





import math





def 						__SCREAMING_SNAKE_CASE  (    UpperCamelCase__			)  ->    bool:







			'''simple docstring'''

			if 1 < number < 4:
						# 2 and 3 are primes
						return True
			elif number < 2 or number % 2 == 0 or number % 3 == 0:
						# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
						return False

			# All primes number are in format of 6k +/- 1
			for i in range(5      ,      int(math.sqrt(UpperCamelCase__			) + 1			)      ,      6			):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True





def 						__SCREAMING_SNAKE_CASE  (    UpperCamelCase__ = 6008_5147_5143			)  ->    int:







			'''simple docstring'''

			try:
						UpperCAmelCase       		=    int(UpperCamelCase__			)
			except (TypeError, ValueError):
						raise TypeError('''Parameter n must be int or castable to int.'''			)
			if n <= 0:
						raise ValueError('''Parameter n must be greater than or equal to one.'''			)
			UpperCAmelCase       		=    0
			if is_prime(UpperCamelCase__			):
						return n
			while n % 2 == 0:
						n //= 2
			if is_prime(UpperCamelCase__			):
						return n
			for i in range(3      ,      int(math.sqrt(UpperCamelCase__			)			) + 1      ,      2			):
						if n % i == 0:
									if is_prime(n // i			):
												UpperCAmelCase       		=    n // i
												break
									elif is_prime(UpperCamelCase__			):
												UpperCAmelCase       		=    i
			return max_number


if __name__ == "__main__":
	print(F'{solution() = }')










from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve





def 						__SCREAMING_SNAKE_CASE  (    UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__			)  ->    np.ndarray:







			'''simple docstring'''

			UpperCAmelCase       		=    np.stack((horizontal_flow, vertical_flow)      ,      2			)

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

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

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

			# Set pixels at invalid locations to 0
			UpperCAmelCase       		=    0

			return warped





def 						__SCREAMING_SNAKE_CASE  (    UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__ = None      ,      )  ->    tuple[np.ndarray, np.ndarray]:







			'''simple docstring'''

			if alpha is None:
						UpperCAmelCase       		=    0.1

			# Initialize flow
			UpperCAmelCase       		=    np.zeros_like(UpperCamelCase__			)
			UpperCAmelCase       		=    np.zeros_like(UpperCamelCase__			)

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

						UpperCAmelCase       		=    convolve(UpperCamelCase__      ,      UpperCamelCase__			)
						UpperCAmelCase       		=    convolve(UpperCamelCase__      ,      UpperCamelCase__			)

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

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

			return horizontal_flow, vertical_flow


if __name__ == "__main__":
				import doctest

				doctest.testmod()



