






from __future__ import annotations

from collections.abc import Callable

__lowerCamelCase      :    Union[str, Any]   		=   list[list[float | int]]







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							Matrix  ,						snake_case_      :							Matrix     ):
	snake_case__				:   int     =						len(snake_case_     )
	snake_case__				:   Matrix     =						[[0 for _ in range(size + 1     )] for _ in range(snake_case_     )]
	snake_case__				:   int
	snake_case__				:   int
	snake_case__				:   int
	snake_case__				:   int
	snake_case__				:   int
	snake_case__				:   float

	for row in range(snake_case_     ):
		for col in range(snake_case_     ):
			snake_case__				:   Union[str, Any]     =						matrix[row][col]

		snake_case__				:   Any     =						vector[row][0]

	snake_case__				:   Any     =						0
	snake_case__				:   Optional[Any]     =						0
	while row < size and col < size:
		# pivoting
		snake_case__				:   Union[str, Any]     =						max((abs(augmented[rowa][col]     ), rowa) for rowa in range(snake_case_  ,						snake_case_     )     )[
		    1
		]
		if augmented[pivot_row][col] == 0:
			col += 1
			continue
		else:
			snake_case__,		snake_case__				:   List[Any]     =						augmented[pivot_row], augmented[row]

		for rowa in range(row + 1  ,						snake_case_     ):
			snake_case__				:   Dict     =						augmented[rowa][col] / augmented[row][col]
			snake_case__				:   Optional[Any]     =						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  ,						snake_case_     ):
		for row in range(snake_case_     ):
			snake_case__				:   Any     =						augmented[row][col] / augmented[col][col]
			for cola in range(snake_case_  ,						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(snake_case_     )
	]







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							list[int]     ):
	snake_case__				:   int     =						len(snake_case_     )
	snake_case__				:   Matrix     =						[[0 for _ in range(snake_case_     )] for _ in range(snake_case_     )]
	snake_case__				:   Matrix     =						[[0] for _ in range(snake_case_     )]
	snake_case__				:   Matrix
	snake_case__				:   int
	snake_case__				:   int
	snake_case__				:   int

	for x_val, y_val in enumerate(snake_case_     ):
		for col in range(snake_case_     ):
			snake_case__				:   Tuple     =						(x_val + 1) ** (size - col - 1)
		snake_case__				:   Tuple     =						y_val

	snake_case__				:   Any     =						solve(snake_case_  ,						snake_case_     )

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

	return interpolated_func







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							int     ):
	return (
	    1
	    - variable
	    + variable**2
	    - variable**3
	    + variable**4
	    - variable**5
	    + variable**6
	    - variable**7
	    + variable**8
	    - variable**9
	    + variable**10
	)







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							Callable[[int], int] = question_function  ,						snake_case_      :							int = 10     ):
	snake_case__				:   list[int]     =						[func(snake_case_     ) for x_val in range(1  ,						order + 1     )]

	snake_case__				:   list[Callable[[int], int]]     =						[
	    interpolate(data_points[:max_coeff]     ) for max_coeff in range(1  ,						order + 1     )
	]

	snake_case__				:   int     =						0
	snake_case__				:   Callable[[int], int]
	snake_case__				:   int

	for poly in polynomials:
		snake_case__				:   Tuple     =						1
		while func(snake_case_     ) == poly(snake_case_     ):
			x_val += 1

		ret += poly(snake_case_     )

	return ret


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











from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
)


__lowerCamelCase      :    Tuple   		=   {
    """configuration_roberta_prelayernorm""": [
        """ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """RobertaPreLayerNormConfig""",
        """RobertaPreLayerNormOnnxConfig""",
    ],
}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	__lowerCamelCase      :    Tuple   		=   [
	    """ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST""",
	    """RobertaPreLayerNormForCausalLM""",
	    """RobertaPreLayerNormForMaskedLM""",
	    """RobertaPreLayerNormForMultipleChoice""",
	    """RobertaPreLayerNormForQuestionAnswering""",
	    """RobertaPreLayerNormForSequenceClassification""",
	    """RobertaPreLayerNormForTokenClassification""",
	    """RobertaPreLayerNormModel""",
	    """RobertaPreLayerNormPreTrainedModel""",
	]

try:
	if not is_tf_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	__lowerCamelCase      :    Union[str, Any]   		=   [
	    """TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST""",
	    """TFRobertaPreLayerNormForCausalLM""",
	    """TFRobertaPreLayerNormForMaskedLM""",
	    """TFRobertaPreLayerNormForMultipleChoice""",
	    """TFRobertaPreLayerNormForQuestionAnswering""",
	    """TFRobertaPreLayerNormForSequenceClassification""",
	    """TFRobertaPreLayerNormForTokenClassification""",
	    """TFRobertaPreLayerNormMainLayer""",
	    """TFRobertaPreLayerNormModel""",
	    """TFRobertaPreLayerNormPreTrainedModel""",
	]

try:
	if not is_flax_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	__lowerCamelCase      :    List[Any]   		=   [
	    """FlaxRobertaPreLayerNormForCausalLM""",
	    """FlaxRobertaPreLayerNormForMaskedLM""",
	    """FlaxRobertaPreLayerNormForMultipleChoice""",
	    """FlaxRobertaPreLayerNormForQuestionAnswering""",
	    """FlaxRobertaPreLayerNormForSequenceClassification""",
	    """FlaxRobertaPreLayerNormForTokenClassification""",
	    """FlaxRobertaPreLayerNormModel""",
	    """FlaxRobertaPreLayerNormPreTrainedModel""",
	]


if TYPE_CHECKING:
	from .configuration_roberta_prelayernorm import (
	    ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP,
	    RobertaPreLayerNormConfig,
	    RobertaPreLayerNormOnnxConfig,
	)

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_roberta_prelayernorm import (
		    ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
		    RobertaPreLayerNormForCausalLM,
		    RobertaPreLayerNormForMaskedLM,
		    RobertaPreLayerNormForMultipleChoice,
		    RobertaPreLayerNormForQuestionAnswering,
		    RobertaPreLayerNormForSequenceClassification,
		    RobertaPreLayerNormForTokenClassification,
		    RobertaPreLayerNormModel,
		    RobertaPreLayerNormPreTrainedModel,
		)

	try:
		if not is_tf_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_tf_roberta_prelayernorm import (
		    TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
		    TFRobertaPreLayerNormForCausalLM,
		    TFRobertaPreLayerNormForMaskedLM,
		    TFRobertaPreLayerNormForMultipleChoice,
		    TFRobertaPreLayerNormForQuestionAnswering,
		    TFRobertaPreLayerNormForSequenceClassification,
		    TFRobertaPreLayerNormForTokenClassification,
		    TFRobertaPreLayerNormMainLayer,
		    TFRobertaPreLayerNormModel,
		    TFRobertaPreLayerNormPreTrainedModel,
		)

	try:
		if not is_flax_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_flax_roberta_prelayernorm import (
		    FlaxRobertaPreLayerNormForCausalLM,
		    FlaxRobertaPreLayerNormForMaskedLM,
		    FlaxRobertaPreLayerNormForMultipleChoice,
		    FlaxRobertaPreLayerNormForQuestionAnswering,
		    FlaxRobertaPreLayerNormForSequenceClassification,
		    FlaxRobertaPreLayerNormForTokenClassification,
		    FlaxRobertaPreLayerNormModel,
		    FlaxRobertaPreLayerNormPreTrainedModel,
		)

else:
	import sys

	__lowerCamelCase      :    Dict   		=   _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



