


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






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


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   A				:					List[Any]    						=			[
       [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 __future__ import annotations


class 			__lowerCamelCase			:
    """simple docstring"""


    def __init__(  self      :							Optional[Any]				,							SCREAMING_SNAKE_CASE      :							Tuple=None):
           _A					:     Any     = data
           _A					:     Optional[Any]     = None


    def __repr__(  self      :							List[str]):
           _A					:     List[Any]     = []
           _A					:     Any     = self
           while temp:
                  string_rep.append(F'{temp.data}')
                  _A					:     List[Any]     = temp.next
           return "->".join(SCREAMING_SNAKE_CASE)






def 				lowerCAmelCase__	(    lowerCamelCase					:      list       ):
       if not elements_list:
              raise Exception('The Elements List is empty'       )

       _A					:     Union[str, Any]     = Node(elements_list[0]       )
       for i in range(1  ,len(lowerCamelCase       )       ):
              _A					:     Dict     = Node(elements_list[i]       )
              _A					:     int     = current.next
       return head






def 				lowerCAmelCase__	(    lowerCamelCase					:      Node       ):
       if head_node is not None and isinstance(lowerCamelCase  ,lowerCamelCase       ):
              print_reverse(head_node.next       )
              print(head_node.data       )






def 				lowerCAmelCase__	(    ):
       from doctest import testmod

       testmod()

       _A					:     List[str]     = make_linked_list([14, 52, 14, 12, 43]       )
       print('Linked List:'       )
       print(lowerCamelCase       )
       print('Elements in Reverse:'       )
       print_reverse(lowerCamelCase       )


if __name__ == "__main__":
   main()






