




from __future__ import annotations

from collections.abc import Callable

__UpperCAmelCase     							=						list[list[float | int]]




def 					lowercase__				(					__snake_case   :							Matrix					,	__snake_case   :							Matrix  ):


					'''simple docstring'''


					UpperCAmelCase_   :				int						=						len(__snake_case  )
					UpperCAmelCase_   :				Matrix						=						[[0 for _ in range(size + 1  )] for _ in range(__snake_case  )]
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				float

					for row in range(__snake_case  ):
										for col in range(__snake_case  ):
															UpperCAmelCase_   :				Dict						=						matrix[row][col]

										UpperCAmelCase_   :				Union[str, Any]						=						vector[row][0]

					UpperCAmelCase_   :				Union[str, Any]						=						0
					UpperCAmelCase_   :				Union[str, Any]						=						0
					while row < size and col < size:
										# pivoting
										UpperCAmelCase_   :				Optional[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:
															UpperCAmelCase_   :				Tuple						=						augmented[pivot_row], augmented[row]

										for rowa in range(row + 1					,	__snake_case  ):
															UpperCAmelCase_   :				Optional[int]						=						augmented[rowa][col] / augmented[row][col]
															UpperCAmelCase_   :				List[str]						=						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  ):
															UpperCAmelCase_   :				Union[str, 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 					lowercase__				(					__snake_case   :							list[int]  ):


					'''simple docstring'''


					UpperCAmelCase_   :				int						=						len(__snake_case  )
					UpperCAmelCase_   :				Matrix						=						[[0 for _ in range(__snake_case  )] for _ in range(__snake_case  )]
					UpperCAmelCase_   :				Matrix						=						[[0] for _ in range(__snake_case  )]
					UpperCAmelCase_   :				Matrix
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int

					for x_val, y_val in enumerate(__snake_case  ):
										for col in range(__snake_case  ):
															UpperCAmelCase_   :				int						=						(x_val + 1) ** (size - col - 1)
										UpperCAmelCase_   :				int						=						y_val

					UpperCAmelCase_   :				List[str]						=						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 					lowercase__				(					__snake_case   :							int  ):


					'''simple docstring'''


					return (
					    1
					    - variable
					    + variable**2
					    - variable**3
					    + variable**4
					    - variable**5
					    + variable**6
					    - variable**7
					    + variable**8
					    - variable**9
					    + variable**10
					)




def 					lowercase__				(					__snake_case   :							Callable[[int], int] = question_function					,	__snake_case   :							int = 10  ):


					'''simple docstring'''


					UpperCAmelCase_   :				list[int]						=						[func(__snake_case  ) for x_val in range(1					,	order + 1  )]

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

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

					for poly in polynomials:
										UpperCAmelCase_   :				Optional[int]						=						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 Any, Dict, List, Union

from ..utils import add_end_docstrings, is_torch_available, is_vision_available, logging, requires_backends
from .base import PIPELINE_INIT_ARGS, Pipeline


if is_vision_available():
		from ..image_utils import load_image


if is_torch_available():
		import torch

		from ..models.auto.modeling_auto import MODEL_FOR_OBJECT_DETECTION_MAPPING, MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING

__UpperCAmelCase     							=						logging.get_logger(__name__)


__UpperCAmelCase     							=						Dict[str, Any]
__UpperCAmelCase     							=						List[Prediction]



@add_end_docstrings(_snake_case      )
class   lowerCamelCase				(_snake_case      ):







		'''simple docstring'''



		def __init__(							self    ,		*_UpperCamelCase    ,		**_UpperCamelCase       )     ->							Optional[int]:
							super().__init__(*_UpperCamelCase    ,		**_UpperCamelCase       )

							if self.framework == "tf":
												raise ValueError(f"The {self.__class__} is only available in PyTorch."       )

							requires_backends(self    ,		'vision'       )
							self.check_model_type(
							    dict(MODEL_FOR_OBJECT_DETECTION_MAPPING.items() + MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING.items()       )       )



		def  __UpperCAmelCase      (							self    ,		**_UpperCamelCase       )     ->							Tuple:
							UpperCAmelCase_   :				str						=						{}
							if "threshold" in kwargs:
												UpperCAmelCase_   :				Tuple						=						kwargs['threshold']
							return {}, {}, postprocess_kwargs



		def __call__(							self    ,		*_UpperCamelCase    ,		**_UpperCamelCase       )     ->							Union[Predictions, List[Prediction]]:
							return super().__call__(*_UpperCamelCase    ,		**_UpperCamelCase       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase       )     ->							Dict:
							UpperCAmelCase_   :				Any						=						load_image(_UpperCamelCase       )
							UpperCAmelCase_   :				Any						=						torch.IntTensor([[image.height, image.width]]       )
							UpperCAmelCase_   :				str						=						self.image_processor(images=[image]    ,		return_tensors='pt'       )
							if self.tokenizer is not None:
												UpperCAmelCase_   :				List[str]						=						self.tokenizer(text=inputs['words']    ,		boxes=inputs['boxes']    ,		return_tensors='pt'       )
							UpperCAmelCase_   :				Any						=						target_size
							return inputs



