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def f n
    step = 0
    _n = n
    while n != 1
        if n.class == Fixnum && $cache[n] != nil
            step += $cache[n]
            break
        end
        if n % 2 == 0
            n = n / 2
        else
            n =  3 * n + 1
        end
        step += 1
    end
    $cache[_n] = step
    return step
end

$cache = []

require 'benchmark'

max_f = 0
max_i = 0

puts Benchmark::CAPTION
puts Benchmark.measure {
    for i in 1..2**20
        f_i = f(i)
        if f_i > max_f
            max_f = f_i
            max_i = i
        end
    end
}

puts "result : f( #{max_i} ) = #{max_f}"