#include "prison.h"
#include <bits/stdc++.h>
using namespace std;
using vi = vector<int>;
vector<vi> multiply(vector<vi> S0, int fact) {
int x0 = S0.size(), n0 = int(S0[0].size()) - 1;
int n = n0 * fact + 2;
vector<vi> S(x0 + fact, vi(n + 1, 0));
for(auto &sir : S0) {
sir[0] ^= 1;
for(auto &it : sir)
if(it < 0) it = -3 - it;
}
S[0][0] = 0;
S[0][1] = -1; S[0][n] = -2;
for(int i = 2; i <= n - 1; ++i)
S[0][i] = (i - 2) / n0 + 1;
///copii de S0[0]
for(int i = 1; i <= fact; ++i) {
S[i][0] = S0[0][0];
///marginile
for(int j = 1; j <= (i - 1) * n0 + 1; ++j)
S[i][j] = -2;
for(int j = i * n0 + 2; j <= n; ++j)
S[i][j] = -1;
///mijlocul, copiat
for(int j = 1; j <= n0; ++j) {
int p = (i - 1) * n0 + j + 1;
if(S0[0][j] < 0) S[i][p] = S0[0][j];
else S[i][p] = S0[0][j] + fact;
}
}
for(int i = fact + 1; i < x0 + fact; ++i) {
S[i][0] = S0[i - fact][0];
for(int j = 1; j < n; ++j)
S[i][j] = S0[i - fact][(j - 1) % n0]; /// efectiv doar copiezi
}
return S;
}
vector<vi> devise_strategy(int N) {
vi V = {1, 2, 2, 3, 3, 3, 3, 3};
vector<vi> S = {{0, -1, -2}};
for(auto it : V) S = multiply(S, it);
int x = S.size();
//printf(" x = %d\nN=%d\n", x, (int)S[0].size());
// for(int v = 0; v < x; ++v) {
// printf("%d: ", v);
// for(auto it : S[v]) printf("%d ", it);
// printf("\n");
// }
for(int i = 0; i < x; ++i)
S[i].resize(N + 1);
return S;
}
