#include "prison.h"
#include <bits/stdc++.h>
using namespace std;
#define sp " "
#define endl "\n"
#define pii pair<int, int>
#define st first
#define nd second
#define fileio() freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout)
#define fastio() cin.tie(0), ios_base::sync_with_stdio(0)
#define pb push_back
#define ll long long
#define LL node * 2
#define RR node * 2 + 1
#define MAXN 300005
const int modulo = 1e9 + 7;
const ll INF = 2e18 + 7;
int find_bit(int num, int base, int bit){
for(int i = 0; i < bit; i++) num /= base;
return num % base;
}
void fill(vector<vector<int>> &a, int base, int bit, int n){
if (bit < 0) return;
int curr = a.size();
vector<int> tmp(n + 1);
tmp[0] = 0;
int subs = 0;
if (bit == 0) subs = 1;
for (int i = 1; i <= n; i++){
int to = find_bit(i, base, bit);
if (bit == 0 && to == 0) tmp[i] = -1;
else if (bit == 0 && to == base - 1) tmp[i] = -2;
else tmp[i] = curr + to + 1 - subs;
}
a.pb(tmp);
int l = 0, r = base;
if (bit == 0) l++, r--;
for (int i = l; i < r; i++){
vector<int> tmp(n + 1, 0);
tmp[0] = 1;
for (int j = 1; j <= n; j++){
int to = find_bit(j, base, bit);
if (to < i) tmp[j] = -2;
else if (to > i) tmp[j] = -1;
else if (bit > 0) tmp[j] = curr + base + 1;
else tmp[j] = -1;
}
a.pb(tmp);
}
fill(a, base, bit - 1, n);
}
vector<vector<int>> devise_strategy(int N) {
vector<vector<int>> a;
int bit = 0, mul = 1, base = 3;
while(mul * base <= N) bit++, mul *= base;
fill(a, base, bit, N);
return a;
}
/*
static constexpr int kNumPrisoners = 500;
static void invalid_strategy(std::string message) {
printf("%s\n", message.c_str());
exit(0);
}
int main() {
fileio();
int N;
assert(1 == scanf("%d", &N));
std::vector<std::vector<int>> strategy = devise_strategy(N);
if (strategy.size() == 0) {
invalid_strategy("s is an empty array");
}
int x = strategy.size() - 1;
cout<<x<<endl;
for (int i = 0; i <= x; ++i) {
if (static_cast<int>(strategy[i].size()) != N + 1) {
invalid_strategy("s[i] contains incorrect length");
}
if (strategy[i][0] < 0 || strategy[i][0] > 1) {
invalid_strategy("First element of s[i] is non-binary");
}
for (int j = 1; j <= N; ++j) {
if (strategy[i][j] < -2 || strategy[i][j] > x) {
invalid_strategy("s[i][j] contains incorrect value");
}
}
}
FILE *log_file = fopen("log.txt","w");
int A, B;
while (1 == scanf("%d", &A) && A != -1) {
assert(1 == scanf("%d", &B));
bool answer = false;
int whiteboard = 0;
for (int i = 0; i < kNumPrisoners && !answer; ++i) {
int check = strategy[whiteboard][0];
whiteboard = strategy[whiteboard][check == 0 ? A : B];
if (whiteboard < 0) {
answer = true;
printf("%c\n", "BA"[whiteboard + 2]);
} else {
if (i > 0) {
fprintf(log_file, " ");
}
fprintf(log_file, "%d", whiteboard);
}
}
if (!answer) {
printf("X\n");
}
fprintf(log_file, "\n");
fflush(log_file);
}
}
*/
