




"""simple docstring"""


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



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


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  _A													=      [
      [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]]))











"""simple docstring"""


from .configuration_bert_masked import MaskedBertConfig
from .modeling_bert_masked import (
    MaskedBertForMultipleChoice,
    MaskedBertForQuestionAnswering,
    MaskedBertForSequenceClassification,
    MaskedBertForTokenClassification,
    MaskedBertModel,
)
from .modules import *





