#include <bits/stdc++.h>
using namespace std;
vector<vector<int>> devise_strategy(int n) {
vector<vector<int>> ans(21, vector<int>(n + 1, -1));
for (int i = 0; i <= 20; i++)
ans[i][0] = 0;
function<void(int, int, int, int)> solve = [&](int turn, int row, int low, int high)
{
int curBag = turn % 2, otherBag = curBag ^ 1;
ans[row][0] = curBag;
ans[row][low++] = -curBag - 1;
if (high > low)
ans[row][--high] = -otherBag - 1;
int rem = high - low;
if (rem <= 1)
return;
vector<int> nextRows;
if (rem <= 4) // divide into block of size 2
{
for (int i = 0; i < rem; i++)
ans[row][low + i] = turn * 3 + i / 2 + 1;
solve(turn + 1, turn * 3 + 1, low, min(low + 2, high));
nextRows.push_back(turn * 3 + 1);
if (rem > 2)
{
solve(turn + 1, turn * 3 + 2, low + 2, high);
nextRows.push_back(turn * 3 + 2);
}
}
else // divide into 3 blocks
{
int each = (rem + 2) / 3;
for (int i = 0; i < rem; i++)
ans[row][low + i] = turn * 3 + i / each + 1;
for (int i = 0; i < 3; i++)
{
solve(turn + 1, turn * 3 + i + 1, low + i * each, min(low + i * each + each, high));
nextRows.push_back(turn * 3 + i + 1);
}
}
for (int r : nextRows)
{
ans[r][low - 1] = -otherBag - 1;
ans[r][high] = -curBag - 1;
}
};
solve(0, 0, 1, n + 1);
return ans;
}
