如何使用java streams将map的值按键分组到列表中？

import java.util.*;
import java.util.stream.Collectors;

public class Main {
    public static void main(String[] args) {
        Map<String, Integer> map = new HashMap<>();
        map.put("A", 1);
        map.put("B", 2);
        map.put("C", 1);
        map.put("D", 3);
        map.put("E", 2);

        Map<Integer, List<Integer>> result = map.entrySet().stream()
                .collect(Collectors.groupingBy(Map.Entry::getValue,
                        Collectors.mapping(Map.Entry::getValue, Collectors.toList())));

        System.out.println(result);
    }
}

{1=[1, 1], 2=[2, 2], 3=[3]}