


def   _UpperCAmelCase       (     UpperCAmelCase      :			list[list]      ):
      """simple docstring"""




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





def   _UpperCAmelCase       (     UpperCAmelCase      :			list[list]      ):
      """simple docstring"""




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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    __UpperCamelCase    :						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_tokenizers_available,
    is_torch_available,
    is_vision_available,
)


__UpperCamelCase    :						Union[str, Any]     =							{
    'configuration_layoutlmv2': ['LAYOUTLMV2_PRETRAINED_CONFIG_ARCHIVE_MAP', 'LayoutLMv2Config'],
    'processing_layoutlmv2': ['LayoutLMv2Processor'],
    'tokenization_layoutlmv2': ['LayoutLMv2Tokenizer'],
}

try:
    if not is_tokenizers_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __UpperCamelCase    :						List[str]     =							['LayoutLMv2TokenizerFast']

try:
    if not is_vision_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __UpperCamelCase    :						List[str]     =							['LayoutLMv2FeatureExtractor']
    __UpperCamelCase    :						Union[str, Any]     =							['LayoutLMv2ImageProcessor']

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __UpperCamelCase    :						Dict     =							[
        'LAYOUTLMV2_PRETRAINED_MODEL_ARCHIVE_LIST',
        'LayoutLMv2ForQuestionAnswering',
        'LayoutLMv2ForSequenceClassification',
        'LayoutLMv2ForTokenClassification',
        'LayoutLMv2Layer',
        'LayoutLMv2Model',
        'LayoutLMv2PreTrainedModel',
    ]

if TYPE_CHECKING:
    from .configuration_layoutlmva import LAYOUTLMV2_PRETRAINED_CONFIG_ARCHIVE_MAP, LayoutLMvaConfig
    from .processing_layoutlmva import LayoutLMvaProcessor
    from .tokenization_layoutlmva import LayoutLMvaTokenizer

    try:
        if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_layoutlmva_fast import LayoutLMvaTokenizerFast

    try:
        if not is_vision_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .feature_extraction_layoutlmva import LayoutLMvaFeatureExtractor, LayoutLMvaImageProcessor

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_layoutlmva import (
            LAYOUTLMV2_PRETRAINED_MODEL_ARCHIVE_LIST,
            LayoutLMvaForQuestionAnswering,
            LayoutLMvaForSequenceClassification,
            LayoutLMvaForTokenClassification,
            LayoutLMvaLayer,
            LayoutLMvaModel,
            LayoutLMvaPreTrainedModel,
        )
else:
    import sys

    __UpperCamelCase    :						Optional[Any]     =							_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)



