Add total of 3 rows for specific id - mysql

Question

I have three tables:
Students
-------------------------------------------------------------
studentId first last gender weight
-------------------------------------------------------------
1 John Doe m 185
2 John Doe2 m 130
3 John Doe3 m 250
Lifts
-------------------
liftId name
-------------------
1 Bench Press
2 Power Clean
3 Parallel Squat
4 Deadlift
5 Shoulder Press
StudentLifts
------------------------------------------------
studentLiftId studentId liftId weight
------------------------------------------------
1 1 1 185
2 2 3 130
3 3 1 190
4 1 2 120
5 2 1 155
6 3 2 145
7 1 1 135
8 1 1 205
9 2 3 200
10 1 3 150
11 2 2 110
12 3 3 250
I would like to have four top lists:
Bench Press
Parallel Squat
Power Clean
Total of the above 3
I can successfully grab a top list for each specific lift using the following query:
SELECT s.studentId, s.first, s.last, s.gender, s.weight, l.name, sl.weight
FROM Students s
LEFT JOIN (
SELECT *
FROM StudentLifts
ORDER BY weight DESC
) sl ON sl.studentId = s.studentId
LEFT JOIN Lifts l ON l.liftId = sl.liftId
WHERE l.name = 'Bench Press'
AND s.gender = 'm'
AND s.weight > 170
GROUP BY s.studentId
ORDER BY sl.weight DESC
However, I am stuck on how to add the highest total of each lift for each student. How can I first find the highest total for each student in each lift, and then add them up to get a total of all three lifts?
Edit
The result set that I am looking for would be something like:
-------------------------------------------------
studentId first last weight
-------------------------------------------------
3 John Doe3 585
1 John Doe 475
2 John Doe2 465
I also forgot to mention that I would actually like two lists, one for students above 170 and one for students below 170.

Answer 1

SELECT -- join student a total weight to the student table
A.studentId,
A.first,
A.last,
C.totalWeight
FROM
Student A,
(
SELECT -- for each studet add the max weights
sum(B.maxWeight) as totalWeight,
B.studentID
FROM (
SELECT -- for each (student,lift) select the max weight
max(weight) as maxWeight,
studentId,
liftID
FROM
StudentLifts
GROUP BY
studentId,
liftID
) B
GROUP BY
studentId
) C
WHERE
A.studentID = C.studentId
-- AND A.weight >= 170
-- AND A.weight < 170
-- pick one here to generate on of the two lists.