


import numpy as np
from PIL import Image






def 		_A		(		_lowercase					,  _lowercase					,  _lowercase )					-> np.ndarray:


     """simple docstring"""


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

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

     return updated_arr






def 		_A		(		_lowercase					,  _lowercase					,  _lowercase )					-> np.ndarray:


     """simple docstring"""


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

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





from math import sqrt
def 							__SCREAMING_SNAKE_CASE     (   a__    :   int = 1000000       )					->				int:
	__A :			int		    =			0
	__A :			int		    =			0
	__A :			int

	while num_cuboids <= limit:
		max_cuboid_size += 1
		for sum_shortest_sides in range(2			,2 * max_cuboid_size + 1       ):
			if sqrt(sum_shortest_sides**2 + max_cuboid_size**2       ).is_integer():
				num_cuboids += (
				    min(a__			,sum_shortest_sides // 2       )
				    - max(1			,sum_shortest_sides - max_cuboid_size       )
				    + 1
				)

	return max_cuboid_size


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





