Questions where accepted answers don't have the highest score (non-self accepted) (AA not HNQ Only)

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select 
distinct q.Id as [Post Link], 
aa.Score as 'accepted answer score', 
hs.Score as 'highest answer score',
hs.Score - aa.Score as 'score difference'
from 
Posts as q 
inner join PostHistory as hnq on q.Id = hnq.PostId and hnq.PostHistoryTypeId=52 --- became Hot Network Question
left join PostHistory as lhnq on q.id = lhnq.PostId and lhnq.PostHistoryTypeId=53 --- left Hot Network Questions
left join Posts as aa on q.Id = aa.ParentId --- aa: accepted answer
left join Posts as hs on q.Id = hs.ParentId --- hs: highest scoring answer
where 
q.PostTypeId = 1 and
q.AcceptedAnswerId is not null and
q.AnswerCount > 1 and
aa.Score < hs.Score and
--(hnq.CreationDate > aa.CreationDate  or lhnq.CreationDate < aa.CreationDate) and -- The accepted answer was posted while it was not a HNQ
aa.Id = q.AcceptedAnswerId and
hs.Score = (Select max(score) from Posts csq where csq.ParentId = q.id) and
aa.OwnerUserID != q.OwnerUserId
order by 'score difference' DESC;

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