Call ‘onehundredandtwentythree’ the concatenated English word for the number \(123\).
The integers from \(1\) to \(999\) are listed in the dictionary order of their concatenated English words.
The list starts \(8, 18, 800, 808, …\)
(eight, eighteen, eighthundred, eighthundredandeight, …)
and ends with \(202\)
(twohundredandtwo).
What is the sum of all the integers to appear after \(8\) and before \(9\) in this list?
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