Problem Description
Many games, tricks and puzzles depend on determining whether two patterns on a rectangular grid are the ``same'' or not. For instance, the 96 different ways of arranging 8 queens safely on a chessboard can be shown to consist of rotations and/or reflections of only 12 basic patterns.
Write a program that will read in pairs of patterns and determine whether there is a simple transformation that will convert one into the other. Because symmetrical patterns bear many relationships to each other, the transformations must be checked in a specific order. The possible transformations (in order) are:
Preservation: The patterns are identical
90 degree rotation : The pattern was rotated clockwise by 90 degrees
180 degree rotation: The pattern was rotated clockwise by 180 degrees
270 degree rotation: The pattern was rotated clockwise by 2