#include <bits/stdc++.h>
#include "prison.h"
/*
author: aykhn
4/21/2023
*/
using namespace std;
typedef long long ll;
#define OPT ios_base::sync_with_stdio(0); \
cin.tie(0); \
cout.tie(0)
#define pii pair<int,int>
#define pll pair<ll,ll>
#define all(v) v.begin(), v.end()
#define mpr make_pair
#define pb push_back
#define ts to_string
#define fi first
#define se second
#define inf 0x3F3F3F3F
#define infll 0x3F3F3F3F3F3F3F3FLL
#define bpc __builtin_popcount
#define print(v) for(int i = 0; i < v.size(); i++) cout << v[i] << " "; cout<<endl;
/*
notes:
divide the bits into consecutive pairs
00 -> 0 = x
01 -> 1 = x
10 -> 2 = x
11 -> 3 = x
can be look as ab where a = 2 and b = 1 so when turned on += them
on whiteboard: x*10 + group number
max group number = lg(MAX)/2 + 1 = lg(5000)/2 + 1 ~~ 12/2 + 1 = 7
max X = 36 (max 1st group = 1 so 17, 36)
25 + 1.5*3 + 10 = 36 points
*/
vector<vector<int>> devise_strategy(int n)
{
vector<vector<int>> s(25, vector<int> (n + 1, 0));
s[0][0] = 0;
for (int i = 1; i <= n; i++) s[0][i] = ((i >> 12) & 1)*12 + 12;
for (int i = 24; i >= 1; i--)
{
int pos = i;
if (i > 12) pos = i - 12;
s[i][0] = 1 - pos%2;
int y = (i > 12);
for (int j = 1; j <= n; j++)
{
int x = ((j >> (pos)) & 1);
if (x > y)
{
if (1 - pos%2) s[i][j] = -1;
else s[i][j] = -2;
}
else if (x < y)
{
if (1 - pos%2) s[i][j] = -2;
else s[i][j] = -1;
}
else
{
if (pos - 1 == 0)
{
if (j & 1)
{
if (1 - pos%2) s[i][j] = -1;
else s[i][j] = -2;
}
else
{
if (1 - pos%2) s[i][j] = -2;
else s[i][j] = -1;
}
}
else s[i][j] = ((j >> (pos - 1)) & 1)*12 + pos - 1;
}
}
}
return s;
}
