {
--code;
if (code < 0) return make_pair(0, 0);
return make_pair(NUM_BIT - code / 2 - 1, code % 2);
}
int encode(int bit, int t) {
if (bit < 0) return 0;
return (NUM_BIT - bit - 1) * 2 + t + 1;
}
vector <vector <int>> devise_strategy(int n) {
vector <vector <int>> res(NUM_STATE, vector<int> (n + 1, 0));
for (int state = 0; state < NUM_STATE; ++state) {
if (!state) {
res[state][0] = 0;
for (int i = 1; i <= n; ++i)
res[state][i] = encode(NUM_BIT - 1, BIT(NUM_BIT - 1, 0));
continue;
}
auto [bit, t] = decode(state);
bool parity = bit & 1;
res[state][0] = !parity;
for (int i = 1; i <= n; ++i) {
int pre_bit = t;
int cur_bit = BIT(i, bit);
if (pre_bit < cur_bit) res[state][i] = parity ? -2 : -1;
else if (pre_bit > cur_bit) res[state][i] = parity ? -1 : -2;
else res[state][i] = encode(bit - 1, BIT(i, bit - 1));
}
}
return res;
}
