Find the total number of permutations of the word STAKEXCHANGEPUZZLING such that the letters STAK always stay together.
Rules:
- No 3 adjacent consonants, no 2 adjacent vowels.
- For every odd pair of adjacent consonants - first letter must be alphabetically smaller than the second.
- For every even pair of adjacent consonants - the opposite (first letter must be alphabetically bigger than the second).
What is odd and even pair - let's say we have hnanh - hn is the first ( odd ) consonants pair, nh is the second ( even ) pair.
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