#include "prison.h"
#include <bits/stdc++.h>
using namespace std;
#define ll int
#define sz(x) (ll)x.size()
#define F first
#define S second
#define endl "\n"
#define pb push_back
typedef vector <ll> vi;
typedef pair <ll,ll> ii;
typedef vector <ii> vii;
#define dbg(x) cout<<#x<<": "<<x<<endl;
#define dbg2(x,y) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<endl;
#define dbg3(x,y,z) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<" "<<#z<<": "<<z<<endl;
void printVct(vi &v){
for(ll i =0; i<sz(v); i++){
cout<<v[i]<<" ";
}
cout<<endl;
}
void printVct2D(vector <vi> v){
for (ll i =0; i<sz(v); i++){
cout<<i<<": ";
for(ll j =0;j<sz(v[i]); j++){
cout<<v[i][j]<<" ";
}
cout<<endl;
}
}
ll getAns(ll bag_that_is_less){
if (bag_that_is_less == 0) return -1;
return -2;
}
vector<vi> devise_strategy(int n) {
//STEP 1: pre-calculate the 3-base representation of all numbers from 0 to 5000
ll p3[8];
p3[0] = 1;
for (ll i =1; i<=7; i++){
p3[i] = p3[i-1] * 3;
}
vector < vi > b3(5001, vi(8,0));
for (ll i =1; i<=5000; i++){
ll num = i;
for (ll pos = 7; pos >= 0; pos--){
b3[i][pos] = num / p3[pos];
num -= b3[i][pos] * p3[pos];
}
}
// cout<<"1: "; printVct(b3[1]);
// cout<<"3: "; printVct(b3[3]);
// cout<<"4: "; printVct(b3[4]);
vector <vi> s(23, vi(n+1));
//STEP 2: Construct first row
ll firstRow = 1;
s[0][0] = 0;
s[0][1] = -1;
s[0][n] = -2;
for (ll i =1; i<=n; i++){
ll d = b3[i][7];
// dbg2(i,d);
if (d == 0) s[0][i] = firstRow;
else if (d == 1) s[0][i] = firstRow+1;
else if (d == 2) s[0][i] = firstRow+2;
}
// printVct2D(s);
//STEP 3: Construct first 7 full row
ll curBag = 1; //0=A, 1=B
for (ll curDigit = 7; curDigit>0; curDigit--){
firstRow += 3;
for (ll row = 0; row<3; row++){ //loop throug all rows current digit
ll rowIdx = (7-curDigit) * 3 + row + 1;
s[rowIdx][0] = curBag;
for (ll i = 1; i<=n; i++){
ll d = b3[i][curDigit];
if (d < row) s[rowIdx][i] = getAns(curBag);
else if (d > row) s[rowIdx][i] = getAns(!curBag);
else{
ll d2 = b3[i][curDigit-1];
if (curDigit != 1){
if (d2 == 0) s[rowIdx][i] = firstRow;
else if (d2 == 1) s[rowIdx][i] = firstRow+1;
else if (d2 == 2) s[rowIdx][i] = firstRow+2;
}
else{ //second last row
if (d2 == 0) s[rowIdx][i] = getAns(curBag);
else if (d2 == 1) s[rowIdx][i] = firstRow;
else if (d2 == 2) s[rowIdx][i] = getAns(!curBag);
}
}
}
}
curBag = !curBag;
}
//STEP 4: Construct last row
const int lastRow = 22;
curBag = 0;
s[lastRow][0] = curBag;
for (ll i =1; i<=n; i++){
ll d = b3[i][0];
if (d == 0) s[lastRow][i] = getAns(curBag);
else if (d == 2) s[lastRow][i] = getAns(!curBag);
//d = 1 is not possible
}
// printVct2D(s);
return s;
}
/*
5
3 4
-1
2
1 2
-1
5000
3 4
2 5
4 1
245 234
12 2304
4019 4000
-1
*/
