"""simple docstring"""
import math





def    lowerCAmelCase__    (			_UpperCamelCase       :				int					)					->				bool:





						"""simple docstring"""






						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(_UpperCamelCase					) + 1					) ,			6					):
												if number % i == 0 or number % (i + 2) == 0:
																		return False
						return True





def    lowerCAmelCase__    (			_UpperCamelCase       :				int = 1_0_0_0_1					)					->				int:





						"""simple docstring"""






						try:
												snake_case								=			int(_UpperCamelCase					)
						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.'					)
						snake_case								=			[]
						snake_case								=			2
						while len(_UpperCamelCase					) < nth:
												if is_prime(_UpperCamelCase					):
																		primes.append(_UpperCamelCase					)
																		num += 1
												else:
																		num += 1
						return primes[len(_UpperCamelCase					) - 1]


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



"""simple docstring"""
import numpy as np
from PIL import Image





def    lowerCAmelCase__    (			_UpperCamelCase       :				np.ndarray ,			_UpperCamelCase       :				int ,			_UpperCamelCase       :				int					)					->				np.ndarray:





						"""simple docstring"""






						snake_case								=			np.array(_UpperCamelCase					)
						if arr.shape[0] != arr.shape[1]:
												raise ValueError('The input array is not a square matrix'					)
						snake_case								=			0
						snake_case								=			0
						snake_case								=			0
						snake_case								=			0

						# compute the shape of the output matrix
						snake_case								=			(arr.shape[0] - size) // stride + 1
						# initialize the output matrix with zeros of shape maxpool_shape
						snake_case								=			np.zeros((maxpool_shape, maxpool_shape)					)

						while i < arr.shape[0]:
												if i + size > arr.shape[0]:
																		# if the end of the matrix is reached, break
																		break
												while j < arr.shape[1]:
																		# if the end of the matrix is reached, break
																		if j + size > arr.shape[1]:
																								break
																		# compute the maximum of the pooling matrix
																		snake_case								=			np.max(arr[i : i + size, j : j + size]					)
																		# shift the pooling matrix by stride of column pixels
																		j += stride
																		mat_j += 1

												# shift the pooling matrix by stride of row pixels
												i += stride
												mat_i += 1

												# reset the column index to 0
												snake_case								=			0
												snake_case								=			0

						return updated_arr





def    lowerCAmelCase__    (			_UpperCamelCase       :				np.ndarray ,			_UpperCamelCase       :				int ,			_UpperCamelCase       :				int					)					->				np.ndarray:





						"""simple docstring"""






						snake_case								=			np.array(_UpperCamelCase					)
						if arr.shape[0] != arr.shape[1]:
												raise ValueError('The input array is not a square matrix'					)
						snake_case								=			0
						snake_case								=			0
						snake_case								=			0
						snake_case								=			0

						# compute the shape of the output matrix
						snake_case								=			(arr.shape[0] - size) // stride + 1
						# initialize the output matrix with zeros of shape avgpool_shape
						snake_case								=			np.zeros((avgpool_shape, avgpool_shape)					)

						while i < arr.shape[0]:
												# if the end of the matrix is reached, break
												if i + size > arr.shape[0]:
																		break
												while j < arr.shape[1]:
																		# if the end of the matrix is reached, break
																		if j + size > arr.shape[1]:
																								break
																		# compute the average of the pooling matrix
																		snake_case								=			int(np.average(arr[i : i + size, j : j + size]					)					)
																		# shift the pooling matrix by stride of column pixels
																		j += stride
																		mat_j += 1

												# shift the pooling matrix by stride of row pixels
												i += stride
												mat_i += 1
												# reset the column index to 0
												snake_case								=			0
												snake_case								=			0

						return updated_arr


# Main Function
if __name__ == "__main__":
					from doctest import testmod

					testmod(name="avgpooling", verbose=True)

					# Loading the image
					SCREAMING_SNAKE_CASE__      						=  Image.open("path_to_image")

					# Converting the image to numpy array and maxpooling, displaying the result
					# Ensure that the image is a square matrix

					Image.fromarray(maxpooling(np.array(image), size=3, stride=2)).show()

					# Converting the image to numpy array and averagepooling, displaying the result
					# Ensure that the image is a square matrix

					Image.fromarray(avgpooling(np.array(image), size=3, stride=2)).show()


