I have two (or more) Map<String, Integer> objects. I'd like to merge them with Java 8 Stream API in a way that values for common keys should be the maximum of the values.

@Test
public void test14() throws Exception {
    Map<String, Integer> m1 = ImmutableMap.of("a", 2, "b", 3);
    Map<String, Integer> m2 = ImmutableMap.of("a", 3, "c", 4);
    List<Map<String, Integer>> list = newArrayList(m1, m2);

    Map<String, Integer> mx = list.stream()... // TODO

    Map<String, Integer> expected = ImmutableMap.of("a", 3, "b", 3, "c", 4);
    assertEquals(expected, mx);
}

How can I make this test method green?

I've played with collect and Collectors for a while without any success.

(ImmutableMap and newArrayList are from Google Guava.)

@Test
public void test14() throws Exception {
    Map<String, Integer> m1 = ImmutableMap.of("a", 2, "b", 3);
    Map<String, Integer> m2 = ImmutableMap.of("a", 3, "c", 4);

    Map<String, Integer> mx = Stream.of(m1, m2)
        .map(Map::entrySet)          // converts each map into an entry set
        .flatMap(Collection::stream) // converts each set into an entry stream, then
                                     // "concatenates" it in place of the original set
        .collect(
            Collectors.toMap(        // collects into a map
                Map.Entry::getKey,   // where each entry is based
                Map.Entry::getValue, // on the entries in the stream
                Integer::max         // such that if a value already exist for
                                     // a given key, the max of the old
                                     // and new value is taken
            )
        )
    ;

    /* Use the following if you want to create the map with parallel streams
    Map<String, Integer> mx = Stream.of(m1, m2)
        .parallel()
        .map(Map::entrySet)          // converts each map into an entry set
        .flatMap(Collection::stream) // converts each set into an entry stream, then
                                     // "concatenates" it in place of the original set
        .collect(
            Collectors.toConcurrentMap(        // collects into a map
                Map.Entry::getKey,   // where each entry is based
                Map.Entry::getValue, // on the entries in the stream
                Integer::max         // such that if a value already exist for
                                     // a given key, the max of the old
                                     // and new value is taken
            )
        )
    ;
    */

    Map<String, Integer> expected = ImmutableMap.of("a", 3, "b", 3, "c", 4);
    assertEquals(expected, mx);
}