MAX_SIZE = 9
V = set()
 
def go(positions):
    if positions in V:
        return
 
    V.add(positions)
 
    if len(positions) == MAX_SIZE:
        return
 
    for (x, y) in positions:
        for dx, dy in zip([0, -1, 0, +1], [-1, 0, +1, 0]):
            nx, ny = x + dx, y + dy
            new_positions = list(positions) + [(nx, ny)]
            new_positions = tuple(sorted(set(new_positions)))
            go(new_positions)
 
go(((0,0),))
print(f"WITH AT MOST {MAX_SIZE} PIECES THERE ARE {len(V)} SETS.")
 

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