Aggregate "once-only" whether 1 or 2 rows in join - mysql

Question

I'm trying to run an aggregate query where a join can find 0, 1 or 2 rows in the join table.
I want to aggregate "once-only" regardless of whether the join finds 1 or 2 matching rows.
Minimal example.
+--------------+--------+-----------+
| container_id | thing | alternate |
+--------------+--------+-----------+
| 1 | box | 0 |
| 1 | box | 1 |
| 1 | hat | 0 |
| 2 | monkey | 0 |
| 3 | monkey | 1 |
| 3 | chair | 1 |
+--------------+--------+-----------+
+--------------+------+
| container_id | uses |
+--------------+------+
| 1 | 3 |
| 2 | 1 |
| 3 | 2 |
+--------------+------+
You can see that 'box' is associated with container_id number 1 twice. Once with alternate=0 and once with alternate=1.
SELECT
thing, COUNT(DISTINCT ct.container_id) AS occurrencs, SUM(uses) AS uses
FROM
container_thing AS ct
INNER JOIN
container_usage AS cu ON cu.container_id = ct.container_id
GROUP BY
thing
gives:
+--------+------------+------+
| thing | occurrencs | uses |
+--------+------------+------+
| box | 1 | 6 |
| chair | 1 | 2 |
| hat | 1 | 3 |
| monkey | 2 | 3 |
+--------+------------+------+
but I really want is:
+--------+------------+------+
| thing | occurrencs | uses |
+--------+------------+------+
| box | 1 | 3 |
| chair | 1 | 2 |
| hat | 1 | 3 |
| monkey | 2 | 3 |
+--------+------------+------+
I want 3 as the value for uses in the first row because 'box' was in containers that were used a total of three times. Because of the 'alternate' column I get 6 for that value. Can I either join differently or group by differently or express in the SUM expression to only SUM once for each distinct thing regardless of the value of alternate?
(Note that a thing can appear in a container with alternate, without alternate or both.)
SQL necessary to set up the minimal example:
-- Set up db
CREATE DATABASE sumtest;
USE sumtest;
-- Set up tables
CREATE TABLE container (id INT PRIMARY KEY);
CREATE TABLE container_thing (container_id INT, thing NVARCHAR(10), alternate BOOLEAN);
CREATE TABLE container_usage (container_id INT, uses INT);
-- Insert data
INSERT INTO container (id) VALUES (1), (2), (3);
INSERT INTO container_thing (container_id, thing, alternate) VALUES (1, 'box', FALSE), (1, 'box', TRUE), (1, 'hat', FALSE), (2, 'monkey', FALSE), (3, 'monkey', TRUE), (3, 'chair', TRUE);
INSERT INTO container_usage VALUES (1, 3), (2, 1), (3, 2);
-- Query
SELECT thing, COUNT(DISTINCT ct.container_id) AS occurrencs, SUM(uses) AS uses FROM container_thing AS ct INNER JOIN container_usage AS cu ON cu.container_id = ct.container_id GROUP BY thing;

Answer 1

You can work around this by only selecting DISTINCT values of container_id and thing from container_thing in a derived table and JOINing that to container_usage:
SELECT thing, COUNT(ct.container_id) AS occurrences, SUM(uses) AS uses
FROM (SELECT DISTINCT container_id, thing
FROM container_thing) AS ct
INNER JOIN container_usage AS cu ON cu.container_id = ct.container_id
GROUP BY thing;
Output
thing occurrences uses
box 1 3
chair 1 2
hat 1 3
monkey 2 3
Demo on dbfiddle

Answer 2

If you want only the use .. then you should not perform the sum in join .. because the join produce T1xT2 rows for each macthing ON clause
where N is the number of row from table1 and M is the number of rows from table2 so in the case of box you have 2 x 1 with value 3 = 6.
for avoid this you should join container_usage with the subqiery for aggreated result for count of container_thing
select t.thing, t.count_container, cu.uses
from (
SELECT thing, container_id, COUNT(DISTINCT ct.container_id) count_container
FROM container_thing
GROUP BY thing, container_id
) t
inner join container_usage AS cu ON cu.container_id = t.container_id