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@aycabta
Last active August 29, 2015 14:02
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Transcribes FGH f_3(n) to TeX
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
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 n} {2^n n}} {2^{2^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}}}}}}}}}} {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 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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^{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 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{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} 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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^{2^n n} {2^n n}} {2^{2^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^{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 n} {2^n n}} {2^{2^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 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 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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^{2^{2^n n} {2^n n}} {2^{2^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}}}}}} {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}}}}}}}}}} {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 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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^{2^{2^n n} {2^n n}} {2^{2^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^{15}(n) = 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 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 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{2^{2^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 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 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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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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 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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 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 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