How many ways are there to arrange the 26 letters of the alphabet in a row such that none of the following words are formed by consecutive letters in the arrangement: inch, lost, or thin?

i'm pretty sure it's 477,585,296, but perhaps my math is incorrect.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)