2016 is absolutely awesome 3

Logic Level 3

For any positive integer kk let f1(k)f_1(k) denote the sum of the squares of the digits of kk (when written in decimal), and for n2n \ge 2 define fn(k)f_n(k) iteratively by fn(k)=f1(fn1(k))f_n(k)=f_1(f_{n-1}(k)).

Find f2017(2016)f_{2017}(2016).

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