Transcribes FGH f_3(n) to TeX

fgh3tex.rb

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

output

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}}}} 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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 n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {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^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {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^{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 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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^n n} {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 n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {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^{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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