Let q be the sum of the expressions a_{1}^{-a_{2}^{a_{3}^{a_{4}}}} over all permutations \left(a_{1}, a_{2}, a_{3}, a_{4}\right) of (1,2,3,4). Determine \lfloor q\rfloor.
Let q be the sum of the expressions a_{1}^{-a_{2}^{a_{3}^{a_{4}}}} over all permutations \left(a_{1}, a_{2}, a_{3}, a_{4}\right) of (1,2,3,4). Determine \lfloor q\rfloor.