Using java streams to create new map from existing map

I have a map which is of the following strucutre:

Map<String, Map<String, String>> input;

It basically contains, a set of IDs and for each ID, a value associated to an attribute.

For ex:
ID:       Attribute    Value
A           X           100
A           Y           200
B           X           40
B           Y           40

I am interested only in the attribute X for each ID and I want to do some processing and store it a new map which will have the same defintion Map>

I am trying this in Java 8:

Map<String, Map<String, String>> getResults(Map<String, Map<String, String>> input) {
    input.entrySet().stream()
        .map(id -> {
            String valueX = id.getValue().get("X");
            String computeX = compute(valueX);
            // Now start adding these results to the new map.
        } )
}

I am not able to follow, how I can add it to a new map.