Score : $700$ points

Problem Statement

Let $N$ be a positive integer. Consider a competition where two teams, each with $2^{N-1}$ players, play against each other.

We have $2^N$ players numbered $1$ through $2^N$. Coach Snuke can do the following operation any number of times: separate the players into two teams A and B, each with $2^{N-1}$ players, and make them play against each other.

He wants to do this operation one or more times so that both of the following conditions are satisfied:

1. there exists an integer $n$ such that, for every $(i, j)$ such that $1 \leq i < j \leq 2^N$, Player $i$ and Player $j$ have belonged to the same team exactly $n$ times.
2. there exists an integer $m$ such that, for every $(i, j)$ such that $1 \leq i < j \leq 2^N$, Player $i$ and Player $j$ have belonged to different teams exactly $m$ times.

We can prove that there exist sequences of operations that achieve Snuke's objective. Among those sequences, present one sequence with the minimum possible number of operations.

Constraints

• All values in input are integers.
• $1 \leq N \leq 8$

Input

Input is given from Standard Input in the following format:

$N$

Output

Print a sequence of operations in the format below:

$K$

$s_1$

$s_2$

$\vdots$

$s_K$

Here, $K$ represents the length of the sequence, and $s_i$ represents the division into teams in the $i$-th operation. $s_i$ should be a string of length $2^N$ consisting of A and B. In the $i$-th operation, if Player $j$ belongs to Team A, the ${j}$-th character of $s_{i}$ should be A; if Player $j$ belongs to Team B, the ${j}$-th character of $s_{i}$ should be B. Note that A and B each must occur exactly $2^{N-1}$ times in each $s_i$.

Your output will be accepted when $K$ is the minimum possible length of a sequence of operations that achieves the objective, and the sequence actually achieves the objective.

1

1
AB

• We can satisfy the objective with one operation.
• Note that we must do at least one operation.