#include <bits/stdc++.h>
using namespace std;
vector<vector<int>> devise_strategy(int N) {
const int L = 8;
vector<array<int, L>> dig(N + 1);
for (int v = 1; v <= N; ++v) {
int x = v - 1;
for (int p = L - 1; p >= 0; --p) {
dig[v][p] = x % 3;
x /= 3;
}
}
auto id = [](int p, int d) {
return 1 + p * 3 + d;
};
const int final_id = 22;
vector<vector<int>> s(23, vector<int>(N + 1, -1));
s[0][0] = 0;
for (int v = 1; v <= N; ++v) {
s[0][v] = id(0, dig[v][0]);
}
for (int p = 0; p <= 6; ++p) {
for (int d = 0; d < 3; ++d) {
int cur = id(p, d);
bool inspect_b = (p % 2 == 0);
s[cur][0] = inspect_b ? 1 : 0;
for (int v = 1; v <= N; ++v) {
int od = dig[v][p];
if (od != d) {
if (inspect_b) {
s[cur][v] = (d < od) ? -1 : -2;
} else {
s[cur][v] = (od < d) ? -1 : -2;
}
continue;
}
int nd = dig[v][p + 1];
if (p < 6) {
s[cur][v] = id(p + 1, nd);
} else {
if (nd == 1) {
s[cur][v] = final_id;
} else if (inspect_b) {
s[cur][v] = (nd == 0) ? -2 : -1;
} else {
s[cur][v] = (nd == 0) ? -1 : -2;
}
}
}
}
}
s[final_id][0] = 0;
for (int v = 1; v <= N; ++v) {
int od = dig[v][7];
if (od < 1) s[final_id][v] = -1;
else if (od > 1) s[final_id][v] = -2;
else s[final_id][v] = -1;
}
return s;
}
