root.cr

require "big/big_rational"

def root(n, acc = BigRational.new(2))
    base = ->(n : BigRational) { 2 + n.inv }
    n.times { acc = base.call(acc) }
    1 + acc.inv
end

puts (1..999).map { |n| root(n) }.map { |r| [r.numerator.digits.size, r.denominator.digits.size] }.count { |(n, d)| n > d }