from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve





def 							_lowerCamelCase			(					lowerCamelCase_:  np.ndarray				,	lowerCamelCase_:  np.ndarray				,	lowerCamelCase_:  np.ndarray		):



				'''simple docstring'''







				A     :  str   =				np.stack((horizontal_flow, vertical_flow)				,	2		)

				# Create a grid of all pixel coordinates and subtract the flow to get the
				# target pixels coordinates
				A     :  Optional[Any]   =				np.stack(
				    np.meshgrid(np.arange(0				,	image.shape[1]		)				,	np.arange(0				,	image.shape[0]		)		)				,	2		)
				A     :  Dict   =				np.round(grid - flow		).astype(np.intaa		)

				# Find the locations outside of the original image
				A     :  Tuple   =				(grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]]		))
				A     :  Tuple   =				0

				A     :  Any   =				image[grid[:, :, 1], grid[:, :, 0]]

				# Set pixels at invalid locations to 0
				A     :  Optional[Any]   =				0

				return warped





def 							_lowerCamelCase			(					lowerCamelCase_:  np.ndarray				,	lowerCamelCase_:  np.ndarray				,	lowerCamelCase_:  SupportsIndex				,	lowerCamelCase_:  float | None = None				,	):



				'''simple docstring'''







				if alpha is None:
								A     :  Dict   =				0.1

				# Initialize flow
				A     :  Any   =				np.zeros_like(lowerCamelCase_		)
				A     :  Optional[int]   =				np.zeros_like(lowerCamelCase_		)

				# Prepare kernels for the calculation of the derivatives and the average velocity
				A     :  int   =				np.array([[-1, 1], [-1, 1]]		) * 0.2_5
				A     :  List[Any]   =				np.array([[-1, -1], [1, 1]]		) * 0.2_5
				A     :  Dict   =				np.array([[1, 1], [1, 1]]		) * 0.2_5
				A     :  Optional[int]   =				np.array(
				    [[1 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]]		)

				# Iteratively refine the flow
				for _ in range(lowerCamelCase_		):
								A     :  Union[str, Any]   =				warp(lowerCamelCase_				,	lowerCamelCase_				,	lowerCamelCase_		)
								A     :  List[Any]   =				convolve(lowerCamelCase_				,	lowerCamelCase_		) + convolve(lowerCamelCase_				,	lowerCamelCase_		)
								A     :  Any   =				convolve(lowerCamelCase_				,	lowerCamelCase_		) + convolve(lowerCamelCase_				,	lowerCamelCase_		)
								A     :  List[Any]   =				convolve(lowerCamelCase_				,	lowerCamelCase_		) + convolve(lowerCamelCase_				,	-kernel_t		)

								A     :  int   =				convolve(lowerCamelCase_				,	lowerCamelCase_		)
								A     :  Optional[int]   =				convolve(lowerCamelCase_				,	lowerCamelCase_		)

								# This updates the flow as proposed in the paper (Step 12)
								A     :  Optional[int]   =				(
								    derivative_x * avg_horizontal_velocity
								    + derivative_y * avg_vertical_velocity
								    + derivative_t
								)
								A     :  int   =				update / (alpha**2 + derivative_x**2 + derivative_y**2)

								A     :  Optional[int]   =				avg_horizontal_velocity - derivative_x * update
								A     :  Union[str, Any]   =				avg_vertical_velocity - derivative_y * update

				return horizontal_flow, vertical_flow


if __name__ == "__main__":
					import doctest

					doctest.testmod()

def 							_lowerCamelCase			(					lowerCamelCase_:  list		):



				'''simple docstring'''







				A     :  Optional[int]   =				1.3
				A     :  List[str]   =				len(lowerCamelCase_		)
				A     :  Optional[Any]   =				False

				while not completed:
								# Update the gap value for a next comb
								A     :  str   =				int(gap / shrink_factor		)
								if gap <= 1:
												A     :  Tuple   =				True

								A     :  List[Any]   =				0
								while index + gap < len(lowerCamelCase_		):
												if data[index] > data[index + gap]:
																# Swap values
																A ,       A     :  int   =				data[index + gap], data[index]
																A     :  Dict   =				False
												index += 1

				return data


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					UpperCamelCase_  =	input("Enter numbers separated by a comma:\n").strip()
					UpperCamelCase_  =	[int(item) for item in user_input.split(",")]
					print(comb_sort(unsorted))