




from __future__ import annotations

from PIL import Image

# Define glider example
UpperCamelCase__         =      [
    [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
UpperCamelCase__         =      [[0, 1, 0], [0, 1, 0], [0, 1, 0]]







def      _a				(						SCREAMING_SNAKE_CASE_							:    list[list[int]]					):
					__lowerCAmelCase           =	[]
					for i in range(len(SCREAMING_SNAKE_CASE_					)					):
										__lowerCAmelCase           =	[]
										for j in range(len(cells[i]					)					):
															# Get the number of live neighbours
															__lowerCAmelCase           =	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(SCREAMING_SNAKE_CASE_					) - 1 and j > 0:
																				neighbour_count += cells[i + 1][j - 1]
															if i < len(SCREAMING_SNAKE_CASE_					) - 1:
																				neighbour_count += cells[i + 1][j]
															if i < len(SCREAMING_SNAKE_CASE_					) - 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.
															__lowerCAmelCase           =	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(SCREAMING_SNAKE_CASE_					)
					return next_generation







def      _a				(						SCREAMING_SNAKE_CASE_							:    list[list[int]]				,				SCREAMING_SNAKE_CASE_							:    int					):
					__lowerCAmelCase           =	[]
					for _ in range(SCREAMING_SNAKE_CASE_					):
										# Create output image
										__lowerCAmelCase           =	Image.new("RGB"				,				(len(cells[0]					), len(SCREAMING_SNAKE_CASE_					))					)
										__lowerCAmelCase           =	img.load()

										# Save cells to image
										for x in range(len(SCREAMING_SNAKE_CASE_					)					):
															for y in range(len(cells[0]					)					):
																				__lowerCAmelCase           =	2_55 - cells[y][x] * 2_55
																				__lowerCAmelCase           =	(colour, colour, colour)

        # Save image
										images.append(SCREAMING_SNAKE_CASE_					)
										__lowerCAmelCase           =	new_generation(SCREAMING_SNAKE_CASE_					)
					return images


if __name__ == "__main__":
					UpperCamelCase__         =      generate_images(GLIDER, 16)
					images[0].save("""out.gif""", save_all=True, append_images=images[1:])












import math







def      _a				(						SCREAMING_SNAKE_CASE_							:    int					):

					if 1 < number < 4:
										# 2 and 3 are primes
										return True
					elif number < 2 or number % 2 == 0 or number % 3 == 0:
										# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
										return False

					# All primes number are in format of 6k +/- 1
					for i in range(5				,				int(math.sqrt(SCREAMING_SNAKE_CASE_					) + 1					)				,				6					):
										if number % i == 0 or number % (i + 2) == 0:
															return False
					return True







def      _a				(						SCREAMING_SNAKE_CASE_							:    int = 1_00_01					):

					try:
										__lowerCAmelCase           =	int(SCREAMING_SNAKE_CASE_					)
					except (TypeError, ValueError):
										raise TypeError("Parameter nth must be int or castable to int."					) from None
					if nth <= 0:
										raise ValueError("Parameter nth must be greater than or equal to one."					)
					__lowerCAmelCase           =	[]
					__lowerCAmelCase           =	2
					while len(SCREAMING_SNAKE_CASE_					) < nth:
										if is_prime(SCREAMING_SNAKE_CASE_					):
															primes.append(SCREAMING_SNAKE_CASE_					)
															num += 1
										else:
															num += 1
					return primes[len(SCREAMING_SNAKE_CASE_					) - 1]


if __name__ == "__main__":
					print(f'''{solution() = }''')




