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# aycabta/fgh3tex.rb

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Transcribes FGH f_3(n) to TeX
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 def oh_great(n) if n == 1 "2^n n" else prev = oh_great(n - 1) "2^{#{prev}} {#{prev}}" end end def output(n) puts "f_2^{#{n}}(n) = #{oh_great(n)}" end (1..16).each do |n| output(n) puts puts end
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 f_2^{1}(n) = 2^n n f_2^{2}(n) = 2^{2^n n} {2^n n} f_2^{3}(n) = 2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}} f_2^{4}(n) = 2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} f_2^{5}(n) = 2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} f_2^{6}(n) = 2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} f_2^{7}(n) = 2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} f_2^{8}(n) = 2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} f_2^{9}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} f_2^{10}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} f_2^{11}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n 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{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n 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{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n 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{2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}}} f_2^{12}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} 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{2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n 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{2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}}}} f_2^{13}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n 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{2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n 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{2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n 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{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n 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{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n 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{2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}}}}} f_2^{14}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} 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{2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n 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{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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{2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n 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n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}}}}}}} f_2^{16}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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