SQL query to return NULL for SUM(expression) whenever an included value IS NULL

For MySQL, I want a query that returns a SUM of an expression, EXCEPT that I want the returned value to be NULL if any of the expressions included in the SUM are NULL. (The normal operation of SUM is to ignore NULL values.

Here's a simple test case that illustrates

CREATE TABLE t4 (fee VARCHAR(3), fi INT);
INSERT INTO t4 VALUES ('fo',10),('fo',200),('fo',NULL),('fum',400);

SELECT fee, SUM(fi) AS sum_fi FROM t4 GROUP BY fee

This returns exactly the result set I开发者_JAVA技巧 expect:

fee sum_fi
--- ------
fo     210
fum    400

What I want is a query that returns a DIFFERENT result set:

fee sum_fi
--- ------
fo    NULL
fum    400

What I want is for the value returned for sum_fi to be NULL whenever an included value is NULL. (This is different than the SUM aggregate function ignores NULL, and returns a total for the non-NULL expressions.)

Question: What query can I use to return the desired result set?

I don't find any built in aggregate function that exhibits this behavior.

How about using SUM(fi is NULL) to determine if you have a NULL value in your data set? This should work:

SELECT fee, IF(SUM(fi is NULL), NULL, SUM(fi)) AS sum_fi FROM t4 GROUP BY fee

You can use this query:

SELECT fee, 
       IF(COUNT(fi) < (SELECT count(fee) FROM t4 temp2 WHERE temp1.fee = temp2.fee),
           NULL, SUM(fi)) AS sum_fi
FROM t4 temp1 GROUP BY fee

There is also this solution:

SELECT fee, CASE WHEN COUNT(*) = COUNT(fi) THEN SUM(fi) ELSE NULL END AS sum_fi
FROM t4 GROUP BY fee

which I derived from the answer of the question Aaron W tagged as a duplicate of this. Admittedly, the latter form looks better than my original idea.