### Theory:

Basic terminologies:
• $$m × n$$ Representation of rectangles.
• "$$m$$" is the number of rows in a rectangle.
• "$$n$$" is the number of columns in a rectangle.
Example:
$$3 × 7$$ rectangle:

Important!
• It is impossible to fill up the rectangle by using all the $$5$$-Tetromino types once, because of using the $$T$$-Tetromino which has its center square covered by the other three squares (in three sides).
• It is possible to fill up the rectangle when each of the $$5$$-Tetromino is used twice.