



from collections import defaultdict

class 	__SCREAMING_SNAKE_CASE     :


					'''simple docstring'''





					def __init__(	self							:  Union[str, Any],  lowerCamelCase							:  List[Any],  lowerCamelCase							:  List[str]					)-> Optional[int]:
								lowerCamelCase__		:		List[Any]		     =total  # total no of tasks (N)

								# DP table will have a dimension of (2^M)*N
								# initially all values are set to -1
								lowerCamelCase__		:		Optional[Any]		     =[
								    [-1 for i in range(total + 1					)] for j in range(2 ** len(lowerCamelCase					)					)
								]

								lowerCamelCase__		:		Any		     =defaultdict(lowerCamelCase					)  # stores the list of persons for each task

								# final_mask is used to check if all persons are included by setting all bits
								# to 1
								lowerCamelCase__		:		List[Any]		     =(1 << len(lowerCamelCase					)) - 1



					def 		snake_case	(	self							:  int,  lowerCamelCase							:  str,  lowerCamelCase							:  Any					)-> Any:
								# if mask == self.finalmask all persons are distributed tasks, return 1
								if mask == self.final_mask:
											return 1

								# if not everyone gets the task and no more tasks are available, return 0
								if task_no > self.total_tasks:
											return 0

								# if case already considered
								if self.dp[mask][task_no] != -1:
											return self.dp[mask][task_no]

								# Number of ways when we don't this task in the arrangement
								lowerCamelCase__		:		Optional[int]		     =self.count_ways_until(lowerCamelCase,  task_no + 1					)

								# now assign the tasks one by one to all possible persons and recursively
								# assign for the remaining tasks.
								if task_no in self.task:
											for p in self.task[task_no]:
														# if p is already given a task
														if mask & (1 << p):
																	continue

														# assign this task to p and change the mask value. And recursively
														# assign tasks with the new mask value.
														total_ways_util += self.count_ways_until(mask | (1 << p),  task_no + 1					)

        # save the value.
								lowerCamelCase__		:		int		     =total_ways_util

								return self.dp[mask][task_no]




					def 		snake_case	(	self							:  Dict,  lowerCamelCase							:  Dict					)-> int:
								# Store the list of persons for each task
								for i in range(len(lowerCamelCase					)					):
											for j in task_performed[i]:
														self.task[j].append(lowerCamelCase					)

        # call the function to fill the DP table, final answer is stored in dp[0][1]
								return self.count_ways_until(0,  1					)


if __name__ == "__main__":
		_lowercase			:			Tuple										=						5  # total no of tasks (the value of N)

		# the list of tasks that can be done by M persons.
		_lowercase			:			Dict										=						[[1, 3, 4], [1, 2, 5], [3, 4]]
		print(
		    AssignmentUsingBitmask(task_performed, total_tasks).count_no_of_ways(
		        task_performed
		    )
		)









"""simple docstring"""






import numpy as np
from PIL import Image






def 					snake_case__       (		__lowerCamelCase    :   np.ndarray							,		__lowerCamelCase    :   int							,		__lowerCamelCase    :   int     ):
			"""simple docstring"""
			lowerCamelCase__		:		List[Any]		     =np.array(__lowerCamelCase     )
			if arr.shape[0] != arr.shape[1]:
						raise ValueError('''The input array is not a square matrix'''     )
			lowerCamelCase__		:		int		     =0
			lowerCamelCase__		:		int		     =0
			lowerCamelCase__		:		Optional[int]		     =0
			lowerCamelCase__		:		List[Any]		     =0

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

			return updated_arr






def 					snake_case__       (		__lowerCamelCase    :   np.ndarray							,		__lowerCamelCase    :   int							,		__lowerCamelCase    :   int     ):
			"""simple docstring"""
			lowerCamelCase__		:		List[Any]		     =np.array(__lowerCamelCase     )
			if arr.shape[0] != arr.shape[1]:
						raise ValueError('''The input array is not a square matrix'''     )
			lowerCamelCase__		:		str		     =0
			lowerCamelCase__		:		List[Any]		     =0
			lowerCamelCase__		:		Optional[int]		     =0
			lowerCamelCase__		:		List[Any]		     =0

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

			return updated_arr


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

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

		# Loading the image
		_lowercase			:			int										=						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()




