#include "prison.h"
#include<bits/stdc++.h>
using namespace std;
#define in insert
#define all(x) x.begin(),x.end()
#define pb push_back
#define eb emplace_back
#define ff first
#define ss second
//#define int long long
typedef long long ll;
typedef vector<int> vi;
typedef set<int> si;
typedef multiset<int> msi;
typedef pair<int, int> pii;
typedef vector<pii> vpii;
vector<vector<int>> devise_strategy(int n) {
vector<vector<int>> ret;
ret.pb(vector<int>{0});
for(int i = 1; i <= n; i++) {
if(i & (1 << 12)) ret[0].pb(2);
else ret[0].pb(1);
}
int bit = 12, now = 1;
// 0 = A 1 = B
while(bit > 0) {
ret.pb(vector<int>{now});
for(int i = 1; i <= n; i++) {
if((i >> bit) & 1) ret.back().pb(now ? -1 : -2);
else {
if((i >> (bit - 1)) & 1) {
if(bit == 1) ret.back().pb(now ? -1 : -2);
else ret.back().pb(ret.size() + 2);
} else {
if(bit == 1) ret.back().pb(now ? -2 : -1);
else ret.back().pb(ret.size() + 1);
}
}
}
ret.pb(vector<int>{now});
for(int i = 1; i <= n; i++) {
if(!((i >> bit) & 1)) ret.back().pb(now ? -2 : -1);
else {
if((i >> (bit - 1)) & 1) {
if(bit == 1) ret.back().pb(now ? -1 : -2);
else ret.back().pb(ret.size() + 2);
} else {
if(bit == 1) ret.back().pb(now ? -2 : -1);
else ret.back().pb(ret.size() + 1);
}
}
}
bit--;
now ^= 1;
}
return ret;
}
