





'''simple docstring'''




def 	UpperCAmelCase_							(					__lowercase							:      list[list]       )		->       list[list]:


     '''simple docstring'''



     _UpperCAmelCase     							=   current_set.copy()
     for row_index, row in enumerate(__lowercase       ):
          _UpperCAmelCase     							=   row[0]
          for column_index, column in enumerate(__lowercase       ):
               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(__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:
          _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(__lowercase       )
          for i in range(len(__lowercase       )       ):
               resultant[i].insert(0			,     current_first_column[i]       )
          resultant.insert(0			,     __lowercase       )
          _UpperCAmelCase     							=   resultant
     return final_set
def 	UpperCAmelCase_							(					__lowercase							:      list[list]       )		->       list:


     '''simple docstring'''



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


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  __SCREAMING_SNAKE_CASE     :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]]))








def 				UpperCamelCase_(      lowerCamelCase_ )    ->						int:
    if not numbers:
        return 0

    if not isinstance(lowerCamelCase_							, (list, tuple) ) or not all(
        isinstance(lowerCamelCase_							, lowerCamelCase_ ) for number in numbers ):
        raise ValueError('numbers must be an iterable of integers' )

    _lowercase       :							int      		=		numbers[0]

    for i in range(1							, len(lowerCamelCase_ ) ):
        # update the maximum and minimum subarray products
        _lowercase       :							Union[str, Any]      		=		numbers[i]
        if number < 0:
            _lowercase		,				_lowercase       :							Any      		=		min_till_now, max_till_now
        _lowercase       :							Union[str, Any]      		=		max(lowerCamelCase_							, max_till_now * number )
        _lowercase       :							Union[str, Any]      		=		min(lowerCamelCase_							, min_till_now * number )

        # update the maximum product found till now
        _lowercase       :							Optional[Any]      		=		max(lowerCamelCase_							, lowerCamelCase_ )

    return max_prod


