


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()






def 		_A		(		_lowercase = 1_00 )					-> int:


     """simple docstring"""


     __UpperCamelCase =			0
     __UpperCamelCase =			0
     for i in range(1					,  n + 1 ):
          sum_of_squares += i**2
          sum_of_ints += i
     return sum_of_ints**2 - sum_of_squares


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


