A conversation in school

Andrei decides to do some random computation in his mind. He starts out with the number xx. First, he multiplies his number by 33. Then, he squares his new number. Lastly, he subtracts 88 times the square of his original number from the new number. His final result is the units digit of 32016+2(251000)3^{2016}+2(25^{1000}). When Kostya tries to figure out the original number, he discovers that there are multiple answers. Andrei then tells Kostya that his starting number was his date of birth (Kostya did not know it). What number did Andrei start with?

This is adapted from a problem in the IMO.
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