#include <bits/stdc++.h>
using namespace std;
vector<vector<int>> devise_strategy(int n) {
int x = 3 * ceil(log2(n)/(float(log2(3)))) - 2; //cout << x << "\n";
vector<vector<int>> ans(x+1,vector<int>(n+1));
vector<int> p = {1};
while (3*p.back() < n) {
p.push_back(3*p.back());
}
ans[0][0] = 0;
for (int j=1;j<=n;j++) {
ans[0][j] = 1 + j/p.back();
}
for (int i=1;i<x;i++) {
ans[i][0] = !(((i-1)/3)&1);
for (int j=1;j<=n;j++) {
int r = (j/p.back())%3 + 1;
if (r == i%3) {
int val = 3 + (i- i%3) + 1 + (j/p[p.size()-2])%3;
if (val < x) {
ans[i][j] = val;
} else if (val == x) {
ans[i][j] = -(ans[i][0]+1);
} else if (val == x+1) {
ans[i][j] = x;
} else {
ans[i][j] = -(!ans[i][0]+1);
}
} else if (r < i%3) {
ans[i][j] = -(ans[i][0]+1);
} else {
ans[i][j] = -(!ans[i][0]+1);
}
}
if (i%3==0) p.pop_back();
}
ans[x][0] = !(((x-1)/3)&1);
for (int j=1;j<=n;j++) {
if ((j%3) == 0) {
ans[x][j] = -(ans[x][0]+1);
} else {
ans[x][j] = -(!ans[x][0]+1);
}
}
return ans;
}
