#include "pt4.h"
#include <string>
#include <fstream>
using namespace std;
ofstream out;

struct Tree
{
    Tree* left = nullptr;
    Tree* right= nullptr;
    int data = 0;
};

Tree* Init(int N, int data)
{
    Tree* Node=new Tree;
    Node->data = data;
    if (N == 0) return nullptr;
    if (N == 1) return Node;
    Node->left = Init(N-1, 1);
    Node->right = Init(N-1, -1);
    return Node;
}

void Walker(Tree* tree, string path, int sum)
{
    if (tree->left == nullptr)
    {
        if (sum==0)
            out << path << endl;
        return;
    }
    else
        Walker(tree->left, path + "A", sum + 1);
    if (tree->right == nullptr)
    {
        if (sum == 0)
            out << path << endl;
        return;
    }
    else
        Walker(tree->right, path + "B", sum - 1);
    return;
}

void Solve()
{
    Task("Recur27");
    Tree* tree = nullptr;
    string filename; int N;
    pt >> N >> filename;
    out.open(filename);
    tree = Init(N+1, 0);
    Walker(tree, "C", 0);
    out.close();
}