How do you invert Map<v1, Set<v2>> to Map<v2, Set<v1>> in Java with stream()

Question

I have a Map object Map<t1, Set<t2>>, and I want to go into the set and turn t2 in the sets into the keys of the new map. The original key t1 will be the new value of the map.
For example, given a map containing two entries

{key1: [a, b, c], key2: [c, d]}

The resulting map would be

{a: [key1], b: [key1], c: [key1, key2], d: [key2]}

[ ] denotes Set in the above examples.

Answer 1

Java 8:

map.entrySet()
        .stream()
        .flatMap(e -> e.getValue()
                .stream()
                .map(v -> new SimpleEntry<>(v, e.getKey())))
        .collect(Collectors.groupingBy(Entry::getKey,
                Collectors.mapping(Entry::getValue, Collectors.toSet())))

Guava:

Multimaps.asMap(map.entrySet()
        .stream()
        .collect(ImmutableSetMultimap.flatteningToImmutableSetMultimap(
                Entry::getKey, e -> e.getValue().stream()))
        .inverse())

StreamEx:

EntryStream.of(map)
        .flatMapValues(Set::stream)
        .invert()
        .grouping(Collectors.toSet())