--powers n : the list of powers of n
-- Int -> [Int]
powers=\n->powp n n

--powp n e : the list of powers of e, multiplied by n#
-- Int -> Int -> [Int]
powp=\n ->\e-> n:(powp (n*e) (e))

--factorals : the list of factorials
-- [Int]
factorials= facp 1 2

--facp n x : the list of numbers of n, multiplied by each number
--           starting from x
-- Int -> Int -> [Int]
facp=\n-> \x -> n:(facp (n*x) (x+1))

--runs ns : the number of block of items in ns#
-- [Int] -> Int
runs=\ns-> runp ns 0

--runp ns cur acc : the number of adjacent blocks in ns, plus acc
-- [Int] -> Int -> Int
runp=\ns->\acc-> if ns ==[] then acc
  else if tail ns == [] then acc+1
    else runp 
      (tail ns) 
      (acc+(if head ns /=head(tail ns) then 1 
                                       else 0))