


from __future__ import annotations

from collections.abc import Callable

__UpperCamelCase    		=       list[list[float | int]]
def        UpperCamelCase_(				_A   :str				,     _A   :str  )->		Union[str, Any]:

			'''simple docstring'''





			UpperCamelCase__					=       len(__A  )
			UpperCamelCase__					=       [[0 for _ in range(size + 1  )] for _ in range(__A  )]
			UpperCamelCase__					=       42
			UpperCamelCase__					=       42
			UpperCamelCase__					=       42
			UpperCamelCase__					=       42
			UpperCamelCase__					=       42
			UpperCamelCase__					=       42

			for row in range(__A  ):
						for col in range(__A  ):
									UpperCamelCase__					=       matrix[row][col]

						UpperCamelCase__					=       vector[row][0]

			UpperCamelCase__					=       0
			UpperCamelCase__					=       0
			while row < size and col < size:
						# pivoting
						UpperCamelCase__					=       max((abs(augmented[rowa][col]  ), rowa) for rowa in range(__A				,     __A  )  )[
						    1
						]
						if augmented[pivot_row][col] == 0:
									col += 1
									continue
						else:
									UpperCamelCase__,      UpperCamelCase__					=       augmented[pivot_row], augmented[row]

						for rowa in range(row + 1				,     __A  ):
									UpperCamelCase__					=       augmented[rowa][col] / augmented[row][col]
									UpperCamelCase__					=       0
									for cola in range(col + 1				,     size + 1  ):
												augmented[rowa][cola] -= augmented[row][cola] * ratio

						row += 1
						col += 1

			# back substitution
			for col in range(1				,     __A  ):
						for row in range(__A  ):
									UpperCamelCase__					=       augmented[row][col] / augmented[col][col]
									for cola in range(__A				,     size + 1  ):
												augmented[row][cola] -= augmented[col][cola] * ratio

						# round to get rid of numbers like 2.000000000000004
			return [
			    [round(augmented[row][size] / augmented[row][row]				,     10  )] for row in range(__A  )
			]
def        UpperCamelCase_(				_A   :str  )->		Dict:

			'''simple docstring'''





			UpperCamelCase__					=       len(__A  )
			UpperCamelCase__					=       [[0 for _ in range(__A  )] for _ in range(__A  )]
			UpperCamelCase__					=       [[0] for _ in range(__A  )]
			UpperCamelCase__					=       42
			UpperCamelCase__					=       42
			UpperCamelCase__					=       42
			UpperCamelCase__					=       42

			for x_val, y_val in enumerate(__A  ):
						for col in range(__A  ):
									UpperCamelCase__					=       (x_val + 1) ** (size - col - 1)
						UpperCamelCase__					=       y_val

			UpperCamelCase__					=       solve(__A				,     __A  )

			def interpolated_func(_A   :Dict  ) -> int:
						return sum(
						    round(coeffs[x_val][0]  ) * (var ** (size - x_val - 1))
						    for x_val in range(__A  )  )

			return interpolated_func
def        UpperCamelCase_(				_A   :int  )->		List[Any]:

			'''simple docstring'''





			return (
			    1
			    - variable
			    + variable**2
			    - variable**3
			    + variable**4
			    - variable**5
			    + variable**6
			    - variable**7
			    + variable**8
			    - variable**9
			    + variable**10
			)
def        UpperCamelCase_(				_A   :Tuple = question_function				,     _A   :str = 10  )->		Dict:

			'''simple docstring'''





			UpperCamelCase__					=       [func(__A  ) for x_val in range(1				,     order + 1  )]

			UpperCamelCase__					=       [
			    interpolate(data_points[:max_coeff]  ) for max_coeff in range(1				,     order + 1  )
			]

			UpperCamelCase__					=       0
			UpperCamelCase__					=       42
			UpperCamelCase__					=       42

			for poly in polynomials:
						UpperCamelCase__					=       1
						while func(__A  ) == poly(__A  ):
									x_val += 1

						ret += poly(__A  )

			return ret


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






import unittest

from diffusers import FlaxAutoencoderKL
from diffusers.utils import is_flax_available
from diffusers.utils.testing_utils import require_flax

from .test_modeling_common_flax import FlaxModelTesterMixin


if is_flax_available():
						import jax







@require_flax
class        lowerCamelCase__	(							UpperCAmelCase					,	unittest.TestCase      ):






			"""simple docstring"""






			_UpperCamelCase		:					List[str]    =		FlaxAutoencoderKL




			@property
			def 				snake_case__				(							self     ):

						'''simple docstring'''


						UpperCamelCase__					=       4
						UpperCamelCase__					=       3
						UpperCamelCase__					=       (32, 32)

						UpperCamelCase__					=       jax.random.PRNGKey(0     )
						UpperCamelCase__					=       jax.random.uniform(snake_case      ,						((batch_size, num_channels) + sizes)     )

						return {"sample": image, "prng_key": prng_key}







			def 				snake_case__				(							self     ):

						'''simple docstring'''


						UpperCamelCase__					=       {
						    "block_out_channels": [32, 64],
						    "in_channels": 3,
						    "out_channels": 3,
						    "down_block_types": ["DownEncoderBlock2D", "DownEncoderBlock2D"],
						    "up_block_types": ["UpDecoderBlock2D", "UpDecoderBlock2D"],
						    "latent_channels": 4,
						}
						UpperCamelCase__					=       self.dummy_input
						return init_dict, inputs_dict


