


"""simple docstring"""




from pathlib import Path

import numpy as np
from PIL import Image





def       a_ (	lowercase__ :np.ndarray     ):
			__lowerCamelCase     ,__lowerCamelCase     ,__lowerCamelCase          =      rgb[:, :, 0], rgb[:, :, 1], rgb[:, :, 2]
			return 0.2989 * r + 0.5870 * g + 0.1140 * b





def       a_ (	lowercase__ :np.ndarray     ):
			return (gray > 127) & (gray <= 255)





def       a_ (	lowercase__ :np.ndarray,			lowercase__ :np.ndarray     ):
			__lowerCamelCase          =      np.zeros_like(lowercase__     )
			__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 > 0     )
			return output


if __name__ == "__main__":
					# read original image
					__magic_name__						: Union[str, Any]    =				Path(__file__).resolve().parent / 'image_data' / 'lena.jpg'
					__magic_name__						: int    =				np.array(Image.open(lena_path))
					# kernel to be applied
					__magic_name__						: List[Any]    =				np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])
					__magic_name__						: Tuple    =				dilation(gray_to_binary(rgb_to_gray(lena)), structuring_element)
					# Save the output image
					__magic_name__						: List[Any]    =				Image.fromarray(output).convert('RGB')
					pil_img.save('result_dilation.png')








"""simple docstring"""




from collections import defaultdict





def       a_ (	lowercase__ :int     ):
			__lowerCamelCase          =      1
			__lowerCamelCase          =      True
			for v in tree[start]:
						if v not in visited:
									ret += dfs(lowercase__     )
			if ret % 2 == 0:
						cuts.append(lowercase__     )
			return ret





def       a_ (	):
			dfs(1     )


if __name__ == "__main__":
					__magic_name__  , __magic_name__						: Tuple    =				1_0, 9
					__magic_name__						: Tuple    =				defaultdict(list)
					__magic_name__						: dict[int, bool]    =				{}
					__magic_name__						: list[int]    =				[]
					__magic_name__						: List[str]    =				0
					__magic_name__						: Tuple    =				[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (1_0, 8)]
					for u, v in edges:
										tree[u].append(v)
										tree[v].append(u)
					even_tree()
					print(len(cuts) - 1)




