IA inside a guild

Everybody knows that I love two things: IA and FAIRY TAIL Now, I will make a quiz involving them. AND THERE IS NO RELATIONSHIP BETWEEN BLUE PEGASUS!

The letters of IA is absolutely a subset of the letters of FAIRYTAIL. Now, I want you to count all the permutations of FAIRYTAIL with conditions:

  1. There will be no space
  2. The permutations of FAIRYTAIL mus consist of at least one of the word "IA". For example, FAIRYTAIL is not considered as the permutations since there is no "IA" whilst FIARYTAIL is considered as the permutations since there is the word "IA" in that permutations.
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