Is there any good and efficient way in Java 8 to convert HashMap values to keys and vice versa when the type is >

Question

Please find programm below :

Map<String, List<String>> map = new HashMap<>();

List<String> l1 = new ArrayList<>();
l1.add("G1");
l1.add("G2");


List<String> l2 = new ArrayList<>();
l2.add("G2");
l2.add("G3");

map.put("R1", l1);
map.put("R2", l2);

Now the current output is :

{R2=[G2, G3], R1=[G1, G2]}

I would like to write logic in Java 8 in such way that, Map keys should become values and values to keys, like below :

{G1=[R1], G2=[R2, R1], G3=[R2]}

I tried with below but it doesn't work :

Map<String, List<String>> mapInversed = 
        map.entrySet()
           .stream()
           .collect(Collectors.groupingBy(Map.Entry::getValue, Collectors.mapping(Map.Entry::getKey, Collectors.toList()))) 

Exception : Type mismatch: cannot convert from Map<Object,List<Object>> to Map<String,List<String>>

But I want it in same type Map<String,List<String>>

anyone could help ?