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require 'benchmark' 

def operation(n)
  return n%2 == 0 ? n/2 : 3*n+1 
end

def recursive(hash, n)
  hash[n] or hash[n] = 1 + recursive(hash, operation(n) )
end

chains = {} 
max_chain_size = 0 
max_chain_start = 1 

Benchmark.bm do |x| 
  x.report do 
    chains[1] = 1
    2.upto(1000000) do |i| 
      chain_size = recursive(chains, i)
      
      if chain_size > max_chain_size 
        max_chain_size = chain_size 
        max_chain_start = i 
      end 
    end 
  end 
  puts "(#{max_chain_start}, #{max_chain_size})" 
end 

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array = []
 
(1..1_000_000).each do |x|
  sum = 0
  while x != 1
    sum += 1
    if x % 2 == 0
      x = x / 2
    else
      x = (3 * x) + 1
    end
  end
  array << sum
end
 
puts array.index(array.max) + 1