Michael's huge numbers

Call a number huge if the sum of its digits is greater than or equal to 23.23. There are 3535 huge three-digit numbers, and there are 22052205 huge four-digit numbers. If NN is the number of huge five-digit numbers, what are the last three digits of NN?

This problem is posed by Michael T.

Details and assumptions

The number 12=01212=012 is a 2-digit number, not a 3-digit number.

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