import Data.Time.Calendar
import Data.Time.Calendar.OrdinalDate



merge [] ys = ys  
merge xs []  = xs 
merge (x:xs) (y:ys) 
 | x > y = y: merge (x:xs) ys
 | otherwise = (x) : merge xs (y:ys)



hailstone x 
 | even x = div x 2 
 | odd x = 3*x + 1 

hailLen n = hailTail a n
  where
    hailTail a 1 = a
    hailTail a n = hailTail (a+1) (hailstone n)
    a=0



fact :: Integer -> Integer
fact 0 = 1
fact n | n > 0 = n * fact (n-1)

fact' n = foldl (*) n [2..n-1]




daysInYear y = [jan1..dec31]
   where jan1  = fromGregorian y 01 01
         dec31 = fromGregorian y 12 31



isFriday y  = snd(mondayStartWeek y)==5




--divisors :: Int -> [Int] 
divisors n = [ i | i <- [2..(n `div` 2)] , n `mod` i == 0] 


isPrimeDay z = numdiv== []
   
  where 
   numdiv= divisors d
   d= getDay (toGregorian z)
   getDay (y,m,d) = d



primeFridays date = primfridays
         where 
         primfridays = filter isPrimeDay (fridays)
         fridays = filter isFriday (daysInYear date)