

"""simple docstring"""






import numpy as np
from PIL import Image



def   lowercase_	(    _lowercase       :		List[Any]							,      _lowercase       :		Dict							,      _lowercase       :		Optional[Any]	):




					'''simple docstring'''






					UpperCAmelCase			:   Union[str, Any]      =				np.array(_lowercase	)
					if arr.shape[0] != arr.shape[1]:
										raise ValueError("The input array is not a square matrix"	)
					UpperCAmelCase			:   List[Any]      =				0
					UpperCAmelCase			:   Optional[Any]      =				0
					UpperCAmelCase			:   List[Any]      =				0
					UpperCAmelCase			:   Dict      =				0

					# compute the shape of the output matrix
					UpperCAmelCase			:   List[Any]      =				(arr.shape[0] - size) // stride + 1
					# initialize the output matrix with zeros of shape maxpool_shape
					UpperCAmelCase			:   Optional[int]      =				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
															UpperCAmelCase			:   Tuple      =				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
										UpperCAmelCase			:   List[str]      =				0
										UpperCAmelCase			:   Union[str, Any]      =				0

					return updated_arr



def   lowercase_	(    _lowercase       :		int							,      _lowercase       :		Tuple							,      _lowercase       :		Any	):




					'''simple docstring'''






					UpperCAmelCase			:   List[Any]      =				np.array(_lowercase	)
					if arr.shape[0] != arr.shape[1]:
										raise ValueError("The input array is not a square matrix"	)
					UpperCAmelCase			:   Dict      =				0
					UpperCAmelCase			:   str      =				0
					UpperCAmelCase			:   Tuple      =				0
					UpperCAmelCase			:   Optional[int]      =				0

					# compute the shape of the output matrix
					UpperCAmelCase			:   List[Any]      =				(arr.shape[0] - size) // stride + 1
					# initialize the output matrix with zeros of shape avgpool_shape
					UpperCAmelCase			:   Any      =				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
															UpperCAmelCase			:   Tuple      =				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
										UpperCAmelCase			:   Dict      =				0
										UpperCAmelCase			:   int      =				0

					return updated_arr


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

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

	# Loading the image
	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()





"""simple docstring"""






from functools import reduce

snake_case_   :   List[Any]        =       (
    """73167176531330624919225119674426574742355349194934"""
    """96983520312774506326239578318016984801869478851843"""
    """85861560789112949495459501737958331952853208805511"""
    """12540698747158523863050715693290963295227443043557"""
    """66896648950445244523161731856403098711121722383113"""
    """62229893423380308135336276614282806444486645238749"""
    """30358907296290491560440772390713810515859307960866"""
    """70172427121883998797908792274921901699720888093776"""
    """65727333001053367881220235421809751254540594752243"""
    """52584907711670556013604839586446706324415722155397"""
    """53697817977846174064955149290862569321978468622482"""
    """83972241375657056057490261407972968652414535100474"""
    """82166370484403199890008895243450658541227588666881"""
    """16427171479924442928230863465674813919123162824586"""
    """17866458359124566529476545682848912883142607690042"""
    """24219022671055626321111109370544217506941658960408"""
    """07198403850962455444362981230987879927244284909188"""
    """84580156166097919133875499200524063689912560717606"""
    """05886116467109405077541002256983155200055935729725"""
    """71636269561882670428252483600823257530420752963450"""
)



def   lowercase_	(    _lowercase       :		str = N	):




					'''simple docstring'''






					return max(
					    # mypy cannot properly interpret reduce
					    int(reduce(lambda _lowercase							,      _lowercase	: str(int(_lowercase	) * int(_lowercase	)	)							,      n[i : i + 13]	)	)
					    for i in range(len(_lowercase	) - 12	)	)


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


