# Fillomino solutions redux

Consider a polyomino $$S$$. We want to divide $$S$$ into several (may be one) smaller polyominoes. The division is called a Fillomino solution if no two polyominoes of equal size share a side. (They may touch at a point.) In other words, the division is a valid solution of a Fillomino puzzle.

Determine the number of distinct Fillomino solutions of the $$3 \times 3$$ square.

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