
import numpy as np
from PIL import Image


def 			UpperCamelCase					(    __lowerCamelCase     : np.ndarray				,					__lowerCamelCase     : int				,					__lowerCamelCase     : int    ):
       snake_case       :   List[str]							=      np.array(__lowerCamelCase    )
       if arr.shape[0] != arr.shape[1]:
              raise ValueError("The input array is not a square matrix"    )
       snake_case       :   int							=      0
       snake_case       :   Optional[int]							=      0
       snake_case       :   Tuple							=      0
       snake_case       :   int							=      0

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

       return updated_arr


def 			UpperCamelCase					(    __lowerCamelCase     : np.ndarray				,					__lowerCamelCase     : int				,					__lowerCamelCase     : int    ):
       snake_case       :   List[str]							=      np.array(__lowerCamelCase    )
       if arr.shape[0] != arr.shape[1]:
              raise ValueError("The input array is not a square matrix"    )
       snake_case       :   Optional[int]							=      0
       snake_case       :   List[str]							=      0
       snake_case       :   Dict							=      0
       snake_case       :   str							=      0

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

       return updated_arr


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

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

   # Loading the image
   __lowerCamelCase							=       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 math import ceil, sqrt


def 				lowerCAmelCase_   (	_lowerCamelCase:   int = 1_00_00_00					):
		__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		0

		for outer_width in range(3       ,      (limit // 4) + 2					):
				if outer_width**2 > limit:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		max(ceil(sqrt(outer_width**2 - limit					)					)       ,      1					)
				else:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		1
				if (outer_width - hole_width_lower_bound) % 2:
						hole_width_lower_bound += 1

				answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

		return answer


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