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 \(A_{1}+A_{2}+A_{3}\) +...+ \(A_{2012}+A_{2013}\)?

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