
from __future__ import annotations

import numpy as np



def        UpperCamelCase    (							lowerCAmelCase__		):
					'''simple docstring'''
					lowercase	,						lowercase							=						np.shape(lowerCAmelCase__		)
					if rows != columns:
										lowercase							=						(
										    '''\'table\' has to be of square shaped array but got a '''
										    f'{rows}x{columns} array:\n{table}'
										)
										raise ValueError(lowerCAmelCase__		)

					lowercase							=						np.zeros((rows, columns)		)
					lowercase							=						np.zeros((rows, columns)		)
					for i in range(lowerCAmelCase__		):
										for j in range(lowerCAmelCase__		):
															lowercase							=						sum(lower[i][k] * upper[k][j] for k in range(lowerCAmelCase__		)		)
															if upper[j][j] == 0:
																				raise ArithmeticError('''No LU decomposition exists'''		)
															lowercase							=						(table[i][j] - total) / upper[j][j]
										lowercase							=						1
										for j in range(lowerCAmelCase__ ,			lowerCAmelCase__		):
															lowercase							=						sum(lower[i][k] * upper[k][j] for k in range(lowerCAmelCase__		)		)
															lowercase							=						table[i][j] - total
					return lower, upper


if __name__ == "__main__":
							import doctest

							doctest.testmod()











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:])



