

'''simple docstring'''







from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve






def 					_SCREAMING_SNAKE_CASE		(						snake_case_							,       snake_case_							,       snake_case_	):
	_lowercase							=     np.stack((horizontal_flow, vertical_flow)							,       2	)

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

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

	_lowercase							=     image[grid[:, :, 1], grid[:, :, 0]]

	# Set pixels at invalid locations to 0
	_lowercase							=     0

	return warped






def 					_SCREAMING_SNAKE_CASE		(						snake_case_							,       snake_case_							,       snake_case_							,       snake_case_ = None							,       ):
	if alpha is None:
		_lowercase							=     0.1

	# Initialize flow
	_lowercase							=     np.zeros_like(__lowerCamelCase	)
	_lowercase							=     np.zeros_like(__lowerCamelCase	)

	# Prepare kernels for the calculation of the derivatives and the average velocity
	_lowercase							=     np.array([[-1, 1], [-1, 1]]	) * 0.25
	_lowercase							=     np.array([[-1, -1], [1, 1]]	) * 0.25
	_lowercase							=     np.array([[1, 1], [1, 1]]	) * 0.25
	_lowercase							=     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	):
		_lowercase							=     warp(__lowerCamelCase							,       __lowerCamelCase							,       __lowerCamelCase	)
		_lowercase							=     convolve(__lowerCamelCase							,       __lowerCamelCase	) + convolve(__lowerCamelCase							,       __lowerCamelCase	)
		_lowercase							=     convolve(__lowerCamelCase							,       __lowerCamelCase	) + convolve(__lowerCamelCase							,       __lowerCamelCase	)
		_lowercase							=     convolve(__lowerCamelCase							,       __lowerCamelCase	) + convolve(__lowerCamelCase							,       -kernel_t	)

		_lowercase							=     convolve(__lowerCamelCase							,       __lowerCamelCase	)
		_lowercase							=     convolve(__lowerCamelCase							,       __lowerCamelCase	)

		# This updates the flow as proposed in the paper (Step 12)
		_lowercase							=     (
		    derivative_x * avg_horizontal_velocity
		    + derivative_y * avg_vertical_velocity
		    + derivative_t
		)
		_lowercase							=     update / (alpha**2 + derivative_x**2 + derivative_y**2)

		_lowercase							=     avg_horizontal_velocity - derivative_x * update
		_lowercase							=     avg_vertical_velocity - derivative_y * update

	return horizontal_flow, vertical_flow


if __name__ == "__main__":
							import doctest

							doctest.testmod()






"""simple docstring"""





def       __a	(						__lowerCamelCase    ):
   for i, _ in enumerate(__lowerCamelCase    ):
      if (i % 2 == 1) == (nums[i - 1] > nums[i]):
         UpperCAmelCase_	,  UpperCAmelCase_   :   List[Any]     	=       nums[i], nums[i - 1]

   return nums


if __name__ == "__main__":
    print('Enter the array elements:')
    _a									=				list(map(int, input().split()))
    print('The unsorted array is:')
    print(array)
    print('Array after Wiggle sort:')
    print(wiggle_sort(array))


