Character Grid

This is an output-only problem.

Your task is to build a square grid with side length $N \ge 13$ and fill it with lowercase English letters such that the following property is held.

Let us denote the character at $i$-th row and $j$-th column as $c\_{i,j}$.

Consider $N^2 \cdot (N-1) / 2$ strings of the form $A\_{i,j,p} = c\_{i,j} c\_{i,j+1} \ldots c\_{i,j+p}$ for every $1 \le i \le N$ and every $1 \le j, p \le N-1$ such that $j + p \le N$.

Consider also $N^2 \cdot (N-1) / 2$ strings of the form $B\_{i,j,p} = c\_{i,j} c\_{i+1,j} \ldots c\_{i+p,j}$ for every $1 \le j \le N$ and every $1 \le i, p \le N-1$ such that $i + p \le N$. 

All those $N^2 \cdot (N-1)$ strings have to be pairwise distinct.

There is no input.

Print the answer in the following format: first print the $N$ ($13 \le N \le 100$). Then print the square grid as $N$ lines; $i$-th line shall contain one string of $N$ characters, representing the $i$-th row of the grid.

If there are several correct solutions, any one of them will be accepted.

For the answer from the sample, the grid property is held, but the grid size is too small to be accepted as a solution.