


def 				lowerCamelCase__	(      a	:   Dict	,  a	:   str	,  a	:   int=False				)    ->	Optional[int]:





   """simple docstring"""

   if isinstance(_UpperCAmelCase	,  _UpperCAmelCase				) and isinstance(_UpperCAmelCase	,  _UpperCAmelCase				):
      a__ :Union[str, Any]						  =    len(set_a.intersection(_UpperCAmelCase				)				)

      if alternative_union:
         a__ :int						  =    len(_UpperCAmelCase				) + len(_UpperCAmelCase				)
      else:
         a__ :Dict						  =    len(set_a.union(_UpperCAmelCase				)				)

      return intersection / union

   if isinstance(_UpperCAmelCase	,  (list, tuple)				) and isinstance(_UpperCAmelCase	,  (list, tuple)				):
      a__ :Optional[int]						  =    [element for element in set_a if element in set_b]

      if alternative_union:
         a__ :Any						  =    len(_UpperCAmelCase				) + len(_UpperCAmelCase				)
         return len(_UpperCAmelCase				) / union
      else:
         a__ :Optional[Any]						  =    set_a + [element for element in set_b if element not in set_a]
         return len(_UpperCAmelCase				) / len(_UpperCAmelCase				)

      return len(_UpperCAmelCase				) / len(_UpperCAmelCase				)
   return None


if __name__ == "__main__":
  snake_case__			 =						{'''a''', '''b''', '''c''', '''d''', '''e'''}
  snake_case__			 =						{'''c''', '''d''', '''e''', '''f''', '''h''', '''i'''}
  print(jaccard_similarity(set_a, set_b))






def 				lowerCamelCase__	(      a	:   list[list]				)    ->	list[list]:





			"""simple docstring"""
			a__ :Any						  =    current_set.copy()
			for row_index, row in enumerate(a				):
						a__ :List[str]						  =    row[0]
						for column_index, column in enumerate(a				):
									if magnitude == 0:
												a__ :Tuple						  =    column
												continue
									a__ :Tuple						  =    column / magnitude
    # Subtract to cancel term
			a__ :Any						  =    current_set[0]
			a__ :Dict						  =    [first_row]
			a__ :Dict						  =    current_set[1::]
			for row in current_set:
						a__ :int						  =    []
						# 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:
						a__ :List[str]						  =    final_set[0]
						a__ :Optional[Any]						  =    []
						a__ :List[Any]						  =    []
						for row in final_set[1::]:
									current_first_column.append(row[0]				)
									next_iteration.append(row[1::]				)
						a__ :Dict						  =    simplify(a				)
						for i in range(len(a				)				):
									resultant[i].insert(0	,  current_first_column[i]				)
						resultant.insert(0	,  a				)
						a__ :Optional[int]						  =    resultant
			return final_set


def 				lowerCamelCase__	(      a	:   list[list]				)    ->	list:





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


if __name__ == "__main__":
		import doctest

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


