#include<bits/stdc++.h>
#ifndef local
#include"prison.h"
#endif
using namespace std;
const int M=24;
const int pw[]={1,3,9,27,81,243,729,2187};
vector<vector<int>> devise_strategy(int N)
{
vector<vector<int>> ans;
vector<int> cur(N+1);
cur[0]=0;
for(int i=1; i<=N; ++i)
cur[i]=22+(i/pw[7])%3;
ans.push_back(cur);
for(int i=0; i<=7; ++i)
for(int j=0; j<3; ++j)
{
cur[0]=i&1;
for(int k=1; k<=N; ++k)
if((k/pw[i])%3<j) cur[k]=-cur[0]-1;
else if((k/pw[i])%3>j) cur[k]=-(cur[0]^1)-1;
else if(i>0) cur[k]=(i-1)*3+1+(k/pw[i-1])%3;
ans.push_back(cur);
}
return ans;
}
#ifdef local
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");
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);
}
}
#endif
