#include <bits/stdc++.h>
using namespace std;
vector<vector<int>> devise_strategy(int n){
int b = 0, cur = 2;
while(cur < 5000){
cur = cur * 3 + 2;
b++;
}
vector<string> dp;
function<void(int, string)> generate = [&](int depth, string str){
dp.push_back(str + string(b - depth + 1, 'L'));
if(depth != b){
for(char i = '0'; i <= '2'; ++i){
generate(depth + 1, str + i);
}
}
dp.push_back(str + string(b - depth + 1, 'R'));
};
generate(0, "");
vector<vector<int>> v(3*b + 1);
for(int i = 0; i <= 3*b; ++i) v[i].resize(n + 1);
for(int i = 0; i <= 3*b; ++i){
int s = (i+2)/3, t = (i+2)%3;
v[i][0] = (s % 2); // s is even: A, s is odd: B
for(int j = 1; j <= n; ++j){
if(s == 0){
if(dp[j][s] == 'L'){
v[i][j] = -1;
}else if(dp[j][s] == 'R'){
v[i][j] = -2;
}else{
v[i][j] = (s * 3) + 1 + (dp[j][s] - '0');
}
}else if(s % 2){
int abit = t;
int bbit = dp[j][s - 1] - '0';
if(dp[j][s - 1] == 'R'){
v[i][j] = -1;
}else if(dp[j][s - 1] == 'L'){
v[i][j] = -2;
}else if(abit < bbit){
v[i][j] = -1;
}else if(bbit < abit){
v[i][j] = -2;
}else if(dp[j][s] == 'L'){
v[i][j] = -2;
}else if(dp[j][s] == 'R'){
v[i][j] = -1;
}else{
v[i][j] = (s * 3) + 1 + (dp[j][s] - '0');
}
}else{
int abit = dp[j][s - 1] - '0';
int bbit = t;
if(dp[j][s - 1] == 'L'){
v[i][j] = -1;
}else if(dp[j][s - 1] == 'R'){
v[i][j] = -2;
}else if(abit < bbit){
v[i][j] = -1;
}else if(bbit < abit){
v[i][j] = -2;
}else if(dp[j][s] == 'L'){
v[i][j] = -1;
}else if(dp[j][s] == 'R'){
v[i][j] = -2;
}else{
v[i][j] = (s * 3) + 1 + (dp[j][s] - '0');
}
}
}
}
return v;
}
