Hard Series

What is the next number in this series?

4,12,84,3612....




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One day Jenifer meets the Lion and the Tiger in the Forest of Forgetfulness. She knows that the Lion lies on Mondays, Tuesdays, and Wednesdays, and tells the truth on the other days of the week. The Tiger, on the other hand, lies on Thursdays, Fridays, and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Jenifer:

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Tiger: Yesterday was one of my lying days too.

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There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.