Use of HAVING in MySQL

Question

I have a table from which I need to select all persons that have a first name that is not unique and that that set should be selected only if among the persons with a similar first name, all have a different last name.

Example:

FirstN    LastN
Bill      Clinton
Bill      Cosby
Bill      Maher
Elvis     Presley
Elvis     Presley
Largo     Winch

I want to obtain

FirstN    LastN
Bill      Clinton

or

FirstN    LastN
Bill      Clinton
Bill      Cosby
Bill      Maher

I tried this but it does not return what I want.

SELECT * FROM Ids
GROUP BY FirstN, LastN
HAVING (COUNT(FirstN)>1 AND COUNT(LastN)=1))

[Edited my post after Aleandre P. Lavasseur remark]

Answer 1

WITH duplicates AS (
  SELECT firstn --, COUNT(*), COUNT(DISTINCT lastn)
    FROM ids
    GROUP BY firstn
    HAVING COUNT(*) = COUNT(DISTINCT lastn)
       AND COUNT(*) > 1
)
SELECT a.firstn, a.lastn
  FROM ids a INNER JOIN duplicates b ON (a.firstn = b.firstn)
  ORDER BY a.firstn, a.lastn

If mysql does not support WITH, then inner query:

SELECT a.firstn, a.lastn
  FROM ids a
      ,(SELECT firstn --, COUNT(*), COUNT(DISTINCT lastn)
          FROM ids
          GROUP BY firstn
          HAVING COUNT(*) = COUNT(DISTINCT lastn)
             AND COUNT(*) > 1
        ) b
  WHERE a.firstn = b.firstn
  ORDER BY a.firstn, a.lastn

Answer 2

can you try this :

SELECT A.FirstN, B.LastN
FROM (
SELECT FirstN
FROM Ids
GROUP BY FirstN
HAVING (COUNT(FirstN)>1)
) AS A
INNER JOIN Ids B ON (A.FirstN = B.FirstN)
GROUP BY A.FirstN, B.LastN
HAVING COUNT(B.LastN)=1