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase       )     ->							List[Any]:
							UpperCAmelCase_   :				Any						=						model_inputs.pop('target_size'       )
							UpperCAmelCase_   :				Optional[Any]						=						self.model(**_UpperCamelCase       )
							UpperCAmelCase_   :				Dict						=						outputs.__class__({'target_size': target_size, **outputs}       )
							if self.tokenizer is not None:
												UpperCAmelCase_   :				List[str]						=						model_inputs['bbox']
							return model_outputs



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase=0.9       )     ->							List[str]:
							UpperCAmelCase_   :				List[Any]						=						model_outputs['target_size']
							if self.tokenizer is not None:
												# This is a LayoutLMForTokenClassification variant.
												# The OCR got the boxes and the model classified the words.
												UpperCAmelCase_	,  UpperCAmelCase_   :				str						=						target_size[0].tolist()

												def unnormalize(_UpperCamelCase       ):
																	return self._get_bounding_box(
																	    torch.Tensor(
																	        [
																	            (width * bbox[0] / 1_0_0_0),
																	            (height * bbox[1] / 1_0_0_0),
																	            (width * bbox[2] / 1_0_0_0),
																	            (height * bbox[3] / 1_0_0_0),
																	        ]       )       )

												UpperCAmelCase_	,  UpperCAmelCase_   :				List[Any]						=						model_outputs['logits'].squeeze(0       ).softmax(dim=-1       ).max(dim=-1       )
												UpperCAmelCase_   :				Union[str, Any]						=						[self.model.config.idalabel[prediction] for prediction in classes.tolist()]
												UpperCAmelCase_   :				Tuple						=						[unnormalize(_UpperCamelCase       ) for bbox in model_outputs['bbox'].squeeze(0       )]
												UpperCAmelCase_   :				List[str]						=						['score', 'label', 'box']
												UpperCAmelCase_   :				Any						=						[dict(zip(_UpperCamelCase    ,		_UpperCamelCase       )       ) for vals in zip(scores.tolist()    ,		_UpperCamelCase    ,		_UpperCamelCase       ) if vals[0] > threshold]
							else:
												# This is a regular ForObjectDetectionModel
												UpperCAmelCase_   :				Union[str, Any]						=						self.image_processor.post_process_object_detection(_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase       )
												UpperCAmelCase_   :				str						=						raw_annotations[0]
												UpperCAmelCase_   :				str						=						raw_annotation['scores']
												UpperCAmelCase_   :				Tuple						=						raw_annotation['labels']
												UpperCAmelCase_   :				List[Any]						=						raw_annotation['boxes']

												UpperCAmelCase_   :				Union[str, Any]						=						scores.tolist()
												UpperCAmelCase_   :				int						=						[self.model.config.idalabel[label.item()] for label in labels]
												UpperCAmelCase_   :				Any						=						[self._get_bounding_box(_UpperCamelCase       ) for box in boxes]

												# {"scores": [...], ...} --> [{"score":x, ...}, ...]
												UpperCAmelCase_   :				int						=						['score', 'label', 'box']
												UpperCAmelCase_   :				Dict						=						[
												    dict(zip(_UpperCamelCase    ,		_UpperCamelCase       )       )
												    for vals in zip(raw_annotation['scores']    ,		raw_annotation['labels']    ,		raw_annotation['boxes']       )
												]

							return annotation



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase       )     ->							Dict[str, int]:
							if self.framework != "pt":
												raise ValueError('The ObjectDetectionPipeline is only available in PyTorch.'       )
							UpperCAmelCase_	,  UpperCAmelCase_	,  UpperCAmelCase_	,  UpperCAmelCase_   :				Dict						=						box.int().tolist()
							UpperCAmelCase_   :				str						=						{
							    'xmin': xmin,
							    'ymin': ymin,
							    'xmax': xmax,
							    'ymax': ymax,
							}
							return bbox






