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  ceiling($v/$p)=ceiling(10/3)=4
  $p! = 3*2*1 = 6
...
  #so... 
  ceiling($v/$p)-1 + $p! = 3 + 6
  = 9

  ceiling($v/$p)=ceiling(36/10) = 4
  $p! = 10!
  #so...
  ceiling($v/$p)-1 + p! = 3 + 10!