Stacking Digits

Level pending

Known that $$A_{2011} = 2011^{2012^{2013}}$$, $$A_{2012} = 2012^{2013}$$, and $$A_{2013} = 2013$$. What is the last digit of $$A_{1}+A_{2}+A_{3}$$ +...+ $$A_{2012}+A_{2013}$$?

×