
'''simple docstring'''

import numpy as np
from PIL import Image







def 					A       ( UpperCamelCase_   :       np.array )   ->    np.array:







			'''simple docstring'''



			lowerCAmelCase__		,lowerCAmelCase__		,lowerCAmelCase__									=							rgb[:, :, 0], rgb[:, :, 1], rgb[:, :, 2]
			return 0.2_989 * r + 0.5_870 * g + 0.1_140 * b







def 					A       ( UpperCamelCase_   :       np.array )   ->    np.array:







			'''simple docstring'''



			return (gray > 1_27) & (gray <= 2_55)







def 					A       ( UpperCamelCase_   :       np.array  ,		UpperCamelCase_   :       np.array )   ->    np.array:







			'''simple docstring'''



			lowerCAmelCase__									=							np.zeros_like(UpperCamelCase_ )
			lowerCAmelCase__									=							np.zeros(
			    (image.shape[0] + kernel.shape[0] - 1, image.shape[1] + kernel.shape[1] - 1) )

			# Copy image to padded image
			lowerCAmelCase__									=							image

			# Iterate over image & apply kernel
			for x in range(image.shape[1] ):
						for y in range(image.shape[0] ):
									lowerCAmelCase__									=							(
									    kernel * image_padded[y : y + kernel.shape[0], x : x + kernel.shape[1]]
									).sum()
									lowerCAmelCase__									=							int(summation == 5 )
			return output


# kernel to be applied
UpperCAmelCase__				:	Any					=						np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])

if __name__ == "__main__":
		# read original image
		UpperCAmelCase__				:	str					=						np.array(Image.open(R"..\image_data\lena.jpg"))
		# Apply erosion operation to a binary image
		UpperCAmelCase__				:	Any					=						erosion(grayabinary(rgbagray(image)), structuring_element)
		# Save the output image
		UpperCAmelCase__				:	Union[str, Any]					=						Image.fromarray(output).convert("RGB")
		pil_img.save("result_erosion.png")







'''simple docstring'''

import math







def 					A       ( UpperCamelCase_   :       int )   ->    list:







			'''simple docstring'''



			if n <= 0:
						raise ValueError("Only positive integers have prime factors" )
			lowerCAmelCase__									=							[]
			while n % 2 == 0:
						pf.append(2 )
						lowerCAmelCase__									=							int(n / 2 )
			for i in range(3  ,		int(math.sqrt(UpperCamelCase_ ) ) + 1  ,		2 ):
						while n % i == 0:
									pf.append(UpperCamelCase_ )
									lowerCAmelCase__									=							int(n / i )
			if n > 2:
						pf.append(UpperCamelCase_ )
			return pf







def 					A       ( UpperCamelCase_   :       int )   ->    int:







			'''simple docstring'''



			if n <= 0:
						raise ValueError("Only positive numbers are accepted" )
			lowerCAmelCase__									=							1
			lowerCAmelCase__									=							1
			while n % 2 == 0:
						temp += 1
						lowerCAmelCase__									=							int(n / 2 )
			div *= temp
			for i in range(3  ,		int(math.sqrt(UpperCamelCase_ ) ) + 1  ,		2 ):
						lowerCAmelCase__									=							1
						while n % i == 0:
									temp += 1
									lowerCAmelCase__									=							int(n / i )
						div *= temp
			if n > 1:
						div *= 2
			return div







def 					A       ( UpperCamelCase_   :       int )   ->    int:







			'''simple docstring'''



			if n <= 0:
						raise ValueError("Only positive numbers are accepted" )
			lowerCAmelCase__									=							1
			lowerCAmelCase__									=							1
			while n % 2 == 0:
						temp += 1
						lowerCAmelCase__									=							int(n / 2 )
			if temp > 1:
						s *= (2**temp - 1) / (2 - 1)
			for i in range(3  ,		int(math.sqrt(UpperCamelCase_ ) ) + 1  ,		2 ):
						lowerCAmelCase__									=							1
						while n % i == 0:
									temp += 1
									lowerCAmelCase__									=							int(n / i )
						if temp > 1:
									s *= (i**temp - 1) / (i - 1)
			return int(UpperCamelCase_ )







def 					A       ( UpperCamelCase_   :       int )   ->    int:







			'''simple docstring'''



			lowerCAmelCase__									=							n
			for x in set(prime_factors(UpperCamelCase_ ) ):
						s *= (x - 1) / x
			return int(UpperCamelCase_ )


if __name__ == "__main__":
		import doctest

		doctest.testmod()





