#include <bits/stdc++.h>
using namespace std;
const int N = 5000;
vector<int> cnt = {2, 3, 3, 3, 3, 2, 2, 2}, sz = {5000, 2499, 833, 277, 92, 30, 14, 6, 2};
int get(int n, int k) {
for (int i = 1; i <= k; i++) {
if (n <= 1) return 1;
n -= 2;
n %= sz[i];
n++;
}
return n;
}
// 0 - A
// 1 - B
vector<vector<int>> devise_strategy(int _) {
int m = (int) cnt.size();
vector<vector<int>> vec;
vector<int> cur(N + 1);
cur[0] = 0;
for (int i = 1; i <= N; i++) {
int val = get(i, 0);
if (val == 1) cur[i] = -1;
else if (val == sz[0]) cur[i] = -2;
else {
int id = (val - 2) / sz[1];
cur[i] = id + 1;
}
}
vec.push_back(cur);
for (int d = 0; d < m; d++) {
int k = (d & 1) ^ 1;
int our = (k == 0 ? -1 : -2);
int their = -3 - our;
int new_sz = vec.size() + cnt[d];
for (int their_id = 0; their_id < cnt[d]; their_id++) {
vector<int> cur(N + 1);
cur[0] = k;
for (int i = 1; i <= N; i++) {
int val = get(i, d);
if (val == 1) cur[i] = our;
else if (val == sz[d]) cur[i] = their;
else {
int our_id = (val - 2) / sz[d + 1];
if (our_id < their_id) cur[i] = our;
else if (our_id > their_id) cur[i] = their;
else {
int val_next = get(i, d + 1);
if (val_next == 1) cur[i] = our;
else if (val_next == sz[d + 1]) cur[i] = their;
else {
if (d + 2 > m) {
cur[i] = -1;
continue;
}
our_id = (val_next - 2) / sz[d + 2];
cur[i] = our_id + new_sz;
}
}
}
}
vec.push_back(cur);
}
}
for (auto &cur : vec) {
cur.resize(_ + 1);
for (int &j : cur)
j = clamp(j, -2, (int) vec.size() - 1);
}
return vec;
}
/*
static constexpr int kNumPrisoners = 500;
static void invalid_strategy(std::string message) {
printf("%s\n", message.c_str());
exit(0);
}
int main() {
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;
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");
for (int A = 1; A <= N; A++)
for (int B = 1; B <= N; B++) if (A != 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) {
if ((whiteboard == -2 && B > A) ||
(whiteboard == -1 && B < A)) {
cout << "BAD: " << A << ' ' << B;
return 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");
return 0;
}
fprintf(log_file, "\n");
fflush(log_file);
}
}
//*/
