Loyd's Problem#4344
Sam Loyd is a famous American puzzle creator. One of his most famous puzzles is the "15 puzzle." He is also the author of many chess puzzles and cutting problems. Now you can try to solve his problem about cutting a chessboard.
You are given an n \times n chessboard. Your goal is to cut it into the maximum number of pieces so that any two pieces are different. Each piece must consist of one or more cells and represent a side-connected region. If one piece can be obtained from another by a sequence of rotations, these pieces are considered equal. For example, there are two one-cell pieces: a black cell and a white cell, and only one two-cell piece.
Here is one possible solution to the original Loyd's problem about cutting a standard 8 \times 8 chessboard into different pieces:
The first line contains the single integer , the length of the chessboard's side (1 \leq n \leq 30).
In the first line, output the maximum number of different pieces the chessboard can be cut into. Then output the required cutting: lines with lowercase Latin letters in each of them. Each piece must consist of the same letters. The same letter may be used to represent several pieces, but any two pieces sharing a common side must be represented by different letters (see example for further clarification). If there are several optimal cuttings, you can output any of them.
Example 1