The units digit of a power tower of consecutive numbers, from 2019 to 1 
Is it possible to find the units digit of
  $2019^{2018^{2017^{.^{.^{.^{3^{2^{1}}}}}}}}$?

Where the expression contains all natural numbers $[1,2018]$ as powers and $2019$ as the main base.
Any help would be appreciated. THANKS!

HINT : Assume $a_n=n^{n-1^{n-2^{.^{.^{.^{3^{2^{1}}}}}}}} \mod 10$, then the sequence will be :
$$
1,2,9,4,5,6,9,8,1,0,1,2,9,4,5,6,9,8,1,0,1,2,9,4,5,6,9,8,1,0,1,2,9,4,5,6,9,8,1,0,1,2,9,4,5,6,9,8,1,0,1,2,9,4,5,6,9,8,1,0,1,2,9,4,5,6,9,8,1,0...
$$
