def        lowerCAmelCase_			(					__A							)					->    list[list]:







      '''simple docstring'''


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




def        lowerCAmelCase_			(					__A							)					->    list:







      '''simple docstring'''


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


if __name__ == "__main__":
      import doctest

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




# Lint as: python3
import itertools
import os
import re


UpperCamelCase__    							= re.compile(R'([A-Z]+)([A-Z][a-z])')
UpperCamelCase__    							= re.compile(R'([a-z\d])([A-Z])')

UpperCamelCase__    							= re.compile(R'(?<!_)_(?!_)')
UpperCamelCase__    							= re.compile(R'(_{2,})')

UpperCamelCase__    							= R'^\w+(\.\w+)*$'

UpperCamelCase__    							= R'<>:/\|?*'




def        lowerCAmelCase_			(					__A							)					->    Dict:







      '''simple docstring'''


      UpperCAmelCase__								=  _uppercase_uppercase_re.sub(r"\1_\2",  __A							)
      UpperCAmelCase__								=  _lowercase_uppercase_re.sub(r"\1_\2",  __A							)
      return name.lower()




def        lowerCAmelCase_			(					__A							)					->    Optional[Any]:







      '''simple docstring'''


      UpperCAmelCase__								=  _single_underscore_re.split(__A							)
      UpperCAmelCase__								=  [_multiple_underscores_re.split(__A							) for n in name]
      return "".join(n.capitalize() for n in itertools.chain.from_iterable(__A							) if n != ""							)




def        lowerCAmelCase_			(					__A							)					->    List[str]:







      '''simple docstring'''


      if os.path.basename(__A							) != name:
            raise ValueError(f"""Should be a dataset name, not a path: {name}"""							)
      return camelcase_to_snakecase(__A							)




def        lowerCAmelCase_			(					__A,  __A							)					->    Optional[int]:







      '''simple docstring'''


      if os.path.basename(__A							) != name:
            raise ValueError(f"""Should be a dataset name, not a path: {name}"""							)
      if not re.match(_split_re,  __A							):
            raise ValueError(f"""Split name should match '{_split_re}'' but got '{split}'."""							)
      return f"""{filename_prefix_for_name(__A							)}-{split}"""




def        lowerCAmelCase_			(					__A,  __A,  __A,  __A=None							)					->    str:







      '''simple docstring'''


      UpperCAmelCase__								=  filename_prefix_for_split(__A,  __A							)
      if filetype_suffix:
            prefix += f""".{filetype_suffix}"""
      UpperCAmelCase__								=  os.path.join(__A,  __A							)
      return f"""{filepath}*"""







def        lowerCAmelCase_			(					__A,  __A,  __A,  __A=None,  __A=None							)					->    Any:







      '''simple docstring'''


      UpperCAmelCase__								=  filename_prefix_for_split(__A,  __A							)
      UpperCAmelCase__								=  os.path.join(__A,  __A							)

      if shard_lengths:
            UpperCAmelCase__								=  len(__A							)
            UpperCAmelCase__								=  [f"""{prefix}-{shard_id:05d}-of-{num_shards:05d}""" for shard_id in range(__A							)]
            if filetype_suffix:
                  UpperCAmelCase__								=  [filename + f""".{filetype_suffix}""" for filename in filenames]
            return filenames
      else:
            UpperCAmelCase__								=  prefix
            if filetype_suffix:
                  filename += f""".{filetype_suffix}"""
            return [filename]



