/*************************************
* 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};
int from[22], to[22];
void solve(int state, int level, vector <vector <int>> &res) {
int l = from[state], r = to[state];
if (l > r) return;
int cur = level & 1;
int pre = cur ^ 1;
res[state][0] = cur;
res[state][l++] = -1 - cur;
res[state][r--] = -1 - pre;
int len = r - l + 1;
if (len <= 1) return;
vector <int> child;
if (len <= 4) {
int m = min(r, l + 1);
from[level * 3 + 1] = l; to[level * 3 + 2] = m;
from[level * 3 + 2] = m + 1; to[level * 3 + 2] = r;
child.push_back(level * 3 + 1);
if (len > 2) child.push_back(level * 3 + 2);
} else {
int mlr = (len + 2) / 3;
int m1 = l + mlr - 1;
int m2 = m1 + mlr;
from[level * 3 + 1] = l; to[level * 3 + 1] = m1;
from[level * 3 + 2] = m1 + 1; to[level * 3 + 2] = m2;
from[level * 3 + 3] = m2 + 1; to[level * 3 + 3] = r;
child.push_back(level * 3 + 1);
child.push_back(level * 3 + 2);
child.push_back(level * 3 + 3);
}
for (int cur_state: child) {
for (int i = from[cur_state]; i <= to[cur_state]; ++i) res[state][i] = cur_state;
res[cur_state][l - 1] = -1 - pre;
res[cur_state][r + 1] = -1 - cur;
for (int pre_state: child) if (pre_state != cur_state) {
for (int i = from[pre_state]; i <= to[pre_state]; ++i)
res[cur_state][i] = -1 - (pre_state < cur_state ? cur : pre);
}
solve(cur_state, level + 1, res);
}
}
vector <vector <int>> devise_strategy(int n) {
vector <vector <int>> res(21, vector<int> (5001, 0));
from[0] = 1; to[0] = 5000;
solve(0, 0, res);
for (int i = 0; i <= 20; ++i) res[i].resize(n + 1);
return res;
}
