def 			A__      (	snake_case_ :		list[list]      ):
	SCREAMING_SNAKE_CASE__:   Union[str, Any]=      current_set.copy()
	for row_index, row in enumerate(_lowercase      ):
		SCREAMING_SNAKE_CASE__:   Optional[int]=      row[0]
		for column_index, column in enumerate(_lowercase      ):
			if magnitude == 0:
				SCREAMING_SNAKE_CASE__:   Optional[Any]=      column
				continue
			SCREAMING_SNAKE_CASE__:   str=      column / magnitude
    # Subtract to cancel term
	SCREAMING_SNAKE_CASE__:   Union[str, Any]=      current_set[0]
	SCREAMING_SNAKE_CASE__:   Optional[Any]=      [first_row]
	SCREAMING_SNAKE_CASE__:   List[Any]=      current_set[1::]
	for row in current_set:
		SCREAMING_SNAKE_CASE__:   Any=      []
		# If first term is 0, it is already in form we want, so we preserve it
		if row[0] == 0:
			final_set.append(_lowercase      )
			continue
		for column_index in range(len(_lowercase      )      ):
			temp_row.append(first_row[column_index] - row[column_index]      )
		final_set.append(_lowercase      )
	# Create next recursion iteration set
	if len(final_set[0]      ) != 3:
		SCREAMING_SNAKE_CASE__:   Tuple=      final_set[0]
		SCREAMING_SNAKE_CASE__:   Any=      []
		SCREAMING_SNAKE_CASE__:   str=      []
		for row in final_set[1::]:
			current_first_column.append(row[0]      )
			next_iteration.append(row[1::]      )
		SCREAMING_SNAKE_CASE__:   List[str]=      simplify(_lowercase      )
		for i in range(len(_lowercase      )      ):
			resultant[i].insert(0       ,				current_first_column[i]      )
		resultant.insert(0       ,				_lowercase      )
		SCREAMING_SNAKE_CASE__:   Union[str, Any]=      resultant
	return final_set







def 			A__      (	snake_case_ :		list[list]      ):






	if len(_lowercase      ) == 0:
		raise IndexError('''solve_simultaneous() requires n lists of length n+1'''      )
	SCREAMING_SNAKE_CASE__:   Optional[int]=      len(_lowercase      ) + 1
	if any(len(_lowercase      ) != _length for item in equations      ):
		raise IndexError('''solve_simultaneous() requires n lists of length n+1'''      )
	for row in equations:
		if any(not isinstance(_lowercase       ,				(int, float)      ) for column in row      ):
			raise ValueError('''solve_simultaneous() requires lists of integers'''      )
	if len(_lowercase      ) == 1:
		return [equations[0][-1] / equations[0][0]]
	SCREAMING_SNAKE_CASE__:   Tuple=      equations.copy()
	if any(0 in row for row in data_set      ):
		SCREAMING_SNAKE_CASE__:   List[str]=      data_set.copy()
		SCREAMING_SNAKE_CASE__:   List[str]=      []
		for row_index, row in enumerate(_lowercase      ):
			if 0 not in row:
				SCREAMING_SNAKE_CASE__:   List[Any]=      data_set.pop(_lowercase      )
				break
		if not full_row:
			raise ValueError('''solve_simultaneous() requires at least 1 full equation'''      )
		data_set.insert(0       ,				_lowercase      )
	SCREAMING_SNAKE_CASE__:   int=      data_set.copy()
	SCREAMING_SNAKE_CASE__:   List[str]=      simplify(_lowercase      )
	SCREAMING_SNAKE_CASE__:   Tuple=      simplified[::-1]
	SCREAMING_SNAKE_CASE__:   list=      []
	for row in simplified:
		SCREAMING_SNAKE_CASE__:   str=      row[-1]
		if not solutions:
			if row[-2] == 0:
				solutions.append(0      )
				continue
			solutions.append(current_solution / row[-2]      )
			continue
		SCREAMING_SNAKE_CASE__:   Optional[Any]=      row.copy()[: len(_lowercase      ) - 1 :]
		while temp_row[0] == 0:
			temp_row.pop(0      )
		if len(_lowercase      ) == 0:
			solutions.append(0      )
			continue
		SCREAMING_SNAKE_CASE__:   Dict=      temp_row[1::]
		SCREAMING_SNAKE_CASE__:   Union[str, Any]=      temp_row[::-1]
		for column_index, column in enumerate(_lowercase      ):
			current_solution -= column * solutions[column_index]
		solutions.append(_lowercase      )
	SCREAMING_SNAKE_CASE__:   List[Any]=      []
	for item in solutions:
		final.append(float(round(_lowercase       ,				5      )      )      )
	return final[::-1]


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						lowercase_     :   Tuple 				=				[
						    [2, 1, 1, 1, 1, 4],
						    [1, 2, 1, 1, 1, 5],
						    [1, 1, 2, 1, 1, 6],
						    [1, 1, 1, 2, 1, 7],
						    [1, 1, 1, 1, 2, 8],
						]
						print(solve_simultaneous(eq))
						print(solve_simultaneous([[4, 2]]))


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


lowercase_     :   List[str] 				=				{
    'configuration_maskformer': ['MASKFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP', 'MaskFormerConfig'],
    'configuration_maskformer_swin': ['MaskFormerSwinConfig'],
}

try:
      if not is_vision_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      lowercase_     :   Optional[Any] 				=				['MaskFormerFeatureExtractor']
      lowercase_     :   Dict 				=				['MaskFormerImageProcessor']


try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      lowercase_     :   str 				=				[
          'MASKFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
          'MaskFormerForInstanceSegmentation',
          'MaskFormerModel',
          'MaskFormerPreTrainedModel',
      ]
      lowercase_     :   Optional[Any] 				=				[
          'MaskFormerSwinBackbone',
          'MaskFormerSwinModel',
          'MaskFormerSwinPreTrainedModel',
      ]

if TYPE_CHECKING:
      from .configuration_maskformer import MASKFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, MaskFormerConfig
      from .configuration_maskformer_swin import MaskFormerSwinConfig

      try:
            if not is_vision_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .feature_extraction_maskformer import MaskFormerFeatureExtractor
            from .image_processing_maskformer import MaskFormerImageProcessor
      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_maskformer import (
                MASKFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
                MaskFormerForInstanceSegmentation,
                MaskFormerModel,
                MaskFormerPreTrainedModel,
            )
            from .modeling_maskformer_swin import (
                MaskFormerSwinBackbone,
                MaskFormerSwinModel,
                MaskFormerSwinPreTrainedModel,
            )


else:
      import sys

      lowercase_     :   Any 				=				_LazyModule(__name__, globals()['__file__'], _import_structure)

