MYSQL特定搜索

I'm trying to ORDER BY a MYSQL query correctly. I need the rand() to include the query with the shortest length, the query with the second shortest length, and the query with the third shortest length. Is there a way to do that with just MYSQL?

SELECT input FROM tableName WHERE input LIKE '%one%' ORDER BY length(input) ASC, rand() limit 1;

one
one one
one one one
one one one one

In this case, the query only include the rand() with the lowest length. So basically, I need the rand() to include the:

one
one one
one one one

So that it selects one of these randomly.

 order by length(input) asc limit 3;

It will return

one
one one
one one one