





from __future__ import annotations







def    __lowerCamelCase					(							__a   :str    ,     __a   :list[str] | None = None    )		->				list[list[str]]:






		"""simple docstring"""

		A__        =   word_bank or []
		# create a table
		A__        =   len(__a    ) + 1

		A__        =   []
		for _ in range(__a    ):
				table.append([]    )
		# seed value
		A__        =   [[]]  # because empty string has empty combination

		# iterate through the indices
		for i in range(__a    ):
				# condition
				if table[i] != []:
						for word in word_bank:
								# slice condition
								if target[i : i + len(__a    )] == word:
										A__        =   [
										    [word, *way] for way in table[i]
										]
										# adds the word to every combination the current position holds
										# now,push that combination to the table[i+len(word)]
										table[i + len(__a    )] += new_combinations

    # combinations are in reverse order so reverse for better output
		for combination in table[len(__a    )]:
				combination.reverse()

		return table[len(__a    )]


if __name__ == "__main__":
					print(all_construct('''jwajalapa''', ['''jwa''', '''j''', '''w''', '''a''', '''la''', '''lapa''']))
					print(all_construct('''rajamati''', ['''s''', '''raj''', '''amat''', '''raja''', '''ma''', '''i''', '''t''']))
					print(
					    all_construct(
					        '''hexagonosaurus''',
					        ['''h''', '''ex''', '''hex''', '''ag''', '''ago''', '''ru''', '''auru''', '''rus''', '''go''', '''no''', '''o''', '''s'''],
					    )
					)










from __future__ import annotations

from PIL import Image

# Define glider example
A    :					Any =      [
    [0, 1, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0, 0],
    [1, 1, 1, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
]

# Define blinker example
A    :					Optional[Any] =      [[0, 1, 0], [0, 1, 0], [0, 1, 0]]







def    __lowerCamelCase					(							__a   :list[list[int]]    )		->				list[list[int]]:






		"""simple docstring"""

		A__        =   []
		for i in range(len(__a    )    ):
				A__        =   []
				for j in range(len(cells[i]    )    ):
						# Get the number of live neighbours
						A__        =   0
						if i > 0 and j > 0:
								neighbour_count += cells[i - 1][j - 1]
						if i > 0:
								neighbour_count += cells[i - 1][j]
						if i > 0 and j < len(cells[i]    ) - 1:
								neighbour_count += cells[i - 1][j + 1]
						if j > 0:
								neighbour_count += cells[i][j - 1]
						if j < len(cells[i]    ) - 1:
								neighbour_count += cells[i][j + 1]
						if i < len(__a    ) - 1 and j > 0:
								neighbour_count += cells[i + 1][j - 1]
						if i < len(__a    ) - 1:
								neighbour_count += cells[i + 1][j]
						if i < len(__a    ) - 1 and j < len(cells[i]    ) - 1:
								neighbour_count += cells[i + 1][j + 1]

						# Rules of the game of life (excerpt from Wikipedia):
						# 1. Any live cell with two or three live neighbours survives.
						# 2. Any dead cell with three live neighbours becomes a live cell.
						# 3. All other live cells die in the next generation.
						#    Similarly, all other dead cells stay dead.
						A__        =   cells[i][j] == 1
						if (
						    (alive and 2 <= neighbour_count <= 3)
						    or not alive
						    and neighbour_count == 3
						):
								next_generation_row.append(1    )
						else:
								next_generation_row.append(0    )

				next_generation.append(__a    )
		return next_generation







def    __lowerCamelCase					(							__a   :list[list[int]]    ,     __a   :int    )		->				list[Image.Image]:






		"""simple docstring"""

		A__        =   []
		for _ in range(__a    ):
				# Create output image
				A__        =   Image.new("""RGB"""    ,     (len(cells[0]    ), len(__a    ))    )
				A__        =   img.load()

				# Save cells to image
				for x in range(len(__a    )    ):
						for y in range(len(cells[0]    )    ):
								A__        =   2_5_5 - cells[y][x] * 2_5_5
								A__        =   (colour, colour, colour)

        # Save image
				images.append(__a    )
				A__        =   new_generation(__a    )
		return images


if __name__ == "__main__":
					A    :					str =      generate_images(GLIDER, 1_6)
					images[0].save('''out.gif''', save_all=True, append_images=images[1:])



