#include <stdio.h>


#define MIN_SIDES 3
#define MAX_SIDES 8


int roll(int x, int num_bits, int roll_amt)
{
    int i, ret = 0;

    for (i = 0; i < num_bits; i++)
    {
        if (x & (1 << i))
        {
            ret |= 1 << ((i + roll_amt) % num_bits);
        }
    }

    return ret;
}

void print_sides(int bits, int size)
{
    int i;

    for (i = 0; i < size; i++)
    {
        if (bits & (1 << i))
        {
            printf("B");
        }
        else
        {
            printf("A");
        }
    }
}

int main(int argc, char **argv)
{
    int n, i, j, bits, b_count, duplicate, total;
    int counts[MAX_SIDES + 1];
    int categories[MAX_SIDES + 1][1 << MAX_SIDES];

    for (n = MIN_SIDES; n <= MAX_SIDES; n++)
    {
        printf("%d sides:\n", n);

        for (i = 0; i <= n; i++)
        {
            counts[i] = 0;
        }

        for (bits = 0; bits < 1 << n; bits++)
        {
//            printf("  %d: ", bits);
//            print_sides(bits, n);

            b_count = 0;

            for (i = 0; i < n; i++)
            {
                if (bits & (1 << i))
                {
                    b_count++;
                }
            }

            duplicate = 0;

            for (i = 0; i < bits; i++)
            {
                for (j = 0; j < n; j++)
                {
                    if (roll(i, n, j) == bits)
                    {
//                        printf(" duplicate of ");
//                        print_sides(i, n);

                        duplicate = 1;
                        break;
                    }
                }

                if (duplicate)
                {
                    break;
                }
            }

            if (!duplicate)
            {
//                printf(" %d Bs, categories[%d][%d] = %d", b_count, b_count, counts[b_count], bits);

                categories[b_count][counts[b_count]] = bits;

                counts[b_count]++;
            }

//            printf("\n");
        }

        total = 0;

        for (i = 0; i <= n; i++)
        {
            printf("  %d Bs, %d As [%d]:", i, n - i, counts[i]);

            for (j = 0; j < counts[i]; j++)
            {
                printf(" ");
                print_sides(categories[i][j], n);
            }

            printf("\n");

            total += counts[i];
        }

        printf("total = %d\n\n", total);
    }

    return 0;
}